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: OK... I will go with A (pending elements to match is 2^2*2^2*11^1 = 176
The answer is (A).

q: The average of nine numbers is 17. The average of first four numbers is 20 and the average of last four numbers is 16. What is the middle number?
Options:
(A) A) 7
(B) B) 8
(C) C) 9
(D) D) 10
(E) E) 11
a: OK... The total of nine numbers = 9X17 = 153
The total of first 4 and last 4 numbers is = 4 X 20+4 X 16 = 144
So, the middle number is (153 - 144 ) = 9
The answer is (C).

q: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 101 players took part in that tournament. How many matches were played?
Options:
(A) 90 matches
(B) 95 matches
(C) 99 matches
(D) 100 matches
(E) 87 matches
a:

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
OK... D
100 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 100 matches were playe
The answer is (D).