q: In a race with 30 runners where 4 trophies will be given to the top 6 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?
Options:
(A) 8^8 ways
(B) 8^9 ways
(C) 6^4 ways
(D) 8^7 ways
(E) 8^6 ways
a: Stream of consciousness: 6 people can be prized with 4 distinct prizes in 6^4 ways The answer is (C).

question: If in the word 'DISTURBANCE', the first letter is interchanged with the last letter, the second letter is interchanged with the tenth letter and so on, which letter would come after the letter T in the newly formed word ?
Options:
(A) S
(B) C
(C) T
(D) R
(E) U
answer: Stream of consciousness: The new letter sequence is E C N A B R U T S I D
Clearly, S comes after T The answer is (A).

q: The average age of 6 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
Options:
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
a: Stream of consciousness: 20 + 24 + 6 * 2 = 56/2 = 28 The answer is (E).

question: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?
Options:
(A) 9 3/7 days
(B) 9 7/8 days
(C) 9 3/8 days
(D) 4 3/8 days
(E) 9 6/8 days
answer: Stream of consciousness: 1/15 + 1/25 = 8/75
75/8 = 9 3/8 days The answer is (C).

q: In e is a positive integer smaller than 200 and (14e)/60 is an integer, then e has how many different positive prime factors?
Options:
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
a: Stream of consciousness: 7e/30 tells us that e is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3. The answer is (B).

q: If 2^4, 2^3, and 11^3 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) 176
(B) 288
(C) 363
(D) 396
(E) 484
a:
Stream of consciousness: I will go with A (pending elements to match is 2^2*2^2*11^1 = 176 The answer is (A).