question: There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.
When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.
So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left.
Finally, they woke up the 7th thief and this time the diamonds were divided equally.
How many diamonds did they steal in total?
Options:
(A) 1961
(B) 1981
(C) 1991
(D) 1971
(E) None of the above
answer: Stream of consciousness: We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60. The answer is (B).


q: At what rate percent on simple interest will a sum of money double itself in 30 years?
Options:
(A) 3 1/9%
(B) 3 7/3%
(C) 7 1/3%
(D) 5 1/3%
(E) 1 1/3%
a: Stream of consciousness: P = (P*30*R)/100
R = 3 1/3% The answer is (A).


question: A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 5, which can be repeated. If the product of the digits in the area code must be odd, how many different codes can be created?
Options:
(A) 20
(B) 22
(C) 24
(D) 1
(E) 30
answer: Stream of consciousness: Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes only the product of 555 will be odd, the remaining 26 will have either 2 or 4 in them, which ensures that their product will be even. Therefore the number of codes where the product of the digits is even = (total) - (restriction) = 27 - 26 = 1. The answer is (D).


q: Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
Options:
(A) 3/140
(B) 1/28
(C) 3/56
(D) 3/35
(E) 7/40
a: Stream of consciousness: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*5/7 + 1/5*5/8*2/7 + 4/5*3/8*2/7 = 7/40. The answer is (E).


question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.160. Find the unknown rate of two blankets?
Options:
(A) 420
(B) 550
(C) 490
(D) 450
(E) 457
answer: Stream of consciousness: 10 * 160 = 1600
3 * 100 + 5 * 150 = 1050
1600 – 1050 = 550 The answer is (B).


question: If 1/2 of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 6 strokes ?
Options:
(A) 63/64
(B) 7/8
(C) 1/4
(D) 1/8
(E) 1/16
answer:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
Stream of consciousness: Left After 1st stroke = 1/2
Left After 2nd stroke = 1/2 * 1/2 = 1/4
Left After 3rd stroke = 1/2 * 1/4 = 1/8
Left After 4th stroke = 1/2 * 1/8 = 1/16
Left After 5th stroke = 1/2 * 1/16 = 1/32
Left After 6th stroke = 1/2 * 1/32 = 1/64
So removed = 1- 1/64 = 63/64 The answer is (A).