q: In how many ways can you seat 4 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
Options:
(A) 720
(B) 6
(C) 2880
(D) 5040
(E) 10080
a: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 1 chairs to sit. The remaining 3 people can sit in 3! ways. Thus the # of arrangements is 1*3! = 6. The answer is (B).
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q: There are 3 teams each with 6 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice?
Options:
(A) 50
(B) 23
(C) 108
(D) 28
(E) 45
a: There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 36 possibilities (6*6) since each team has 6 players. So there are a total of 108 possibilities (36*3). I hope this method is easier for you to understand. The answer is (C).
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q: Find the value of y from (12)^3 x 6^4÷432 = y?
Options:
(A) 5618
(B) 5232
(C) 5889
(D) 5184
(E) 5132
a: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62 The answer is (D).
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q: Amy, Bob, Cindy, and Daniel all have the same birthday, but they are all different ages. Today is their birthday. Cindy's age is divisible by Bob's age, and Amy's age is divisible by Cindy's age. If A is Amy's age in years, B is Bob's age, and C is Cindy's age, which of the following CANNOT be Daniel's age?
Options:
(A) AC/B
(B) (A+C) /B
(C) (A+B) /C
(D) AB/C
(E) (A-C) /B
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
Since today's is Daniel's birthday, his age must be an integer. As per the question, let A = 12, B = 2, and C = 6. Plugging these into the answer choices, only C does not yield an integer. The answer is (C).
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