Reasoning: On the first three flips, you must get heads. Whats the probability of getting heads ? Its 1/2
So for the first three flips, your probability is (1/2)^3 = 1/8
Now for the last two, you want to get tails only. Whats the prob of getting tails ? Well, its the same as prob of getting a heads, namely, 1/2
For the last two flips, your probability is (1/2)^2 = 1/4
So your overall probability for the event in question is 1/8*1/4 = 1/32
Ans: (E)
Question: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?
Options:
(A) 3/5
(B) 1/2
(C) 1/5
(D) 1/8
(E) 1/32

Rationale: 5 people can be prized with 3 distinct prizes in 5^3 ways
The answer: (A)
Question: In a race with 30 runners where 3 trophies will be given to the top 5 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?
Options:
(A) 5^3 ways
(B) 8^9 ways
(C) 7^8 ways
(D) 8^7 ways
(E) 8^6 ways

Reasoning: Average of the first 'n' natural numbers = (n + 1)/2
We get (41 + 1)/2 = 21
Ans: (E)
Question: Find the average of the first 41 natural numbers?
Options:
(A) 8
(B) 9
(C) 10
(D) 11
(E) 21

Rationale: Increase = (10/50)*100 = (1/5)*100 = 20%.
The answer: (E)
Question: John makes $50 a week from his job. He earns a raise and now makes $60 a week. What is the % increase?
Options:
(A) 16%
(B) 16.66%
(C) 17.9%
(D) 18.12%
(E) 20%

Reasoning: 8C4 [Select any four] - 7C4 [Select all hard backs] = 35.
Ans: (A)
Question: There are 8 books in a shelf that consist of 1 paperback books and 7 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
Options:
(A) 35
(B) 45
(C) 50
(D) 55
(E) 60

Reasoning: Population after n years = P [1 + (R/100)]2
Population after 2 years = 110000 * [1 + 6/100]2 = (110000 x 53/50 x 53/50) = 123596
Ans: (A)

Question: he population of a city is 110,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?
Options:
(A) 123596
(B) 1237723
(C) 123776
(D) 123728
(E) 123718