question: How many distinct prime numbers are factors of 33150?
Options:
(A) Four
(B) Five
(C) Six
(D) Seven
(E) Eight
answer: Stream of consciousness: Start with the prime factorization:
33150 = 50*663 = (2*5*5)*3*221 = (2)*(3)*(5^2)*(13)*(17)
There are five distinct prime factors, {2, 3, 5, 13, and 17} The answer is (B).

q: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Options:
(A) 19 1/7 min
(B) 15 1/7 min
(C) 17 1/7 min
(D) 7 1/7 min
(E) 7 2/7 min
a: Stream of consciousness: 1/20 + 1/30 - 1/40 = 7/120
120/7 = 17 1/7 The answer is (C).

question: If P(A) = 2/15, P(B) = 4/15, and P(A B) = 12/15 Find P(B|A)
Options:
(A) 1/2
(B) 2/3
(C) 3/2
(D) 4/5
(E) 6
answer: Stream of consciousness: P(B|A) = P(A B)/P(A)
P(B|A) = (12/15)/(2/15) = 6. The answer is (E).

q: If x is a positive odd integer and y is a negative even integer, which of the following must be true?
Options:
(A) x^3 + y is a positive odd integer
(B) x^2 + y^2 is a negative odd integer
(C) x^0 + y^11 is a negative odd integer
(D) x + y is a positive odd integer
(E) x + y is a negative odd integer
a: Stream of consciousness: Anything power 0 is always 1 and given that Y is even and negative, then
1 + (-2) will be negative with odd power values for Y. The answer is (C).

question: What approximate value should come in place of question mark (?) in the following equation
287.532 + 1894.029 657.48 = 643.095 + ?
Options:
(A) 870
(B) 790
(C) 880
(D) 770
(E) 890
answer: Stream of consciousness: ? = 285 + 1895 655 645 or, ? = 880 The answer is (C).

question: Twenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $5 million from its orange exports, how much money does it generate from its yearly total of exports?
Options:
(A) $21.25m
(B) $25.5m
(C) $106.25m
(D) $127.5m
(E) $150m
answer:
Stream of consciousness: 2/10*1/6*(total) = 5
1/30*(total) = 5
(total) = 5*30 = 150 The answer is (E).