q: If 2^4, 3^3, and 13^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?
Options:
(A) 198
(B) 288
(C) 363
(D) 396
(E) 468
a: Stream of consciousness: I will go with E (pending elements to match is 2^2*3^2*13^1 = 468 The answer is (E).

question: Four of the five parts numbered as (a), (b), (c), (d) and (e)in the following equations are exactly equal. You have to find out the part that is not equal to the other parts. The number of that part is the answer.
Options:
(A) a2 + 5ab + 6b2
(B) (a + 3b) (a + 2b)
(C) a(a + 3b) + 2b(a + 3b)
(D) (3a + b) (a + 2b)
(E) a(a + 2b) + 3b(a + 2b)
answer: Stream of consciousness: The other parts are equal to a2 + 5ab + 6b2. The answer is (D).

q: What is the area of a square with perimeter 2P ?
Options:
(A) 16p^2
(B) 4P
(C) P^2/5
(D) P/16
(E) P^2/4
a: Stream of consciousness: Each side is p/2
A = (p/2)^2 = (p^2)/4 The answer is (E).

question: If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K 4 and 5K + 1 is 63, what is the value of K?
Options:
(A) 22 10/11
(B) 15 3/4
(C) 22
(D) 23
(E) 25 3/10
answer: Stream of consciousness: K + 2K +3 + 3K - 4 + 5K +1 = 11K
(11K -1)/4 = 63
11K = 63 * 4 = 252
K = 252 / 11 = 22 10/11 The answer is (A).

q: A small company employs 3 men and 4 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
Options:
(A) 1/14
(B) 1/7
(C) 20/70
(D) 18/70
(E) 1/2
a: Stream of consciousness: Total ways to choose 4 employees from 8 employees = 8C4
Two women = 4C2
Two Men = 3C2
P = (5C2 * 3C2)/8C2 = 18/70 hence The answer is (D).

q: A fair coin is tossed repeatedly. If head appears on the first four tosses, then the probability of appearance of tail on the fifth toss is.
Options:
(A) 1/7
(B) 1/2
(C) 3/7
(D) 2/3
(E) 1/3
a:
Stream of consciousness: Since the coin is a fair coin, every toss is independent of any other toss. Hence, the probability of appearance of tail on the fifth toss is = 1/2 The answer is (B).