Question: Which one of the following is the least number of four digits divisible by 71?
Options:
(A) 1006
(B) 1065
(C) 1094
(D) 1056
(E) 1057
Answer: 1000/71 = 14 6/71
1000 + 71 6 = 1065
The answer is (B).

Question: If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)?
Options:
(A) -f(x)
(B) f(x)
(C) 2*f(x)
(D) 1/f(x)
(E) 2/f(x)
Answer: If x = 2 then f(x) = 8/15 and f(1/x) = -8/15 which is equal to -f(x)
The answer is (A).

Question: a, b, c, and d are positive integers where a is divisible by b and c is divisible by d. Which of the following is NOT necessarily an integer?
Options:
(A) (ac) /(bd)
(B) a/b + c/d
(C) (a + c) /(b + d)
(D) (abc) /d
(E) (acd) /b
Answer: As per the question, let a = 10, b = 5, c = 6, and d = 2. Plugging these into the answer choices, only C does not yield an integer.
The answer is (C).

Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
Options:
(A) 92/37
(B) 33/91
(C) 71/28
(D) 91/42
(E) 91/33
Answer:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = C/C = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91
The answer is (B).