Rationale: 1 to 11 = 11 * 44 = 484
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 â€“ 484 = 122
The answer: (A)
Question: The average of 11 results is 44, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
(A) 122
(B) 156
(C) 118
(D) 125
(E) 123

Reasoning: The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot)
The probability that she misses every shot = (prob that she misses from 40 yards)*(prob that she misses from 50 yards)*(prob that she misses from 60 yards)
Prob that she misses from 40 yards = 1 - 4/5 = 1/5; Prob that she misses from 50 yards = 1 - 3/4 = 1/4; Prob that she misses from 60 yards = 1 - 2/3 = 1/3
Thus the probability that she misses all shots = (1/5)*(1/4)*(1/3) = 1/60
Thus the probability that she makes at least one shot = 1 - (1/60) = 59/60
Ans: (C)
Question: An archer is shooting arrows from various distances. She shoots at a target from 40 yards, 50 yards, and 60 yards. The probability that she hits within the bullseye from 40 yards is 4/5, the probability that she hits within the bullseye from 50 yards is 3/4, and the probability that she hits within the bullseye from 60 yards is 2/3. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed.
Options:
(A) 39/40
(B) 49/50
(C) 59/60
(D) 9/10
(E) 14/15

Rationale: Sum of all the 13 results = 13 * 20 = 260
Sum of the first 7 of them = 8 * 20 = 160
Sum of the last 7 of them = 8 * 40 = 320
So, the 8th number = 260 + 160 - 320 = 100.
The answer: (E)
Question: The average of 13 result is 20. Average of the first 8 of them is 20 and that of the last 8 is 40. Find the 8th result?
Options:
(A) 35
(B) 37
(C) 46
(D) 90
(E) 100

Reasoning: 3872 = 11*11*2*2*2*2*2
Required smallest number = 2
2 is the smallest number which should be divided with 3872 to make it a perfect square.
Ans: (C)
Question: Find the smallest number which should be divided with 3872 to make it a perfect square.
Options:
(A) 8
(B) 6
(C) 2
(D) 4
(E) 1

Rationale: Plug in an even integer; in this case 2
(3*2)-3 = 6-3 = 3 Odd
2+2^2 = 6 Even
(5*2)-3 = 10 - 3 = 7 Odd
(2*2)+1 = 4 + 1 = 5 Odd
(9*2)-5 = 18 - 5 = 13 Odd
The answer: (B)
Question: If x is an even integer, which of the following is an even integer?
Options:
(A) 3x-3
(B) x+x^2
(C) 5x-3
(D) 2x+1
(E) 9x-5

Rationale: 100 * 100 = 10000
120 * 80 = 9600
The answer: (B)

Question: The length of a rectangle is increased by 20% and its breadth is decreased by 20%. What is the effect on its area?
Options:
(A) 1288
(B) 9600
(C) 1000
(D) 10000
(E) 2887