Hanhpt23/IQBench · Datasets at Hugging Face

id int32 1 500	topic stringclasses 10 values	link stringlengths 13 13	question stringlengths 41 507	answer stringclasses 17 values	pattern stringlengths 31 1.28k ⌀	source stringclasses 59 values
1	Mechanical Deductive Reasoning Test	image_001.png	The smaller gear makes 36 revolutions by the time the larger ones make 18. If the smaller gear makes 56 revolutions, how many turns will the larger one make? A. 24 B. 26 C. 28 D. 25	C	Explanation: \[ u = \frac{18}{36} = 0.5 \] \[ n_{\text{larger}} = u \cdot 56 = 28 \]	https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning
2	Mechanical Deductive Reasoning Test	image_002.png	Gear A: 5 teeth Gear B: 50 teeth Gear C: 20 teeth Gear D: 10 teeth How many revolutions per second is gear C turning? A. 5 B. 10 C. 15 D. 20	B	If a cog with 5 teeth can do a full 40 revolutions in a second, a cog with four times as many teeth will take 4 times as long to do a full revolution. This means, it will do 4 times fewer revolutions. So the correct answer is 10.	https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning
3	Mechanical Deductive Reasoning Test	image_003.png	Which image is the front view of the given part in the direction of the arrow?	B	The front view is determined by looking in the direction of the arrow. Option A shows a circle, which represents the top view. Option C makes the cylinder appear too small, which is inaccurate. Option B correctly shows the rectangular base with the cylinder as a smaller rectangle on top. Conclusion: The correct answer is B.	https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning
4	Mechanical Deductive Reasoning Test	image_004.png	In which direction will the orange gear rotate? A. Clockwise B. Counterclockwise C. No rotation	A	The driving gear and the orange gear are connected through an intermediate gear, so the orange gear rotates in the same direction as the driving gear.	https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning
5	Mechanical Deductive Reasoning Test	image_005.png	In which direction will the orange gear rotate? A. Clockwise B. Counterclockwise C. No rotation	B	the driving gear rotates clockwise (CW), the orange gear will rotate counterclockwise (CCW).	https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning
6	Mechanical Deductive Reasoning Test	image_006.png	In which direction will the orange gear rotate? A. Clockwise B. Counterclockwise C. No rotation	B	The driving gear and the orange gear are continuously meshed through two intermediate gears. Therefore, the orange gear rotates in the opposite direction of the driving gear.	https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning
7	Mechanical Deductive Reasoning Test	image_007.png	In which direction will the orange gear rotate? A. Clockwise B. Counterclockwise C. No rotation	B	The driving rack moves to the right, causing the meshing gear to rotate clockwise. The orange gear is connected to this gear through two intermediate gears. Therefore, the orange gear rotates counterclockwise.	https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning
8	Mechanical Deductive Reasoning Test	image_008.png	In which direction will the orange gear rotate? A. Clockwise B. Counterclockwise C. No rotation	B	The driving gear rotates counterclockwise and transmits motion through a belt to the large gear, which also rotates counterclockwise. This large gear meshes with a smaller gear, making it rotate clockwise. The small gear then drives another gear, causing it to rotate counterclockwise. Finally, the orange gear meshes with this last gear, making it rotate counterclockwise	https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning
9	Mechanical Deductive Reasoning Test	image_009.png	The scale is balanced. What is the weight of the weight with the question mark? A. 4 kg B. 10 kg C. 20 kg D. 40 kg E. 50 kg	A	\[ m = \frac{10 \cdot 2}{5} = 4 \, \text{kg} \]	https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning
10	Mechanical Deductive Reasoning Test	image_010.png	On which pole does the weight press harder? A. (A) B. (B) C. None	B	(B) experiences greater force because it is closer to the fulcrum of the heavier mass (A).	https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning
11	Mechanical Deductive Reasoning Test	image_011.png	What pulleys turn in the same direction as 1? A. 2 and 8 B. 6 and 4 C. 2, 3, 7 and 8 D. 4, 5 and 6	B	Pulley 1 rotates clockwise. Pulley 2 and 8 rotate in the opposite directions to pulley 1. Pulley 8 and 7 rotate in the same direction. Pulley 2 and 3 rotate in the same direction. Pulley 3 and 4 rotate in opposite directions. Pulley 6 and 7 rotate in opposite directions. Pulley 5 and 6 rotate in opposite directions.	https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning
12	Mechanical Deductive Reasoning Test	image_012.png	Consider the following pulley system. Pulley A is fixed, and Pulley B is moveable. If the system is balanced, how much does the weight with the question mark weigh? A. 5 kg B. 10 kg C. 20 kg D. 40 kg E. 50 kg	C	The force transmitted on a single rope is the same. Pulley B has two ropes, so the mass of the object to be found is: \[ m = 2 \cdot 10 = 20 \, \text{kg} \]	https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning
13	Mechanical Deductive Reasoning Test	image_013.png	What is the weight of the weight with the question mark? A. 15 kg B. 20 kg C. 25 kg D. 30 kg E. 35 kg	E	\[ m = \frac{20 \cdot 6 + 30 \cdot 3}{6} = 35 \ \text{kg} \]	https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning
14	Mechanical Deductive Reasoning Test	image_014.png	Which is the side view projection of the given part according to the first angle projections?	B	According to the first angle projections, the side view projection is seen from the left. Therefore, the correct answer is B.	https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning
15	Mechanical Deductive Reasoning Test	image_015.png	What weight does the blue box have to be in order for the seesaw to be in equilibrium? A. 20 kg B. 30 kg C. 40 kg D. None	D	In order for the seesaw to be in equilibrium, the net force must equal zero. Moment of a force = force x distance to pivot. Therefore, the moment of a force on the left side of the seesaw is 10 kg x 5 = 50. The right side must equal 50 for the seesaw to be balanced, therefore 50 divided by 2 (2 meters distance from pivot) = 25.	https://www.assessmentday.com/mechanical-reasoning.htm#free-mechanical-reasoning-test
16	Mechanical Deductive Reasoning Test	image_016.png	Consider two spheres as shown in the figure. Sphere 1 moves and undergoes a perfectly elastic head-on collision with sphere 2. Determine the direction of motion of sphere 1 after the collision. A. Opposite to the initial direction B. Same as the initial direction C. None of the answers	A	Since the collision is central and perfectly elastic, the total momentum before and after the collision must be equal: \[ m_1 \cdot v_1(0) + m_2 \cdot v_2(0) = m_1 \cdot v_1 + m_2 \cdot v_2 \] Since the collision is perfectly elastic, kinetic energy is also conserved: \[ \frac{1}{2} \cdot m_1 \cdot v_1(0)^2 + \frac{1}{2} \cdot m_2 \cdot v_2(0)^2 = \frac{1}{2} \cdot m_1 \cdot v_1^2 + \frac{1}{2} \cdot m_2 \cdot v_2^2 \] Solving for \( v_1 \), we get: \[ v_1 = -\frac{5}{3} \, \text{m/s} \] Hence, option A is the correct choice.	null
17	Mechanical Deductive Reasoning Test	image_017.png	A speeding motorist travelling passes a stopped police car. The police car immediately begins to chase the speeder, accelerating at a constant 2.5 m/s2. How long does it take for the police car to intercept the speeder? A. 25.6 s B. 26.6 s C. 27.6 s D. 28.6 s	B	The speeder’s car's equation of motion is given by: \[ X_s \coloneqq \frac{120 \cdot 1000 \cdot t}{3600} = \frac{100}{3} \cdot t, \, \text{m/s} \] The police car's equation of motion is: \[ X_{\text{police}} = 0.5 \cdot 2.5 \cdot t^2 \] When the two vehicles are at the same position: \[ X_s = X_{\text{police}} \] Solving for time \( t \), we get: \[ t = \frac{33.3}{0.5 \cdot 2.5} = 26.6 \, \text{s} \]	https://sciencenotes.org/equations-motion-constant-acceleration-intercept-example-problem/
18	Mechanical Deductive Reasoning Test	image_018.png	A child pulls a heavy object using a rope that passes over a pulley. Neglect the mass of the pulley and assume the rope remains taut throughout the motion. What is the minimum force the child must exert in order to lift the object upward? A. 49 N B. 50 N C. 51 N D. 52 N	B	The minimum force the child must exert in order to lift the object upward is: \[ F = g \cdot m = 9.81 \cdot 5 = 49.05 \, \text{N} \] Hence, option B is the correct answer, with: \[ F = 50 \, \text{N} \]	null
19	Mechanical Deductive Reasoning Test	image_019.png	The angular velocity of the disk is defined by like the picture. Determine the magnitudes of the velocity of point A on the disk when t = 0.5 s. _x000B_ A. 2.5 m/s B. 2.6 m/s C. 2.7 m/s D. 2.8 m/s	B	V_A = \omega \cdot 0.8 = \left(2 \cdot 0.5^2 + 2\right) \cdot 0.8 = 2.6 \, \text{m/s}	https://www.assessmentday.com/spatial-reasoning.htm
20	Mechanical Deductive Reasoning Test	image_020.png	The disk is originally rotating at 𝜔_0. If it is subjected to a constant angular acceleration, determine the magnitudes of the normal component of acceleration of point A at the instant t = 2 s. A. 1350 m/s^2 B. 1352 m/s^2 C. 1354 m/s^2 D. 1356 m/s^2	B	The angular velocity of the disk can be determined using :\\ \[ \omega = \omega_0 + \alpha t = 12 + 20 \ast 2 = 52 \, \text{rad/s} \] The normal component of acceleration are:\\ \[ a_n = \omega^2 R = 1352 \, \text{m/s}^2 \]	https://www.assessmentday.com/spatial-reasoning.htm
21	Mechanical Deductive Reasoning Test	image_021.png	If gear A rotates with a constant angular acceleration of starting from rest, determine the angular velocity of gear B if the angular velocity of gear A is 600 rpm. A. 180 rad/s B. 190 rad/s C. 200 rad/s D. 210 rad/s	A	\[ \omega_B = \frac{15\omega_A}{50} = 180 \, \text{rad/s} \]	https://www.assessmentday.com/spatial-reasoning.htm
22	Mechanical Deductive Reasoning Test	image_022.png	The power of a bus engine is transmitted using the belt-andpulley arrangement shown. Determine the angular velocities of the generator pulley B when t = 3 s. A. 300 rad/s B. 320 rad/s C. 340 rad/s D. 360 rad/s	A	\text{When } t = 3 \, \text{s} \[ \omega_A = 20(3) + 40 = 100 \, \text{rad/s} \] \text{The speed of a point } P \text{ on the belt wrapped around } A \text{ is} \[ v_P = \omega_A r_A = 100(0.075) = 7.5 \, \text{m/s} \] \[ \omega_B = \frac{v_P}{r_D} = \frac{7.5}{0.025} = 300 \, \text{rad/s} \]	https://www.123test.com/spatial-reasoning-test/id=LZ9UJNDIC2TH&version=
23	Mechanical Deductive Reasoning Test	image_023.png	If the motor turns gear A with an angular acceleration and the angular velocity, determine the angular velocity of gear D. A. 2 rad/s B. 3 rad/s C. 4 rad/s D. 5 rad/s	C	\textbf{Angular Motion:} \text{ The angular velocity and acceleration of gear } B \text{ must be determined first. Here, } \omega_A r_A = \omega_B r_B \text{ and } \alpha_A r_A = \alpha_B r_B. \text{ Then,} \[ \omega_B = \frac{r_A}{r_B} \omega_A = \left( \frac{40}{100} \right)(20) = 8.00 \, \text{rad/s} \] \[ \alpha_B = \frac{r_A}{r_B} \alpha_A = \left( \frac{40}{100} \right)(2) = 0.800 \, \text{rad/s}^2 \] \text{Since gear } C \text{ is attached to gear } B, \text{ then } \omega_C = \omega_B = 8 \, \text{rad/s and } \alpha_C = \alpha_B = 0.8 \, \text{rad/s}^2. \text{ Realizing that } \omega_C r_C = \omega_D r_D \text{ and } \alpha_C r_C = \alpha_D r_D, \text{ then} \[ \omega_D = \frac{r_C}{r_D} \omega_C = \left( \frac{50}{100} \right)(8.00) = 4.00 \, \text{rad/s} \]	https://www.123test.com/spatial-reasoning-test/id=LZ9UJNDIC2TH&version=
24	Mechanical Deductive Reasoning Test	image_024.png	The gear A on the drive shaft of the outboard motor has a radius 𝑟_𝐴=0.5 in. and the meshed pinion gear B on the propeller shaft has a radius 𝑟_𝐵=1.2 in. Determine the angular velocity of the propeller in t=1.5 𝑠, if the drive shaft rotates with an angular acceleration 𝛼=〖400𝑡〗^3 𝑟𝑎𝑑/𝑠^2 , where t is in seconds. The propeller is originally at rest and the motor frame does not move. _x000B_ A. 209 m/s^2 B. 211 m/s^2 C. 213 m/s^2 D. 215 m/s^2	B	\textbf{Angular Motion:} \text{ The angular velocity of gear } A \text{ at } t = 1.5 \, \text{s must be determined first. Applying Eq. 16--2, we have} \[ d\omega = \alpha dt \] \[ \int_0^{\omega_A} d\omega = \int_0^{1.5 \, s} 400t^3 \, dt \] \[ \omega_A = 100t^4 \big\|_0^{1.5 \, s} = 506.25 \, \text{rad/s} \] \text{However, } \omega_A r_A = \omega_B r_B \text{ where } \omega_B \text{ is the angular velocity of propeller. Then,} \[ \omega_B = \frac{r_A}{r_B} \omega_A = \left( \frac{0.5}{1.2} \right)(506.25) = 211 \, \text{rad/s} \]	https://www.123test.com/spatial-reasoning-test/id=LZ9UJNDIC2TH&version=
25	Mechanical Deductive Reasoning Test	image_025.png	The pinion gear A on the motor shaft is given a constant angular acceleration 𝛼. If the gears A and B have the dimensions shown, determine the angular velocity of the output shaft C, when t=2s starting from rest. The shaft is fixed to B and turns with it. A. 1.62 rad/s B. 1.64 rad/s C. 1.66 rad/s D. 1.68 rad/s	D	\begin{align} \omega &= \omega_0 + \alpha_c t \\ \omega_A &= 0 + 3(2) = 6 \, \text{rad/s} \\ \\ \theta &= \theta_0 + \omega_0 t + \frac{1}{2} \alpha_c t^2 \\ \theta_A &= 0 + 0 + \frac{1}{2}(3)(2)^2 \\ \theta_A &= 6 \, \text{rad} \\ \\ \omega_A r_A &= \omega_B r_B \\ 6(35) &= \omega_B (125) \\ \omega_C = \omega_B &= 1.68 \, \text{rad/s} \end{align}	https://www.123test.com/spatial-reasoning-test/id=LZ9UJNDIC2TH&version=
26	Mechanical Deductive Reasoning Test	image_026.png	Which piece corresponds to the given solid?	C	The third piece corresponds to the given solid	https://www.123test.com/spatial-reasoning-test/id=LZ9UJNDIC2TH&version=
27	Mechanical Deductive Reasoning Test	image_027.png	Which picture can be formed with the given pieces?	C	null	https://www.assessmentday.com/spatial-reasoning.htm
28	Mechanical Deductive Reasoning Test	image_028.png	To which object does the given top view correspond?	A	null	https://www.assessmentday.com/spatial-reasoning.htm
29	Mechanical Deductive Reasoning Test	image_029.png	Which of these image is the top view of the given object?	B	null	https://www.assessmentday.com/spatial-reasoning.htm
30	Mechanical Deductive Reasoning Test	image_030.png	For protection, the barrel barrier is placed in front of the bridge pier. If the relation between the force and deflection of the barrier is lb, where is in ft, determine the car’s maximum penetration in the barrier. The car has a weight of 4000 lb and it is traveling with a constant speed before it hits the barrier. A. 3.20 ft B. 3.22 ft C. 3.24 ft D. 3.26 ft	C	\[ T_{1}+\Sigma U_{12}=T_{2} \] \[ 0.5\cdot \left(\frac{4000}{ 32.2}\right)\cdot \left(75^{2}\right)+\int_{0}^{x_{\max}}90\cdot 10^{3}\cdot x^{ 0.5}d{x}=0 \] \[ x_{\max}= 3.24 \text{ ft} \]	null
31	Mechanical Deductive Reasoning Test	image_031.png	A man kicks the ball such that it leaves the ground at an angle and strikes the ground at the same elevation a distance of Sx m away. Determine the impulse of his foot on the ball at A. Neglect the impulse caused by the ball’s weight while it’s being kicked. A. 1.75 N.s B. 1.76 N.s C. 1.77 N.s D. 1.78 N.s	A	Consider the vertical motion of the ball, where: \[ S_y = v \cdot \sin(60^\circ) \cdot t + \frac{1}{2} \cdot (-9.81) \cdot t^2 = 0 \] Factorizing the equation: \[ t \left( v \cdot \sin(60^\circ) - 4.905 \cdot t \right) = 0 \] Since \( t \ne 0 \), we solve: \[ v \cdot \sin(60^\circ) - 4.905 \cdot t = 0 \] \[ t \approx \frac{v \cdot \sin(60^\circ)}{4.905} \] \[ t \approx 0.1766v \] \section{Horizontal Motion of the Ball} \[ S_x = v \cdot \cos(60^\circ) \cdot t = 12 \] \[ t = \frac{12}{v \cdot \cos(60^\circ)} = \frac{24}{v} \] Equating the two expressions for \( t \): \[ 0.1766v = \frac{24}{v} \] Solving for \( v \): \[ v^2 = \frac{24}{0.1766} \Rightarrow v \approx 11.66 \, \text{m/s} \] \section{Principle of Impulse and Momentum} \[ I = m (v_2 - v_1) = m \cdot v = 1.75 \, \text{N$\cdot$s} \]	null
32	Mechanical Deductive Reasoning Test	image_032.png	The jet car is initially traveling at a initial velocity when it is subjected to the acceleration shown. Determine the car's maximum velocity and the time 𝑡' when it comes to a stop. Assume that when t=0, the displacement s=0. A. 𝑉_𝑚𝑎𝑥=100 m/s; 𝑡′=40 s B. 𝑉_𝑚𝑎𝑥=102 m/s; 𝑡′=42 s C. 𝑉_𝑚𝑎𝑥=104 m/s; 𝑡′=44 s D. 𝑉_𝑚𝑎𝑥=106 m/s; 𝑡′=46 s	A	Because acceleration is constant, the equation of car motion is: \[ v = 10 + a \cdot t \] The maximum velocity is: \[ V_{\text{max}} = 10 + 6 \cdot 15 = 100 \, \text{m/s} \] When the jet car stops: \[ 0 = 100 - 4 \cdot (t' - 15) \] Solving for \( t' \): \[ t' = \frac{160}{4} = 40 \, \text{s} \]	null
33	Mechanical Deductive Reasoning Test	image_033.png	Determine the minimum initial velocity 𝑣_0 at which the ball must be kicked. A. 𝑣_0=22.5 m/s B. 𝑣_0=23.5 m/s C. 𝑣_0=24.5 m/s D. 𝑣_0=25.5 m/s	A	Time to reach the horizontal position: \[ x = v_0 \cdot t \cdot \cos(30^\circ) = 6 \] The vertical position at that time: \[ y = v_0 \cdot t \cdot \sin(30^\circ) - 0.5 \cdot g \cdot t^2 = 3 \] From these two equations, we can determine: \[ v_0 = 22.5 \, \text{m/s} \]	null
34	Mechanical Deductive Reasoning Test	image_034.png	A golf ball is struck with a velocity as shown. Determine the distance d to where it will land. A. 𝑑=156 ft B. 𝑑=166 ft C. 𝑑=176 ft D. 𝑑=186 ft	B	Given the following equations: \[ d \cdot \cos(10^\circ) = 80 \cdot \cos(55^\circ) \cdot t \text{ (1)} \] \[ d \cdot \sin(10^\circ) = 80 \cdot \sin(55^\circ) \cdot t - 0.5 \cdot (32.5) \cdot t^2 \text{ (2)} \] Solving these equations, we get the result: \[ d = 166 \, \text{ft} \]	null
35	Mechanical Deductive Reasoning Test	image_035.png	A passenger in an automobile observes that raindrops make an angle with the horizontal as the auto travels forward with a constant speed as shown. Compute the terminal (constant) velocity of the rain if it is assumed to fall vertically. A. 33.6 km/h B. 34.6 km/h C. 35.6 km/h D. 36.6 kh/h	B	The relative velocity is given by: \[ V_r = 60 \cdot \tan(30^\circ) = 34.6 \, \text{km/h} \]	null
36	Mechanical Deductive Reasoning Test	image_036.png	If the coefficient of kinetic friction between the crate and the ground is 𝜇 as shown. Determine the distance traveled by the crate at 𝑡=t', if it starts from rest.. A. 5.01 m B. 5.02 m C. 5.03 m D. 5.04 m	D	The acceleration of the crate is given by: \[ a = \frac{200 \cdot \cos(30^\circ) - 0.3 \cdot (-200 \cdot \sin(30^\circ) + 9.81 \cdot 50)}{50} = 1.121 \, \text{m/s}^2 \] The motion equation is: \[ s = 0.5 \cdot a \cdot t^2 = 0.5 \cdot 1.121 \cdot 9 = 5.04 \, \text{m} \]	null
37	Mechanical Deductive Reasoning Test	image_037.png	The conveyor belt is moving. If the coeffcient of static friction between the conveyor and the package B is 𝜇 as shown, determine the shortest time the belt can stop so that the package does not slide on the belt. A. 2.02 s B. 2.04 s C. 2.06 s D. 2.08 s	B	When the conveyor belt decelerates, the package wants to keep moving due to inertia. Static friction must provide the force to decelerate the package at the same rate as the belt, to avoid sliding. The maximum static friction force is given by: \[ f = 0.2 \cdot 10 \cdot 9.81 = 19.62 \, \text{N} \] This force is responsible for the maximum possible deceleration: \[ a = \frac{19.62}{10} = 1.962 \, \text{m/s}^2 \] To find the shortest time to stop, we use kinematics: \[ v = 4 - a \cdot t = 0 \] Solving for time: \[ t_{\text{min}} = \frac{4}{1.962} = 2.04 \, \text{s} \]	null
38	Mechanical Deductive Reasoning Test	image_038.png	Determine the magnitude of the resultant force Fr. A. 392 lb B. 393 lb C. 394 lb D. 395 lb	B	The resultant force \( F_r \) is given by the equation: \[ F_r = \sqrt{F_1^2 + F_2^2 - 2 \cdot F_1 \cdot F_2 \cdot \cos(75^\circ)} = 393 \, \text{lb} \]	null
39	Mechanical Deductive Reasoning Test	image_039.png	A vertical force F acts downward on the two-membered frame. Determine the magnitudes of the two components of F directed along the axes of members AB and AC. A. 𝐹_𝐴𝐵=366 N; 𝐹_𝐴𝐶=448 N B. 𝐹_𝐴𝐵=448 N; 𝐹_𝐴𝐶=366 N C. 𝐹_𝐴𝐵=446 N; 𝐹_𝐴𝐶=368 N D. 𝐹_𝐴𝐵=368 N; 𝐹_𝐴𝐶= 448 N	B	he forces \( F_{ab} \) and \( F_{ac} \) are calculated as follows: \[ F_{ab} = \frac{500 \cdot \sin(60^\circ)}{\sin(75^\circ)} = 448 \, \text{N} \] \[ F_{ac} = \frac{500 \cdot \sin(45^\circ)}{\sin(75^\circ)} = 366 \, \text{N} \]	null
40	Mechanical Deductive Reasoning Test	image_040.png	If the resultant force of the two tugboats is required to be directed towards the positive 𝑥 axis, and 𝐹_𝐵 is to be a minimum, determine the magnitude of the resultant force 𝐹_𝑅 and 𝐹_𝐵 and the angle 𝜃._x000B_ A. 𝜃=70^𝑜;𝐹_𝑅=1.73 kN; 𝐹_𝐵=1 kN B. 𝜃=80^𝑜;𝐹_𝑅=1 kN; 𝐹_𝐵= 1.73 kN C. 𝜃=90^𝑜;𝐹_𝑅=1.73 kN; 𝐹_𝐵=1 kN D. 𝜃=100^𝑜;𝐹_𝑅=1 kN; 𝐹_𝐵= 1.73 kN	C	For \( F_R \) to be minimum, it has to be directed perpendicular to \( F_R \). Thus, \[ \theta = 90^\circ \] The forces \( F_R \) and \( F_B \) are calculated as follows: \[ F_R = F_A \cdot \cos(30^\circ) = 1.73 \, \text{kN} \] \[ F_B = F_A \cdot \sin(30^\circ) = 1 \, \text{kN} \]	null
41	Mechanical Deductive Reasoning Test	image_041.png	A non-pressurized cylindrical metal tank filled with air is submerged underwater. As the air escapes, the tank gradually moves deeper underwater. Which statement provides the best reason for this motion? A. The bubbles provide a downward thrust on the tank B. The metal increases in density so it gets heavier C. The bubbles lower the density of the water which lowers its buoyancy D. Water replaces the air in the tank which makes it heavier E. Impossible to tell	D	As air escapes the available space is quickly replaced with water, so the tank's density becomes the same as that of the water and with the added weight and density of the tank itself continues to sink.	https://www.assessmentday.co.uk/free/mechanical/index.php?_gl=115fxlw5_gcl_auNjAzOTg0MzE5LjE3NDM1OTAzMjA._gaMzA1Mjc0MTEwLjE3NDM1OTAzMjA._ga_S04NDDMHWQ*MTc0NDc5MDY1NS41LjAuMTc0NDc5MDY1OS41Ni4wLjA.&_ga=2.55850920.2091287029.1744790656-305274110.1743590320
42	Mechanical Deductive Reasoning Test	image_042.png	There are two identical cars along a bridge. If the bridge has the same thickness along it, which part(s) of the bridge would undergo the most deflection? A. Under the towers B. Below the cars C. Middle of the bridge D. All of the above will have equal deflection E. Impossible to tell	C	The middle of the bridge would undergo the most deflection because it is furthest away from the towers and pillars supporting the bridge. Imagine a piece of string held at either end over a gap between two tables. The point right in the middle would droop the most.	https://www.assessmentday.co.uk/free/mechanical/index.php?_gl=115fxlw5_gcl_auNjAzOTg0MzE5LjE3NDM1OTAzMjA._gaMzA1Mjc0MTEwLjE3NDM1OTAzMjA._ga_S04NDDMHWQ*MTc0NDc5MDY1NS41LjAuMTc0NDc5MDY1OS41Ni4wLjA.&_ga=2.55850920.2091287029.1744790656-305274110.1743590321
43	Mechanical Deductive Reasoning Test	image_043.png	Convex mirrors are used for rear-view mirrors of vehicles. What is the advantage of using a convex mirror instead of a flat mirror? A. It provides a clearer reflection B. It has a more accurate reflection C. The wider angle of view reduces blind spots D. It is easier to clean a convex mirror E. A convex mirror provides no advantage	C	A convex mirror has a wider field of view because of its shape. A wider field of view can eliminate blind spots or reduce the size of the area that's not easily visible.	https://www.assessmentday.co.uk/free/mechanical/index.php?_gl=115fxlw5_gcl_auNjAzOTg0MzE5LjE3NDM1OTAzMjA._gaMzA1Mjc0MTEwLjE3NDM1OTAzMjA._ga_S04NDDMHWQ*MTc0NDc5MDY1NS41LjAuMTc0NDc5MDY1OS41Ni4wLjA.&_ga=2.55850920.2091287029.1744790656-305274110.1743590322
44	Mechanical Deductive Reasoning Test	image_044.png	It is a cold winter outside and a well-insulated house has its heater turned on. The front door is opened and cold air rushes in. If the wind speed outside is very low, how would the cold air enter the house? A. Scenario A, the cold air will flow towards the floor B. Scenario B, the cold air will flow towards the ceiling C. A combination of A and B D. The cold air will not enter the house E. Impossible to tell	A	Cold air sinks, whereas hot air rises. The house and the air inside it are warmer than the outside air temperature, so if these two systems (house and outside) were to be suddenly connected (door opening) the cold air would sink and the hot air would sit above the cold air until the heat transferred between the two.	https://www.assessmentday.co.uk/free/mechanical/index.php?_gl=115fxlw5_gcl_auNjAzOTg0MzE5LjE3NDM1OTAzMjA._gaMzA1Mjc0MTEwLjE3NDM1OTAzMjA._ga_S04NDDMHWQ*MTc0NDc5MDY1NS41LjAuMTc0NDc5MDY1OS41Ni4wLjA.&_ga=2.55850920.2091287029.1744790656-305274110.1743590323
45	Mechanical Deductive Reasoning Test	image_045.png	A bucket of water has a leak on its lower side. As the water level goes down, what happens to the speed of the water coming out of the hole? A. It increases B. It stays the same C. It decreases D. It reverses E. Impossible to tell	C	The speed of the water exiting the bucket by the hole is proportional to the pressure exerted upon it. When the bucket is full there is a greater volume of water trying to exit the bucket via the hole. A greater volume of water is a greater mass of water and therefore exerts a greater pressure, the greater pressure translates to faster speed. As more water leaves the bucket via the hole the volume decreased, therefore so does the mass of the water and the pressure then drops.	https://www.assessmentday.co.uk/free/mechanical/index.php?_gl=115fxlw5_gcl_auNjAzOTg0MzE5LjE3NDM1OTAzMjA._gaMzA1Mjc0MTEwLjE3NDM1OTAzMjA._ga_S04NDDMHWQ*MTc0NDc5MDY1NS41LjAuMTc0NDc5MDY1OS41Ni4wLjA.&_ga=2.55850920.2091287029.1744790656-305274110.1743590324
46	Mechanical Deductive Reasoning Test	image_046.png	Three identical candles were lit and covered by individual jars at the same time. Which candle would have its flame extinguish first? A. A, candle in a small sealed jar B. B, candle in a big sealed jar C. C, candle in a small jar with holes D. They will all extinguish at the same time E. Impossible to tell	A	A flame needs fuel and oxygen to continue burning. The wax provides the fuel in all of three instances. There is air exchange in jar C, so more oxygen can be used by the candle to continue burning. Jars A and B are closed systems. No oxygen can get in. Once the oxygen is used up the flame will suffocate itself. The air available in the small jar, A, is less than that in the large jar, B, therefore A shall be extinguished first.	https://www.assessmentday.co.uk/free/mechanical/index.php?_gl=115fxlw5_gcl_auNjAzOTg0MzE5LjE3NDM1OTAzMjA._gaMzA1Mjc0MTEwLjE3NDM1OTAzMjA._ga_S04NDDMHWQ*MTc0NDc5MDY1NS41LjAuMTc0NDc5MDY1OS41Ni4wLjA.&_ga=2.55850920.2091287029.1744790656-305274110.1743590325
47	Mechanical Deductive Reasoning Test	image_047.png	Fire doors have a spring which automatically pushes and forces shut the door when it's open. If the springs were made thicker, what effect would this have on how the door closes? A. The door will close slower B. The door will not fully close C. The door will make a screeching noise as it closes D. The door will close faster E. It will not make a difference	D	The spring forces the door shut. A thicker spring is stronger which will shut the door more forcefully than before.	https://www.assessmentday.co.uk/free/mechanical/index.php?_gl=115fxlw5_gcl_auNjAzOTg0MzE5LjE3NDM1OTAzMjA._gaMzA1Mjc0MTEwLjE3NDM1OTAzMjA._ga_S04NDDMHWQ*MTc0NDc5MDY1NS41LjAuMTc0NDc5MDY1OS41Ni4wLjA.&_ga=2.55850920.2091287029.1744790656-305274110.1743590326
48	Mechanical Deductive Reasoning Test	image_048.png	A bolt cutter has long handles with handle grips that are located as far away as possible from the neck. Which statement provides the best reason for this design? A. Longer handles make the cutting blade move faster B. It provides mechanical advantage which allows cutting through thick bolts. C. The appearance of the tool is significantly more aesthetic with longer handles D. It makes the bolt cutter more durable when dropped accidentally E. Longer handles are more ergonomic and allows easier storage	B	The further the distance that the force is applied to the pivot point, the less force that's required to cut through the bolts, or the stronger the force that can be applied to the bolts is. This is the advantage in having long handles on many tools.	https://www.assessmentday.co.uk/free/mechanical/index.php?_gl=115fxlw5_gcl_auNjAzOTg0MzE5LjE3NDM1OTAzMjA._gaMzA1Mjc0MTEwLjE3NDM1OTAzMjA._ga_S04NDDMHWQ*MTc0NDc5MDY1NS41LjAuMTc0NDc5MDY1OS41Ni4wLjA.&_ga=2.55850920.2091287029.1744790656-305274110.1743590327
49	Mechanical Deductive Reasoning Test	image_049.png	A car is behind a moving fire engine on a motorway. The fire engine is traveling at a speed of 60 mph. If the distance between the two moving vehicles is not changing, what is the car's speed? A. 80 mph B. 70 mph C. 60 mph D. 50 mph E. Impossible to tell	C	If the distance between the two vehicles remains the same, they must be traveling at the same speed. The car is therefore also traveling at 60mph. Note: This is not the same as how much energy is required to get the vehicles moving at the same speed. This depends on a lot of factors, mostly; air resistance and mass of each vehicle, which is not what's being asked in this question.	https://www.assessmentday.co.uk/free/mechanical/index.php?_gl=115fxlw5_gcl_auNjAzOTg0MzE5LjE3NDM1OTAzMjA._gaMzA1Mjc0MTEwLjE3NDM1OTAzMjA._ga_S04NDDMHWQ*MTc0NDc5MDY1NS41LjAuMTc0NDc5MDY1OS41Ni4wLjA.&_ga=2.55850920.2091287029.1744790656-305274110.1743590328
50	Mechanical Deductive Reasoning Test	image_050.png	Firefighters use a halligan to forcibly enter locked doors during fire rescue operations. Which halligan would require the least effort to forcibly open the door? A. Figure A B. Figure B C. Figure C D. Figure D	D	Halligan D would require the least effort to forcibly open the door because it has the longest distance from the point where the force is applied to where it is being leveraged.	https://www.assessmentday.co.uk/free/mechanical/index.php?_gl=115fxlw5_gcl_auNjAzOTg0MzE5LjE3NDM1OTAzMjA._gaMzA1Mjc0MTEwLjE3NDM1OTAzMjA._ga_S04NDDMHWQ*MTc0NDc5MDY1NS41LjAuMTc0NDc5MDY1OS41Ni4wLjA.&_ga=2.55850920.2091287029.1744790656-305274110.1743590329
51	Deductive Reasoning Test with Figures	image_051.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\equiv$, B: $\Sigma$, C: $\neq$, D: $\pi$	D	Row 6 contains $\neq$, $\sqrt$, $\Sigma$, missing $\pi$. Column 2 contains $\equiv$, $\neq$, $\sqrt$, $\Sigma$, $\approx$, missing $\pi$. Thus, the answer is $\pi$.	null
52	Deductive Reasoning Test with Figures	image_052.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 11, B: 13, C: 9, D: 12	D	Row 3 contains 14, 20, 13, 1, 11, missing 12. Column 6 contains 9, 14, 20, 13, missing 12. Thus, the answer is 12.	null
53	Deductive Reasoning Test with Figures	image_053.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\iota$, B: $\phi$, C: $\lambda$, D: $\theta$	D	Row 2 contains $\lambda$, $\iota$, missing $\theta$. Column 3 contains $\lambda$, $\iota$, $\phi$, missing $\theta$. Thus, the answer is $\theta$.	null
54	Deductive Reasoning Test with Figures	image_054.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\tau$, B: $\upsilon$, C: $\mu$, D: $\kappa$	C	Row 5 contains $\upsilon$, $\chi$, $\kappa$, $\tau$, missing $\mu$. Column 6 contains $\omicron$, $\upsilon$, $\rho$, $\chi$, $\tau$, $\omega$, missing $\mu$. Thus, the answer is $\mu$.	null
55	Deductive Reasoning Test with Figures	image_055.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 17, B: 8, C: 6, D: 16	C	Row 1 contains 14, 4, 10, 8, 5, missing 6. Column 2 contains 4, 17, 10, 8, 16, 3, 5, 14, missing 6. Thus, the answer is 6.	null
56	Deductive Reasoning Test with Figures	image_056.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\lozenge$, B: $\blacktriangledown$, C: $\bigstar$, D: $\bullet$	D	Row 1 contains $\blacktriangledown$, $\triangleright$, o, $\blacksquare$, $\bigstar$, missing $\bullet$. Column 2 contains $\blacklozenge$, $\triangleright$, $\blacktriangle$, $\lozenge$, $\blacktriangledown$, missing $\bullet$. Thus, the answer is $\bullet$.	null
57	Deductive Reasoning Test with Figures	image_057.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 18, B: 19, C: 17, D: 8	C	Row 5 contains 19, 8, 6, missing 17. Column 6 contains 1, 18, 3, 19, missing 17. Thus, the answer is 17.	null
58	Deductive Reasoning Test with Figures	image_058.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\blacktriangle$, B: $\blacklozenge$, C: o, D: $\bigstar$	A	Row 2 contains o, $\blacklozenge$, $\blacktriangledown$, $\bigstar$, missing $\blacktriangle$. Column 1 contains $\bigstar$, o, $\blacktriangledown$, $\bullet$, missing $\blacktriangle$. Thus, the answer is $\blacktriangle$.	null
59	Deductive Reasoning Test with Figures	image_059.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\blacksquare$, B: $\bigstar$, C: $\bullet$, D: $\triangleright$	C	Row 4 contains $\blacksquare$, $\triangleright$, missing $\bullet$. Column 2 contains $\bigstar$, $\triangleright$, $\blacksquare$, missing $\bullet$. Thus, the answer is $\bullet$.	null
60	Deductive Reasoning Test with Figures	image_060.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 14, B: 2, C: 8, D: 11	A	Row 5 contains 8, 11, 2, missing 14. Column 4 contains 2, 8, 3, missing 14. Thus, the answer is 14.	null
61	Deductive Reasoning Test with Figures	image_061.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\pm$, B: $\infty$, C: $\int$, D: $\div$	A	Row 3 contains $\int$, $\div$, missing $\pm$. Column 3 contains $\int$, $\div$, $\infty$, missing $\pm$. Thus, the answer is $\pm$.	null
62	Deductive Reasoning Test with Figures	image_062.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 1, B: 15, C: 19, D: 8	C	Row 1 contains 8, 1, 12, 4, missing 19. Column 5 contains 6, 4, 15, 1, missing 19. Thus, the answer is 19.	null
63	Deductive Reasoning Test with Figures	image_063.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: e, B: r, C: a, D: c	B	Row 4 contains e, c, a, missing r. Column 4 contains c, a, missing r. Thus, the answer is r.	null
64	Deductive Reasoning Test with Figures	image_064.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\upsilon$, B: $\lambda$, C: $\alpha$, D: $\eta$	C	Row 2 contains $\beta$, $\textvarsigma$, $\lambda$, $\phi$, $\eta$, $\upsilon$, $\sigma$, missing $\alpha$. Column 5 contains $\phi$, $\omicron$, $\upsilon$, $\sigma$, $\textvarsigma$, $\lambda$, missing $\alpha$. Thus, the answer is $\alpha$.	null
65	Deductive Reasoning Test with Figures	image_065.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: o, B: $\bullet$, C: $\blacklozenge$, D: $\blacktriangledown$	B	Row 5 contains $\blacksquare$, $\blacklozenge$, o, $\blacktriangledown$, missing $\bullet$. Column 2 contains $\lozenge$, $\blacktriangledown$, $\triangleright$, $\triangleleft$, $\bigstar$, $\blacklozenge$, missing $\bullet$. Thus, the answer is $\bullet$.	null
66	Deductive Reasoning Test with Figures	image_066.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\sqrt$, B: $\equiv$, C: $\pm$, D: $\int$	C	Row 8 contains $\infty$, $\approx$, $\pi$, $\sqrt$, $\int$, $\times$, missing $\pm$. Column 7 contains $\infty$, $\approx$, $\equiv$, $\int$, missing $\pm$. Thus, the answer is $\pm$.	null
67	Deductive Reasoning Test with Figures	image_067.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\pi$, B: $\div$, C: $\int$, D: $\equiv$	C	Row 1 contains $\equiv$, $\div$, missing $\int$. Column 4 contains $\pi$, $\div$, missing $\int$. Thus, the answer is $\int$.	null
68	Deductive Reasoning Test with Figures	image_068.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\triangleright$, B: o, C: $\blacktriangledown$, D: $\lozenge$	C	Row 9 contains $\lozenge$, $\bullet$, o, $\triangleright$, $\blacksquare$, $\blacklozenge$, $\blacktriangle$, missing $\blacktriangledown$. Column 4 contains $\triangleleft$, $\blacklozenge$, $\lozenge$, o, missing $\blacktriangledown$. Thus, the answer is $\blacktriangledown$.	null
69	Deductive Reasoning Test with Figures	image_069.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\sqrt$, B: $\equiv$, C: $\div$, D: $\Sigma$	A	Row 5 contains $\equiv$, $\approx$, $\pi$, $\neq$, $\Delta$, $\div$, $\Sigma$, $\int$, missing $\sqrt$. Column 5 contains $\approx$, $\pi$, $\neq$, $\Delta$, $\int$, missing $\sqrt$. Thus, the answer is $\sqrt$.	null
70	Deductive Reasoning Test with Figures	image_070.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: c, B: f, C: a, D: l	B	Row 5 contains c, a, l, s, missing f. Column 1 contains a, h, s, c, missing f. Thus, the answer is f.	null
71	Deductive Reasoning Test with Figures	image_071.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\int$, B: $\div$, C: $\infty$, D: $\Sigma$	B	Row 8 contains $\Sigma$, $\approx$, $\equiv$, $\int$, $\sqrt$, missing $\div$. Column 2 contains $\approx$, $\int$, $\infty$, $\pi$, $\Sigma$, missing $\div$. Thus, the answer is $\div$.	null
72	Deductive Reasoning Test with Figures	image_072.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\iota$, B: $\tau$, C: $\phi$, D: $\xi$	D	Row 4 contains $\tau$, $\iota$, missing $\xi$. Column 1 contains $\phi$, missing $\xi$. Thus, the answer is $\xi$.	null
73	Deductive Reasoning Test with Figures	image_073.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: o, B: $\triangleright$, C: $\lozenge$, D: $\bullet$	B	Row 1 contains $\lozenge$, o, missing $\triangleright$. Column 2 contains o, $\bullet$, missing $\triangleright$. Thus, the answer is $\triangleright$.	null
74	Deductive Reasoning Test with Figures	image_074.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\times$, B: $\div$, C: $\sqrt$, D: $\neq$	A	Row 5 contains $\Sigma$, $\Delta$, $\sqrt$, $\div$, missing $\times$. Column 3 contains $\neq$, $\Sigma$, $\Delta$, $\sqrt$, missing $\times$. Thus, the answer is $\times$.	null
75	Deductive Reasoning Test with Figures	image_075.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\blacktriangledown$, B: $\blacktriangle$, C: o, D: $\lozenge$	D	Row 5 contains o, $\blacktriangle$, $\blacksquare$, $\bigstar$, missing $\lozenge$. Column 8 contains $\blacklozenge$, $\blacksquare$, $\bigstar$, $\blacktriangledown$, $\bullet$, missing $\lozenge$. Thus, the answer is $\lozenge$.	null
76	Deductive Reasoning Test with Figures	image_076.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: q, B: k, C: y, D: p	B	Row 4 contains e, p, y, q, missing k. Column 1 contains p, e, missing k. Thus, the answer is k.	null
77	Deductive Reasoning Test with Figures	image_077.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\leftrightarrow$, B: $\swarrow$, C: $\downarrow$, D: $\searrow$	D	Row 4 contains $\swarrow$, missing $\searrow$. Column 2 contains $\leftrightarrow$, $\downarrow$, $\swarrow$, missing $\searrow$. Thus, the answer is $\searrow$.	null
78	Deductive Reasoning Test with Figures	image_078.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 11, B: 10, C: 8, D: 2	C	Row 3 contains 10, 11, 14, missing 8. Column 3 contains 2, 10, 14, missing 8. Thus, the answer is 8.	null
79	Deductive Reasoning Test with Figures	image_079.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 14, B: 20, C: 11, D: 1	B	Row 4 contains 15, 17, 11, 1, 14, 16, missing 20. Column 1 contains 9, 14, 15, 17, 11, 1, missing 20. Thus, the answer is 20.	null
80	Deductive Reasoning Test with Figures	image_080.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 15, B: 7, C: 14, D: 4	B	Row 2 contains 15, 14, 4, missing 7. Column 3 contains 14, 4, 15, missing 7. Thus, the answer is 7.	null
81	Deductive Reasoning Test with Figures	image_081.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\Delta$, B: $\neq$, C: $\approx$, D: $\div$	C	Row 5 contains $\Delta$, $\div$, $\sqrt$, missing $\approx$. Column 5 contains $\neq$, $\div$, $\sqrt$, missing $\approx$. Thus, the answer is $\approx$.	null
82	Deductive Reasoning Test with Figures	image_082.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\rho$, B: $\pi$, C: $\kappa$, D: $\sigma$	B	Row 4 contains $\kappa$, $\rho$, $\sigma$, missing $\pi$. Column 1 contains $\kappa$, $\rho$, missing $\pi$. Thus, the answer is $\pi$.	null
83	Deductive Reasoning Test with Figures	image_083.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 17, B: 9, C: 14, D: 19	D	Row 6 contains 18, 14, 17, 6, 9, missing 19. Column 3 contains 17, 6, missing 19. Thus, the answer is 19.	null
84	Deductive Reasoning Test with Figures	image_084.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: t, B: e, C: d, D: f	B	Row 2 contains f, p, missing e. Column 5 contains p, t, d, missing e. Thus, the answer is e.	null
85	Deductive Reasoning Test with Figures	image_085.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\int$, B: $\Sigma$, C: $\neq$, D: $\approx$	D	Row 1 contains $\times$, $\neq$, $\Delta$, $\equiv$, $\int$, missing $\approx$. Column 6 contains $\equiv$, $\int$, $\div$, $\pm$, $\neq$, $\Sigma$, missing $\approx$. Thus, the answer is $\approx$.	null
86	Deductive Reasoning Test with Figures	image_086.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\alpha$, B: $\textvarsigma$, C: $\eta$, D: $\phi$	D	Row 2 contains $\textvarsigma$, $\iota$, $\omicron$, $\psi$, $\tau$, missing $\phi$. Column 1 contains $\eta$, $\textvarsigma$, $\omega$, $\omicron$, $\psi$, $\tau$, $\alpha$, missing $\phi$. Thus, the answer is $\phi$.	null
87	Deductive Reasoning Test with Figures	image_087.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\text{laughingface}$, B: $\text{joy}$, C: $\text{blush}$, D: $\text{smileface}$	B	Row 6 contains $\text{smileyface}$, $\text{grinningface}$, $\text{smileface}$, $\text{laughingface}$, missing $\text{joy}$. Column 1 contains $\text{blush}$, missing $\text{joy}$. Thus, the answer is $\text{joy}$.	null
88	Deductive Reasoning Test with Figures	image_088.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\leftarrow$, B: $\rightarrow$, C: $\updownarrow$, D: $\nearrow$	C	Row 3 contains $\uparrow$, $\rightarrow$, $\downarrow$, $\nearrow$, $\nwarrow$, $\swarrow$, $\leftarrow$, $\leftrightarrow$, missing $\updownarrow$. Column 7 contains $\nwarrow$, $\leftarrow$, $\leftrightarrow$, $\rightarrow$, $\downarrow$, $\nearrow$, missing $\updownarrow$. Thus, the answer is $\updownarrow$.	null
89	Deductive Reasoning Test with Figures	image_089.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: w, B: t, C: s, D: p	B	Row 6 contains v, p, w, s, missing t. Column 6 contains v, u, b, s, missing t. Thus, the answer is t.	null
90	Deductive Reasoning Test with Figures	image_090.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\chi$, B: $\pi$, C: $\iota$, D: $\lambda$	B	Row 1 contains $\psi$, $\lambda$, $\iota$, missing $\pi$. Column 1 contains $\chi$, $\mu$, $\psi$, $\lambda$, $\iota$, missing $\pi$. Thus, the answer is $\pi$.	null
91	Deductive Reasoning Test with Figures	image_091.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\blacklozenge$, B: $\triangleleft$, C: $\blacksquare$, D: o	C	Row 1 contains o, $\bullet$, $\blacklozenge$, $\triangleleft$, missing $\blacksquare$. Column 1 contains o, missing $\blacksquare$. Thus, the answer is $\blacksquare$.	null
92	Deductive Reasoning Test with Figures	image_092.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: n, B: c, C: g, D: r	D	Row 3 contains a, n, missing r. Column 5 contains c, n, g, y, a, missing r. Thus, the answer is r.	null
93	Deductive Reasoning Test with Figures	image_093.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: d, B: u, C: h, D: t	B	Row 3 contains h, j, d, t, missing u. Column 5 contains d, t, h, missing u. Thus, the answer is u.	null
94	Deductive Reasoning Test with Figures	image_094.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\iota$, B: $\tau$, C: $\upsilon$, D: $\xi$	D	Row 8 contains $\tau$, $\upsilon$, $\iota$, $\chi$, $\eta$, $\epsilon$, $\nu$, missing $\xi$. Column 4 contains $\eta$, $\epsilon$, $\mu$, $\tau$, $\iota$, $\chi$, missing $\xi$. Thus, the answer is $\xi$.	null
95	Deductive Reasoning Test with Figures	image_095.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 14, B: 3, C: 1, D: 12	C	Row 7 contains 7, 14, 12, 3, 2, 20, 13, 11, missing 1. Column 6 contains 14, 3, 13, missing 1. Thus, the answer is 1.	null
96	Deductive Reasoning Test with Figures	image_096.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\lozenge$, B: $\bullet$, C: $\blacksquare$, D: $\triangleleft$	A	Row 5 contains $\bullet$, $\blacksquare$, missing $\lozenge$. Column 5 contains $\triangleleft$, $\bullet$, $\blacktriangle$, $\blacksquare$, missing $\lozenge$. Thus, the answer is $\lozenge$.	null
97	Deductive Reasoning Test with Figures	image_097.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 13, B: 4, C: 18, D: 8	B	Row 3 contains 3, 8, 9, 18, 13, missing 4. Column 6 contains 13, 8, 9, missing 4. Thus, the answer is 4.	null
98	Deductive Reasoning Test with Figures	image_098.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\text{sweatsmile}$, B: $\text{joy}$, C: $\text{smileface}$, D: $\text{laughingface}$	D	Row 3 contains $\text{sweatsmile}$, $\text{smileface}$, $\text{joy}$, missing $\text{laughingface}$. Column 2 contains $\text{joy}$, missing $\text{laughingface}$. Thus, the answer is $\text{laughingface}$.	null
99	Deductive Reasoning Test with Figures	image_099.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\text{joy}$, B: $\text{grinningface}$, C: $\text{blush}$, D: $\text{sweatsmile}$	D	Row 6 contains $\text{joy}$, $\text{grinningface}$, missing $\text{sweatsmile}$. Column 4 contains $\text{blush}$, $\text{grinningface}$, $\text{smileyface}$, $\text{joy}$, $\text{beamingface}$, $\text{innocent}$, missing $\text{sweatsmile}$. Thus, the answer is $\text{sweatsmile}$.	null
100	Deductive Reasoning Test with Figures	image_100.png	Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\theta$, B: $\zeta$, C: $\sigma$, D: $\gamma$	B	Row 2 contains $\theta$, $\sigma$, $\mu$, $\gamma$, missing $\zeta$. Column 5 contains $\gamma$, $\sigma$, $\mu$, missing $\zeta$. Thus, the answer is $\zeta$.	null

1

Mechanical Deductive Reasoning Test

image_001.png

The smaller gear makes 36 revolutions by the time the larger ones make 18. If the smaller gear makes 56 revolutions, how many turns will the larger one make? A. 24 B. 26 C. 28 D. 25

C

Explanation: \[ u = \frac{18}{36} = 0.5 \] \[ n_{\text{larger}} = u \cdot 56 = 28 \]

https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning

2

Mechanical Deductive Reasoning Test

image_002.png

Gear A: 5 teeth Gear B: 50 teeth Gear C: 20 teeth Gear D: 10 teeth How many revolutions per second is gear C turning? A. 5 B. 10 C. 15 D. 20

B

If a cog with 5 teeth can do a full 40 revolutions in a second, a cog with four times as many teeth will take 4 times as long to do a full revolution. This means, it will do 4 times fewer revolutions. So the correct answer is 10.

https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning

3

Mechanical Deductive Reasoning Test

image_003.png

Which image is the front view of the given part in the direction of the arrow?

B

The front view is determined by looking in the direction of the arrow. Option A shows a circle, which represents the top view. Option C makes the cylinder appear too small, which is inaccurate. Option B correctly shows the rectangular base with the cylinder as a smaller rectangle on top. Conclusion: The correct answer is B.

https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning

4

Mechanical Deductive Reasoning Test

image_004.png

In which direction will the orange gear rotate? A. Clockwise B. Counterclockwise C. No rotation

A

The driving gear and the orange gear are connected through an intermediate gear, so the orange gear rotates in the same direction as the driving gear.

https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning

5

Mechanical Deductive Reasoning Test

image_005.png

In which direction will the orange gear rotate? A. Clockwise B. Counterclockwise C. No rotation

B

the driving gear rotates clockwise (CW), the orange gear will rotate counterclockwise (CCW).

https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning

6

Mechanical Deductive Reasoning Test

image_006.png

In which direction will the orange gear rotate? A. Clockwise B. Counterclockwise C. No rotation

B

The driving gear and the orange gear are continuously meshed through two intermediate gears. Therefore, the orange gear rotates in the opposite direction of the driving gear.

https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning

7

Mechanical Deductive Reasoning Test

image_007.png

In which direction will the orange gear rotate? A. Clockwise B. Counterclockwise C. No rotation

B

The driving rack moves to the right, causing the meshing gear to rotate clockwise. The orange gear is connected to this gear through two intermediate gears. Therefore, the orange gear rotates counterclockwise.

https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning

8

Mechanical Deductive Reasoning Test

image_008.png

In which direction will the orange gear rotate? A. Clockwise B. Counterclockwise C. No rotation

B

The driving gear rotates counterclockwise and transmits motion through a belt to the large gear, which also rotates counterclockwise. This large gear meshes with a smaller gear, making it rotate clockwise. The small gear then drives another gear, causing it to rotate counterclockwise. Finally, the orange gear meshes with this last gear, making it rotate counterclockwise

https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning

9

Mechanical Deductive Reasoning Test

image_009.png

The scale is balanced. What is the weight of the weight with the question mark? A. 4 kg B. 10 kg C. 20 kg D. 40 kg E. 50 kg

A

\[ m = \frac{10 \cdot 2}{5} = 4 \, \text{kg} \]

https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning

10

Mechanical Deductive Reasoning Test

image_010.png

On which pole does the weight press harder? A. (A) B. (B) C. None

B

(B) experiences greater force because it is closer to the fulcrum of the heavier mass (A).

https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning

11

Mechanical Deductive Reasoning Test

image_011.png

What pulleys turn in the same direction as 1? A. 2 and 8 B. 6 and 4 C. 2, 3, 7 and 8 D. 4, 5 and 6

B

Pulley 1 rotates clockwise. Pulley 2 and 8 rotate in the opposite directions to pulley 1. Pulley 8 and 7 rotate in the same direction. Pulley 2 and 3 rotate in the same direction. Pulley 3 and 4 rotate in opposite directions. Pulley 6 and 7 rotate in opposite directions. Pulley 5 and 6 rotate in opposite directions.

https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning

12

Mechanical Deductive Reasoning Test

image_012.png

Consider the following pulley system. Pulley A is fixed, and Pulley B is moveable. If the system is balanced, how much does the weight with the question mark weigh? A. 5 kg B. 10 kg C. 20 kg D. 40 kg E. 50 kg

C

The force transmitted on a single rope is the same. Pulley B has two ropes, so the mass of the object to be found is: \[ m = 2 \cdot 10 = 20 \, \text{kg} \]

https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning

13

Mechanical Deductive Reasoning Test

image_013.png

What is the weight of the weight with the question mark? A. 15 kg B. 20 kg C. 25 kg D. 30 kg E. 35 kg

E

\[ m = \frac{20 \cdot 6 + 30 \cdot 3}{6} = 35 \ \text{kg} \]

https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning

14

Mechanical Deductive Reasoning Test

image_014.png

Which is the side view projection of the given part according to the first angle projections?

B

According to the first angle projections, the side view projection is seen from the left. Therefore, the correct answer is B.

https://www.iqtests.org/deductive-reasoning-tests/mechanical-deductive-reasoning

15

Mechanical Deductive Reasoning Test

image_015.png

What weight does the blue box have to be in order for the seesaw to be in equilibrium? A. 20 kg B. 30 kg C. 40 kg D. None

D

In order for the seesaw to be in equilibrium, the net force must equal zero. Moment of a force = force x distance to pivot. Therefore, the moment of a force on the left side of the seesaw is 10 kg x 5 = 50. The right side must equal 50 for the seesaw to be balanced, therefore 50 divided by 2 (2 meters distance from pivot) = 25.

https://www.assessmentday.com/mechanical-reasoning.htm#free-mechanical-reasoning-test

16

Mechanical Deductive Reasoning Test

image_016.png

Consider two spheres as shown in the figure. Sphere 1 moves and undergoes a perfectly elastic head-on collision with sphere 2. Determine the direction of motion of sphere 1 after the collision. A. Opposite to the initial direction B. Same as the initial direction C. None of the answers

A

Since the collision is central and perfectly elastic, the total momentum before and after the collision must be equal: \[ m_1 \cdot v_1(0) + m_2 \cdot v_2(0) = m_1 \cdot v_1 + m_2 \cdot v_2 \] Since the collision is perfectly elastic, kinetic energy is also conserved: \[ \frac{1}{2} \cdot m_1 \cdot v_1(0)^2 + \frac{1}{2} \cdot m_2 \cdot v_2(0)^2 = \frac{1}{2} \cdot m_1 \cdot v_1^2 + \frac{1}{2} \cdot m_2 \cdot v_2^2 \] Solving for $ v_1 $, we get: \[ v_1 = -\frac{5}{3} \, \text{m/s} \] Hence, option A is the correct choice.

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17

Mechanical Deductive Reasoning Test

image_017.png

A speeding motorist travelling passes a stopped police car. The police car immediately begins to chase the speeder, accelerating at a constant 2.5 m/s2. How long does it take for the police car to intercept the speeder? A. 25.6 s B. 26.6 s C. 27.6 s D. 28.6 s

B

The speeder’s car's equation of motion is given by: \[ X_s \coloneqq \frac{120 \cdot 1000 \cdot t}{3600} = \frac{100}{3} \cdot t, \, \text{m/s} \] The police car's equation of motion is: \[ X_{\text{police}} = 0.5 \cdot 2.5 \cdot t^2 \] When the two vehicles are at the same position: \[ X_s = X_{\text{police}} \] Solving for time $ t $, we get: \[ t = \frac{33.3}{0.5 \cdot 2.5} = 26.6 \, \text{s} \]

https://sciencenotes.org/equations-motion-constant-acceleration-intercept-example-problem/

18

Mechanical Deductive Reasoning Test

image_018.png

A child pulls a heavy object using a rope that passes over a pulley. Neglect the mass of the pulley and assume the rope remains taut throughout the motion. What is the minimum force the child must exert in order to lift the object upward? A. 49 N B. 50 N C. 51 N D. 52 N

B

The minimum force the child must exert in order to lift the object upward is: \[ F = g \cdot m = 9.81 \cdot 5 = 49.05 \, \text{N} \] Hence, option B is the correct answer, with: \[ F = 50 \, \text{N} \]

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19

Mechanical Deductive Reasoning Test

image_019.png

The angular velocity of the disk is defined by like the picture. Determine the magnitudes of the velocity of point A on the disk when t = 0.5 s. _x000B_ A. 2.5 m/s B. 2.6 m/s C. 2.7 m/s D. 2.8 m/s

B

V_A = \omega \cdot 0.8 = \left(2 \cdot 0.5^2 + 2\right) \cdot 0.8 = 2.6 \, \text{m/s}

https://www.assessmentday.com/spatial-reasoning.htm

20

Mechanical Deductive Reasoning Test

image_020.png

The disk is originally rotating at 𝜔_0. If it is subjected to a constant angular acceleration, determine the magnitudes of the normal component of acceleration of point A at the instant t = 2 s. A. 1350 m/s^2 B. 1352 m/s^2 C. 1354 m/s^2 D. 1356 m/s^2

B

The angular velocity of the disk can be determined using :\\ \[ \omega = \omega_0 + \alpha t = 12 + 20 \ast 2 = 52 \, \text{rad/s} \] The normal component of acceleration are:\\ \[ a_n = \omega^2 R = 1352 \, \text{m/s}^2 \]

https://www.assessmentday.com/spatial-reasoning.htm

21

Mechanical Deductive Reasoning Test

image_021.png

If gear A rotates with a constant angular acceleration of starting from rest, determine the angular velocity of gear B if the angular velocity of gear A is 600 rpm. A. 180 rad/s B. 190 rad/s C. 200 rad/s D. 210 rad/s

A

\[ \omega_B = \frac{15\omega_A}{50} = 180 \, \text{rad/s} \]

https://www.assessmentday.com/spatial-reasoning.htm

22

Mechanical Deductive Reasoning Test

image_022.png

The power of a bus engine is transmitted using the belt-andpulley arrangement shown. Determine the angular velocities of the generator pulley B when t = 3 s. A. 300 rad/s B. 320 rad/s C. 340 rad/s D. 360 rad/s

A

\text{When } t = 3 \, \text{s} \[ \omega_A = 20(3) + 40 = 100 \, \text{rad/s} \] \text{The speed of a point } P \text{ on the belt wrapped around } A \text{ is} \[ v_P = \omega_A r_A = 100(0.075) = 7.5 \, \text{m/s} \] \[ \omega_B = \frac{v_P}{r_D} = \frac{7.5}{0.025} = 300 \, \text{rad/s} \]

https://www.123test.com/spatial-reasoning-test/id=LZ9UJNDIC2TH&version=

23

Mechanical Deductive Reasoning Test

image_023.png

If the motor turns gear A with an angular acceleration and the angular velocity, determine the angular velocity of gear D. A. 2 rad/s B. 3 rad/s C. 4 rad/s D. 5 rad/s

C

\textbf{Angular Motion:} \text{ The angular velocity and acceleration of gear } B \text{ must be determined first. Here, } \omega_A r_A = \omega_B r_B \text{ and } \alpha_A r_A = \alpha_B r_B. \text{ Then,} \[ \omega_B = \frac{r_A}{r_B} \omega_A = \left( \frac{40}{100} \right)(20) = 8.00 \, \text{rad/s} \] \[ \alpha_B = \frac{r_A}{r_B} \alpha_A = \left( \frac{40}{100} \right)(2) = 0.800 \, \text{rad/s}^2 \] \text{Since gear } C \text{ is attached to gear } B, \text{ then } \omega_C = \omega_B = 8 \, \text{rad/s and } \alpha_C = \alpha_B = 0.8 \, \text{rad/s}^2. \text{ Realizing that } \omega_C r_C = \omega_D r_D \text{ and } \alpha_C r_C = \alpha_D r_D, \text{ then} \[ \omega_D = \frac{r_C}{r_D} \omega_C = \left( \frac{50}{100} \right)(8.00) = 4.00 \, \text{rad/s} \]

https://www.123test.com/spatial-reasoning-test/id=LZ9UJNDIC2TH&version=

24

Mechanical Deductive Reasoning Test

image_024.png

The gear A on the drive shaft of the outboard motor has a radius 𝑟_𝐴=0.5 in. and the meshed pinion gear B on the propeller shaft has a radius 𝑟_𝐵=1.2 in. Determine the angular velocity of the propeller in t=1.5 𝑠, if the drive shaft rotates with an angular acceleration 𝛼=〖400𝑡〗^3 𝑟𝑎𝑑/𝑠^2 , where t is in seconds. The propeller is originally at rest and the motor frame does not move. _x000B_ A. 209 m/s^2 B. 211 m/s^2 C. 213 m/s^2 D. 215 m/s^2

B

\textbf{Angular Motion:} \text{ The angular velocity of gear } A \text{ at } t = 1.5 \, \text{s must be determined first. Applying Eq. 16--2, we have} \[ d\omega = \alpha dt \] \[ \int_0^{\omega_A} d\omega = \int_0^{1.5 \, s} 400t^3 \, dt \] \[ \omega_A = 100t^4 \big|_0^{1.5 \, s} = 506.25 \, \text{rad/s} \] \text{However, } \omega_A r_A = \omega_B r_B \text{ where } \omega_B \text{ is the angular velocity of propeller. Then,} \[ \omega_B = \frac{r_A}{r_B} \omega_A = \left( \frac{0.5}{1.2} \right)(506.25) = 211 \, \text{rad/s} \]

https://www.123test.com/spatial-reasoning-test/id=LZ9UJNDIC2TH&version=

25

Mechanical Deductive Reasoning Test

image_025.png

The pinion gear A on the motor shaft is given a constant angular acceleration 𝛼. If the gears A and B have the dimensions shown, determine the angular velocity of the output shaft C, when t=2s starting from rest. The shaft is fixed to B and turns with it. A. 1.62 rad/s B. 1.64 rad/s C. 1.66 rad/s D. 1.68 rad/s

D

\begin{align*} \omega &= \omega_0 + \alpha_c t \\ \omega_A &= 0 + 3(2) = 6 \, \text{rad/s} \\ \\ \theta &= \theta_0 + \omega_0 t + \frac{1}{2} \alpha_c t^2 \\ \theta_A &= 0 + 0 + \frac{1}{2}(3)(2)^2 \\ \theta_A &= 6 \, \text{rad} \\ \\ \omega_A r_A &= \omega_B r_B \\ 6(35) &= \omega_B (125) \\ \omega_C = \omega_B &= 1.68 \, \text{rad/s} \end{align*}

https://www.123test.com/spatial-reasoning-test/id=LZ9UJNDIC2TH&version=

26

Mechanical Deductive Reasoning Test

image_026.png

Which piece corresponds to the given solid?

C

The third piece corresponds to the given solid

https://www.123test.com/spatial-reasoning-test/id=LZ9UJNDIC2TH&version=

27

Mechanical Deductive Reasoning Test

image_027.png

Which picture can be formed with the given pieces?

C

null

https://www.assessmentday.com/spatial-reasoning.htm

28

Mechanical Deductive Reasoning Test

image_028.png

To which object does the given top view correspond?

A

null

https://www.assessmentday.com/spatial-reasoning.htm

29

Mechanical Deductive Reasoning Test

image_029.png

Which of these image is the top view of the given object?

B

null

https://www.assessmentday.com/spatial-reasoning.htm

30

Mechanical Deductive Reasoning Test

image_030.png

For protection, the barrel barrier is placed in front of the bridge pier. If the relation between the force and deflection of the barrier is lb, where is in ft, determine the car’s maximum penetration in the barrier. The car has a weight of 4000 lb and it is traveling with a constant speed before it hits the barrier. A. 3.20 ft B. 3.22 ft C. 3.24 ft D. 3.26 ft

C

\[ T_{1}+\Sigma U_{12}=T_{2} \] \[ 0.5\cdot \left(\frac{4000}{ 32.2}\right)\cdot \left(75^{2}\right)+\int_{0}^{x_{\max}}90\cdot 10^{3}\cdot x^{ 0.5}d{x}=0 \] \[ x_{\max}= 3.24 \text{ ft} \]

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31

Mechanical Deductive Reasoning Test

image_031.png

A man kicks the ball such that it leaves the ground at an angle and strikes the ground at the same elevation a distance of Sx m away. Determine the impulse of his foot on the ball at A. Neglect the impulse caused by the ball’s weight while it’s being kicked. A. 1.75 N.s B. 1.76 N.s C. 1.77 N.s D. 1.78 N.s

A

Consider the vertical motion of the ball, where: \[ S_y = v \cdot \sin(60^\circ) \cdot t + \frac{1}{2} \cdot (-9.81) \cdot t^2 = 0 \] Factorizing the equation: \[ t \left( v \cdot \sin(60^\circ) - 4.905 \cdot t \right) = 0 \] Since $ t \ne 0 $, we solve: \[ v \cdot \sin(60^\circ) - 4.905 \cdot t = 0 \] \[ t \approx \frac{v \cdot \sin(60^\circ)}{4.905} \] \[ t \approx 0.1766v \] \section*{Horizontal Motion of the Ball} \[ S_x = v \cdot \cos(60^\circ) \cdot t = 12 \] \[ t = \frac{12}{v \cdot \cos(60^\circ)} = \frac{24}{v} \] Equating the two expressions for $ t $: \[ 0.1766v = \frac{24}{v} \] Solving for $ v $: \[ v^2 = \frac{24}{0.1766} \Rightarrow v \approx 11.66 \, \text{m/s} \] \section*{Principle of Impulse and Momentum} \[ I = m (v_2 - v_1) = m \cdot v = 1.75 \, \text{N$\cdot$s} \]

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32

Mechanical Deductive Reasoning Test

image_032.png

The jet car is initially traveling at a initial velocity when it is subjected to the acceleration shown. Determine the car's maximum velocity and the time 𝑡' when it comes to a stop. Assume that when t=0, the displacement s=0. A. 𝑉_𝑚𝑎𝑥=100 m/s; 𝑡′=40 s B. 𝑉_𝑚𝑎𝑥=102 m/s; 𝑡′=42 s C. 𝑉_𝑚𝑎𝑥=104 m/s; 𝑡′=44 s D. 𝑉_𝑚𝑎𝑥=106 m/s; 𝑡′=46 s

A

Because acceleration is constant, the equation of car motion is: \[ v = 10 + a \cdot t \] The maximum velocity is: \[ V_{\text{max}} = 10 + 6 \cdot 15 = 100 \, \text{m/s} \] When the jet car stops: \[ 0 = 100 - 4 \cdot (t' - 15) \] Solving for $ t' $: \[ t' = \frac{160}{4} = 40 \, \text{s} \]

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33

Mechanical Deductive Reasoning Test

image_033.png

Determine the minimum initial velocity 𝑣_0 at which the ball must be kicked. A. 𝑣_0=22.5 m/s B. 𝑣_0=23.5 m/s C. 𝑣_0=24.5 m/s D. 𝑣_0=25.5 m/s

A

Time to reach the horizontal position: \[ x = v_0 \cdot t \cdot \cos(30^\circ) = 6 \] The vertical position at that time: \[ y = v_0 \cdot t \cdot \sin(30^\circ) - 0.5 \cdot g \cdot t^2 = 3 \] From these two equations, we can determine: \[ v_0 = 22.5 \, \text{m/s} \]

null

34

Mechanical Deductive Reasoning Test

image_034.png

A golf ball is struck with a velocity as shown. Determine the distance d to where it will land. A. 𝑑=156 ft B. 𝑑=166 ft C. 𝑑=176 ft D. 𝑑=186 ft

B

Given the following equations: \[ d \cdot \cos(10^\circ) = 80 \cdot \cos(55^\circ) \cdot t \text{ (1)} \] \[ d \cdot \sin(10^\circ) = 80 \cdot \sin(55^\circ) \cdot t - 0.5 \cdot (32.5) \cdot t^2 \text{ (2)} \] Solving these equations, we get the result: \[ d = 166 \, \text{ft} \]

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35

Mechanical Deductive Reasoning Test

image_035.png

A passenger in an automobile observes that raindrops make an angle with the horizontal as the auto travels forward with a constant speed as shown. Compute the terminal (constant) velocity of the rain if it is assumed to fall vertically. A. 33.6 km/h B. 34.6 km/h C. 35.6 km/h D. 36.6 kh/h

B

The relative velocity is given by: \[ V_r = 60 \cdot \tan(30^\circ) = 34.6 \, \text{km/h} \]

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36

Mechanical Deductive Reasoning Test

image_036.png

If the coefficient of kinetic friction between the crate and the ground is 𝜇 as shown. Determine the distance traveled by the crate at 𝑡=t', if it starts from rest.. A. 5.01 m B. 5.02 m C. 5.03 m D. 5.04 m

D

The acceleration of the crate is given by: \[ a = \frac{200 \cdot \cos(30^\circ) - 0.3 \cdot (-200 \cdot \sin(30^\circ) + 9.81 \cdot 50)}{50} = 1.121 \, \text{m/s}^2 \] The motion equation is: \[ s = 0.5 \cdot a \cdot t^2 = 0.5 \cdot 1.121 \cdot 9 = 5.04 \, \text{m} \]

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37

Mechanical Deductive Reasoning Test

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The conveyor belt is moving. If the coeffcient of static friction between the conveyor and the package B is 𝜇 as shown, determine the shortest time the belt can stop so that the package does not slide on the belt. A. 2.02 s B. 2.04 s C. 2.06 s D. 2.08 s

B

When the conveyor belt decelerates, the package wants to keep moving due to inertia. Static friction must provide the force to decelerate the package at the same rate as the belt, to avoid sliding. The maximum static friction force is given by: \[ f = 0.2 \cdot 10 \cdot 9.81 = 19.62 \, \text{N} \] This force is responsible for the maximum possible deceleration: \[ a = \frac{19.62}{10} = 1.962 \, \text{m/s}^2 \] To find the shortest time to stop, we use kinematics: \[ v = 4 - a \cdot t = 0 \] Solving for time: \[ t_{\text{min}} = \frac{4}{1.962} = 2.04 \, \text{s} \]

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38

Mechanical Deductive Reasoning Test

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Determine the magnitude of the resultant force Fr. A. 392 lb B. 393 lb C. 394 lb D. 395 lb

B

The resultant force $ F_r $ is given by the equation: \[ F_r = \sqrt{F_1^2 + F_2^2 - 2 \cdot F_1 \cdot F_2 \cdot \cos(75^\circ)} = 393 \, \text{lb} \]

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39

Mechanical Deductive Reasoning Test

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A vertical force F acts downward on the two-membered frame. Determine the magnitudes of the two components of F directed along the axes of members AB and AC. A. 𝐹_𝐴𝐵=366 N; 𝐹_𝐴𝐶=448 N B. 𝐹_𝐴𝐵=448 N; 𝐹_𝐴𝐶=366 N C. 𝐹_𝐴𝐵=446 N; 𝐹_𝐴𝐶=368 N D. 𝐹_𝐴𝐵=368 N; 𝐹_𝐴𝐶= 448 N

B

he forces $ F_{ab} $ and $ F_{ac} $ are calculated as follows: \[ F_{ab} = \frac{500 \cdot \sin(60^\circ)}{\sin(75^\circ)} = 448 \, \text{N} \] \[ F_{ac} = \frac{500 \cdot \sin(45^\circ)}{\sin(75^\circ)} = 366 \, \text{N} \]

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40

Mechanical Deductive Reasoning Test

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If the resultant force of the two tugboats is required to be directed towards the positive 𝑥 axis, and 𝐹_𝐵 is to be a minimum, determine the magnitude of the resultant force 𝐹_𝑅 and 𝐹_𝐵 and the angle 𝜃._x000B_ A. 𝜃=70^𝑜;𝐹_𝑅=1.73 kN; 𝐹_𝐵=1 kN B. 𝜃=80^𝑜;𝐹_𝑅=1 kN; 𝐹_𝐵= 1.73 kN C. 𝜃=90^𝑜;𝐹_𝑅=1.73 kN; 𝐹_𝐵=1 kN D. 𝜃=100^𝑜;𝐹_𝑅=1 kN; 𝐹_𝐵= 1.73 kN

C

For $ F_R $ to be minimum, it has to be directed perpendicular to $ F_R $. Thus, \[ \theta = 90^\circ \] The forces $ F_R $ and $ F_B $ are calculated as follows: \[ F_R = F_A \cdot \cos(30^\circ) = 1.73 \, \text{kN} \] \[ F_B = F_A \cdot \sin(30^\circ) = 1 \, \text{kN} \]

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41

Mechanical Deductive Reasoning Test

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A non-pressurized cylindrical metal tank filled with air is submerged underwater. As the air escapes, the tank gradually moves deeper underwater. Which statement provides the best reason for this motion? A. The bubbles provide a downward thrust on the tank B. The metal increases in density so it gets heavier C. The bubbles lower the density of the water which lowers its buoyancy D. Water replaces the air in the tank which makes it heavier E. Impossible to tell

D

As air escapes the available space is quickly replaced with water, so the tank's density becomes the same as that of the water and with the added weight and density of the tank itself continues to sink.

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42

Mechanical Deductive Reasoning Test

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There are two identical cars along a bridge. If the bridge has the same thickness along it, which part(s) of the bridge would undergo the most deflection? A. Under the towers B. Below the cars C. Middle of the bridge D. All of the above will have equal deflection E. Impossible to tell

C

The middle of the bridge would undergo the most deflection because it is furthest away from the towers and pillars supporting the bridge. Imagine a piece of string held at either end over a gap between two tables. The point right in the middle would droop the most.

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43

Mechanical Deductive Reasoning Test

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Convex mirrors are used for rear-view mirrors of vehicles. What is the advantage of using a convex mirror instead of a flat mirror? A. It provides a clearer reflection B. It has a more accurate reflection C. The wider angle of view reduces blind spots D. It is easier to clean a convex mirror E. A convex mirror provides no advantage

C

A convex mirror has a wider field of view because of its shape. A wider field of view can eliminate blind spots or reduce the size of the area that's not easily visible.

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44

Mechanical Deductive Reasoning Test

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It is a cold winter outside and a well-insulated house has its heater turned on. The front door is opened and cold air rushes in. If the wind speed outside is very low, how would the cold air enter the house? A. Scenario A, the cold air will flow towards the floor B. Scenario B, the cold air will flow towards the ceiling C. A combination of A and B D. The cold air will not enter the house E. Impossible to tell

A

Cold air sinks, whereas hot air rises. The house and the air inside it are warmer than the outside air temperature, so if these two systems (house and outside) were to be suddenly connected (door opening) the cold air would sink and the hot air would sit above the cold air until the heat transferred between the two.

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45

Mechanical Deductive Reasoning Test

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A bucket of water has a leak on its lower side. As the water level goes down, what happens to the speed of the water coming out of the hole? A. It increases B. It stays the same C. It decreases D. It reverses E. Impossible to tell

C

The speed of the water exiting the bucket by the hole is proportional to the pressure exerted upon it. When the bucket is full there is a greater volume of water trying to exit the bucket via the hole. A greater volume of water is a greater mass of water and therefore exerts a greater pressure, the greater pressure translates to faster speed. As more water leaves the bucket via the hole the volume decreased, therefore so does the mass of the water and the pressure then drops.

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46

Mechanical Deductive Reasoning Test

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Three identical candles were lit and covered by individual jars at the same time. Which candle would have its flame extinguish first? A. A, candle in a small sealed jar B. B, candle in a big sealed jar C. C, candle in a small jar with holes D. They will all extinguish at the same time E. Impossible to tell

A

A flame needs fuel and oxygen to continue burning. The wax provides the fuel in all of three instances. There is air exchange in jar C, so more oxygen can be used by the candle to continue burning. Jars A and B are closed systems. No oxygen can get in. Once the oxygen is used up the flame will suffocate itself. The air available in the small jar, A, is less than that in the large jar, B, therefore A shall be extinguished first.

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47

Mechanical Deductive Reasoning Test

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Fire doors have a spring which automatically pushes and forces shut the door when it's open. If the springs were made thicker, what effect would this have on how the door closes? A. The door will close slower B. The door will not fully close C. The door will make a screeching noise as it closes D. The door will close faster E. It will not make a difference

D

The spring forces the door shut. A thicker spring is stronger which will shut the door more forcefully than before.

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48

Mechanical Deductive Reasoning Test

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A bolt cutter has long handles with handle grips that are located as far away as possible from the neck. Which statement provides the best reason for this design? A. Longer handles make the cutting blade move faster B. It provides mechanical advantage which allows cutting through thick bolts. C. The appearance of the tool is significantly more aesthetic with longer handles D. It makes the bolt cutter more durable when dropped accidentally E. Longer handles are more ergonomic and allows easier storage

B

The further the distance that the force is applied to the pivot point, the less force that's required to cut through the bolts, or the stronger the force that can be applied to the bolts is. This is the advantage in having long handles on many tools.

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49

Mechanical Deductive Reasoning Test

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A car is behind a moving fire engine on a motorway. The fire engine is traveling at a speed of 60 mph. If the distance between the two moving vehicles is not changing, what is the car's speed? A. 80 mph B. 70 mph C. 60 mph D. 50 mph E. Impossible to tell

C

If the distance between the two vehicles remains the same, they must be traveling at the same speed. The car is therefore also traveling at 60mph. Note: This is not the same as how much energy is required to get the vehicles moving at the same speed. This depends on a lot of factors, mostly; air resistance and mass of each vehicle, which is not what's being asked in this question.

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50

Mechanical Deductive Reasoning Test

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Firefighters use a halligan to forcibly enter locked doors during fire rescue operations. Which halligan would require the least effort to forcibly open the door? A. Figure A B. Figure B C. Figure C D. Figure D

D

Halligan D would require the least effort to forcibly open the door because it has the longest distance from the point where the force is applied to where it is being leveraged.

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51

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\equiv$, B: $\Sigma$, C: $\neq$, D: $\pi$

D

Row 6 contains $\neq$, $\sqrt$, $\Sigma$, missing $\pi$. Column 2 contains $\equiv$, $\neq$, $\sqrt$, $\Sigma$, $\approx$, missing $\pi$. Thus, the answer is $\pi$.

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52

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 11, B: 13, C: 9, D: 12

D

Row 3 contains 14, 20, 13, 1, 11, missing 12. Column 6 contains 9, 14, 20, 13, missing 12. Thus, the answer is 12.

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53

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\iota$, B: $\phi$, C: $\lambda$, D: $\theta$

D

Row 2 contains $\lambda$, $\iota$, missing $\theta$. Column 3 contains $\lambda$, $\iota$, $\phi$, missing $\theta$. Thus, the answer is $\theta$.

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54

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\tau$, B: $\upsilon$, C: $\mu$, D: $\kappa$

C

Row 5 contains $\upsilon$, $\chi$, $\kappa$, $\tau$, missing $\mu$. Column 6 contains $\omicron$, $\upsilon$, $\rho$, $\chi$, $\tau$, $\omega$, missing $\mu$. Thus, the answer is $\mu$.

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55

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 17, B: 8, C: 6, D: 16

C

Row 1 contains 14, 4, 10, 8, 5, missing 6. Column 2 contains 4, 17, 10, 8, 16, 3, 5, 14, missing 6. Thus, the answer is 6.

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56

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\lozenge$, B: $\blacktriangledown$, C: $\bigstar$, D: $\bullet$

D

Row 1 contains $\blacktriangledown$, $\triangleright$, o, $\blacksquare$, $\bigstar$, missing $\bullet$. Column 2 contains $\blacklozenge$, $\triangleright$, $\blacktriangle$, $\lozenge$, $\blacktriangledown$, missing $\bullet$. Thus, the answer is $\bullet$.

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57

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 18, B: 19, C: 17, D: 8

C

Row 5 contains 19, 8, 6, missing 17. Column 6 contains 1, 18, 3, 19, missing 17. Thus, the answer is 17.

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58

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\blacktriangle$, B: $\blacklozenge$, C: o, D: $\bigstar$

A

Row 2 contains o, $\blacklozenge$, $\blacktriangledown$, $\bigstar$, missing $\blacktriangle$. Column 1 contains $\bigstar$, o, $\blacktriangledown$, $\bullet$, missing $\blacktriangle$. Thus, the answer is $\blacktriangle$.

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59

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\blacksquare$, B: $\bigstar$, C: $\bullet$, D: $\triangleright$

C

Row 4 contains $\blacksquare$, $\triangleright$, missing $\bullet$. Column 2 contains $\bigstar$, $\triangleright$, $\blacksquare$, missing $\bullet$. Thus, the answer is $\bullet$.

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60

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 14, B: 2, C: 8, D: 11

A

Row 5 contains 8, 11, 2, missing 14. Column 4 contains 2, 8, 3, missing 14. Thus, the answer is 14.

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61

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\pm$, B: $\infty$, C: $\int$, D: $\div$

A

Row 3 contains $\int$, $\div$, missing $\pm$. Column 3 contains $\int$, $\div$, $\infty$, missing $\pm$. Thus, the answer is $\pm$.

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62

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 1, B: 15, C: 19, D: 8

C

Row 1 contains 8, 1, 12, 4, missing 19. Column 5 contains 6, 4, 15, 1, missing 19. Thus, the answer is 19.

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63

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: e, B: r, C: a, D: c

B

Row 4 contains e, c, a, missing r. Column 4 contains c, a, missing r. Thus, the answer is r.

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64

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\upsilon$, B: $\lambda$, C: $\alpha$, D: $\eta$

C

Row 2 contains $\beta$, $\textvarsigma$, $\lambda$, $\phi$, $\eta$, $\upsilon$, $\sigma$, missing $\alpha$. Column 5 contains $\phi$, $\omicron$, $\upsilon$, $\sigma$, $\textvarsigma$, $\lambda$, missing $\alpha$. Thus, the answer is $\alpha$.

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65

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: o, B: $\bullet$, C: $\blacklozenge$, D: $\blacktriangledown$

B

Row 5 contains $\blacksquare$, $\blacklozenge$, o, $\blacktriangledown$, missing $\bullet$. Column 2 contains $\lozenge$, $\blacktriangledown$, $\triangleright$, $\triangleleft$, $\bigstar$, $\blacklozenge$, missing $\bullet$. Thus, the answer is $\bullet$.

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66

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\sqrt$, B: $\equiv$, C: $\pm$, D: $\int$

C

Row 8 contains $\infty$, $\approx$, $\pi$, $\sqrt$, $\int$, $\times$, missing $\pm$. Column 7 contains $\infty$, $\approx$, $\equiv$, $\int$, missing $\pm$. Thus, the answer is $\pm$.

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67

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\pi$, B: $\div$, C: $\int$, D: $\equiv$

C

Row 1 contains $\equiv$, $\div$, missing $\int$. Column 4 contains $\pi$, $\div$, missing $\int$. Thus, the answer is $\int$.

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68

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\triangleright$, B: o, C: $\blacktriangledown$, D: $\lozenge$

C

Row 9 contains $\lozenge$, $\bullet$, o, $\triangleright$, $\blacksquare$, $\blacklozenge$, $\blacktriangle$, missing $\blacktriangledown$. Column 4 contains $\triangleleft$, $\blacklozenge$, $\lozenge$, o, missing $\blacktriangledown$. Thus, the answer is $\blacktriangledown$.

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69

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\sqrt$, B: $\equiv$, C: $\div$, D: $\Sigma$

A

Row 5 contains $\equiv$, $\approx$, $\pi$, $\neq$, $\Delta$, $\div$, $\Sigma$, $\int$, missing $\sqrt$. Column 5 contains $\approx$, $\pi$, $\neq$, $\Delta$, $\int$, missing $\sqrt$. Thus, the answer is $\sqrt$.

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70

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: c, B: f, C: a, D: l

B

Row 5 contains c, a, l, s, missing f. Column 1 contains a, h, s, c, missing f. Thus, the answer is f.

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71

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\int$, B: $\div$, C: $\infty$, D: $\Sigma$

B

Row 8 contains $\Sigma$, $\approx$, $\equiv$, $\int$, $\sqrt$, missing $\div$. Column 2 contains $\approx$, $\int$, $\infty$, $\pi$, $\Sigma$, missing $\div$. Thus, the answer is $\div$.

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72

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\iota$, B: $\tau$, C: $\phi$, D: $\xi$

D

Row 4 contains $\tau$, $\iota$, missing $\xi$. Column 1 contains $\phi$, missing $\xi$. Thus, the answer is $\xi$.

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73

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: o, B: $\triangleright$, C: $\lozenge$, D: $\bullet$

B

Row 1 contains $\lozenge$, o, missing $\triangleright$. Column 2 contains o, $\bullet$, missing $\triangleright$. Thus, the answer is $\triangleright$.

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74

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\times$, B: $\div$, C: $\sqrt$, D: $\neq$

A

Row 5 contains $\Sigma$, $\Delta$, $\sqrt$, $\div$, missing $\times$. Column 3 contains $\neq$, $\Sigma$, $\Delta$, $\sqrt$, missing $\times$. Thus, the answer is $\times$.

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75

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\blacktriangledown$, B: $\blacktriangle$, C: o, D: $\lozenge$

D

Row 5 contains o, $\blacktriangle$, $\blacksquare$, $\bigstar$, missing $\lozenge$. Column 8 contains $\blacklozenge$, $\blacksquare$, $\bigstar$, $\blacktriangledown$, $\bullet$, missing $\lozenge$. Thus, the answer is $\lozenge$.

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76

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: q, B: k, C: y, D: p

B

Row 4 contains e, p, y, q, missing k. Column 1 contains p, e, missing k. Thus, the answer is k.

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77

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\leftrightarrow$, B: $\swarrow$, C: $\downarrow$, D: $\searrow$

D

Row 4 contains $\swarrow$, missing $\searrow$. Column 2 contains $\leftrightarrow$, $\downarrow$, $\swarrow$, missing $\searrow$. Thus, the answer is $\searrow$.

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78

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 11, B: 10, C: 8, D: 2

C

Row 3 contains 10, 11, 14, missing 8. Column 3 contains 2, 10, 14, missing 8. Thus, the answer is 8.

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79

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 14, B: 20, C: 11, D: 1

B

Row 4 contains 15, 17, 11, 1, 14, 16, missing 20. Column 1 contains 9, 14, 15, 17, 11, 1, missing 20. Thus, the answer is 20.

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80

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 15, B: 7, C: 14, D: 4

B

Row 2 contains 15, 14, 4, missing 7. Column 3 contains 14, 4, 15, missing 7. Thus, the answer is 7.

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81

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\Delta$, B: $\neq$, C: $\approx$, D: $\div$

C

Row 5 contains $\Delta$, $\div$, $\sqrt$, missing $\approx$. Column 5 contains $\neq$, $\div$, $\sqrt$, missing $\approx$. Thus, the answer is $\approx$.

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82

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\rho$, B: $\pi$, C: $\kappa$, D: $\sigma$

B

Row 4 contains $\kappa$, $\rho$, $\sigma$, missing $\pi$. Column 1 contains $\kappa$, $\rho$, missing $\pi$. Thus, the answer is $\pi$.

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83

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 17, B: 9, C: 14, D: 19

D

Row 6 contains 18, 14, 17, 6, 9, missing 19. Column 3 contains 17, 6, missing 19. Thus, the answer is 19.

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84

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: t, B: e, C: d, D: f

B

Row 2 contains f, p, missing e. Column 5 contains p, t, d, missing e. Thus, the answer is e.

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85

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\int$, B: $\Sigma$, C: $\neq$, D: $\approx$

D

Row 1 contains $\times$, $\neq$, $\Delta$, $\equiv$, $\int$, missing $\approx$. Column 6 contains $\equiv$, $\int$, $\div$, $\pm$, $\neq$, $\Sigma$, missing $\approx$. Thus, the answer is $\approx$.

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86

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\alpha$, B: $\textvarsigma$, C: $\eta$, D: $\phi$

D

Row 2 contains $\textvarsigma$, $\iota$, $\omicron$, $\psi$, $\tau$, missing $\phi$. Column 1 contains $\eta$, $\textvarsigma$, $\omega$, $\omicron$, $\psi$, $\tau$, $\alpha$, missing $\phi$. Thus, the answer is $\phi$.

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87

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\text{laughingface}$, B: $\text{joy}$, C: $\text{blush}$, D: $\text{smileface}$

B

Row 6 contains $\text{smileyface}$, $\text{grinningface}$, $\text{smileface}$, $\text{laughingface}$, missing $\text{joy}$. Column 1 contains $\text{blush}$, missing $\text{joy}$. Thus, the answer is $\text{joy}$.

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88

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\leftarrow$, B: $\rightarrow$, C: $\updownarrow$, D: $\nearrow$

C

Row 3 contains $\uparrow$, $\rightarrow$, $\downarrow$, $\nearrow$, $\nwarrow$, $\swarrow$, $\leftarrow$, $\leftrightarrow$, missing $\updownarrow$. Column 7 contains $\nwarrow$, $\leftarrow$, $\leftrightarrow$, $\rightarrow$, $\downarrow$, $\nearrow$, missing $\updownarrow$. Thus, the answer is $\updownarrow$.

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89

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: w, B: t, C: s, D: p

B

Row 6 contains v, p, w, s, missing t. Column 6 contains v, u, b, s, missing t. Thus, the answer is t.

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90

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\chi$, B: $\pi$, C: $\iota$, D: $\lambda$

B

Row 1 contains $\psi$, $\lambda$, $\iota$, missing $\pi$. Column 1 contains $\chi$, $\mu$, $\psi$, $\lambda$, $\iota$, missing $\pi$. Thus, the answer is $\pi$.

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91

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\blacklozenge$, B: $\triangleleft$, C: $\blacksquare$, D: o

C

Row 1 contains o, $\bullet$, $\blacklozenge$, $\triangleleft$, missing $\blacksquare$. Column 1 contains o, missing $\blacksquare$. Thus, the answer is $\blacksquare$.

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92

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: n, B: c, C: g, D: r

D

Row 3 contains a, n, missing r. Column 5 contains c, n, g, y, a, missing r. Thus, the answer is r.

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93

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: d, B: u, C: h, D: t

B

Row 3 contains h, j, d, t, missing u. Column 5 contains d, t, h, missing u. Thus, the answer is u.

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94

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\iota$, B: $\tau$, C: $\upsilon$, D: $\xi$

D

Row 8 contains $\tau$, $\upsilon$, $\iota$, $\chi$, $\eta$, $\epsilon$, $\nu$, missing $\xi$. Column 4 contains $\eta$, $\epsilon$, $\mu$, $\tau$, $\iota$, $\chi$, missing $\xi$. Thus, the answer is $\xi$.

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95

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 14, B: 3, C: 1, D: 12

C

Row 7 contains 7, 14, 12, 3, 2, 20, 13, 11, missing 1. Column 6 contains 14, 3, 13, missing 1. Thus, the answer is 1.

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96

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\lozenge$, B: $\bullet$, C: $\blacksquare$, D: $\triangleleft$

A

Row 5 contains $\bullet$, $\blacksquare$, missing $\lozenge$. Column 5 contains $\triangleleft$, $\bullet$, $\blacktriangle$, $\blacksquare$, missing $\lozenge$. Thus, the answer is $\lozenge$.

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97

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 13, B: 4, C: 18, D: 8

B

Row 3 contains 3, 8, 9, 18, 13, missing 4. Column 6 contains 13, 8, 9, missing 4. Thus, the answer is 4.

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98

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\text{sweatsmile}$, B: $\text{joy}$, C: $\text{smileface}$, D: $\text{laughingface}$

D

Row 3 contains $\text{sweatsmile}$, $\text{smileface}$, $\text{joy}$, missing $\text{laughingface}$. Column 2 contains $\text{joy}$, missing $\text{laughingface}$. Thus, the answer is $\text{laughingface}$.

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99

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\text{joy}$, B: $\text{grinningface}$, C: $\text{blush}$, D: $\text{sweatsmile}$

D

Row 6 contains $\text{joy}$, $\text{grinningface}$, missing $\text{sweatsmile}$. Column 4 contains $\text{blush}$, $\text{grinningface}$, $\text{smileyface}$, $\text{joy}$, $\text{beamingface}$, $\text{innocent}$, missing $\text{sweatsmile}$. Thus, the answer is $\text{sweatsmile}$.

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100

Deductive Reasoning Test with Figures

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Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\theta$, B: $\zeta$, C: $\sigma$, D: $\gamma$

B

Row 2 contains $\theta$, $\sigma$, $\mu$, $\gamma$, missing $\zeta$. Column 5 contains $\gamma$, $\sigma$, $\mu$, missing $\zeta$. Thus, the answer is $\zeta$.

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