q: There are 3 teams each with 3 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) 27
(D) 28
(E) 45
a: Stream of consciousness: 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 9 possibilities (3*3) since each team has 3 players. So there are a total of 27 possibilities (9*3). I hope this method is easier for you to understand. The answer is (C).

question: The measure of the side of a square is doubled. If x represents the perimeter of the original square, what is the value of the new perimeter?
Options:
(A) 2x
(B) 4x
(C) 9x
(D) 12x
(E) 27x
answer: Stream of consciousness: Original perimeter = x
Hence original side = x/4
New side = 2x/4
New perimeter = 4*2x/4 = 2x The answer is (A).

q: A can do a piece of work in 16 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
Options:
(A) 18
(B) 77
(C) 66
(D) 55
(E) 12
a: Stream of consciousness: 8/16 + 6/x = 1
X = 12 days The answer is (E).

question: For some integer n, n^2 - 5 is divisible by all of the following EXCEPT
Options:
(A) 41
(B) 38
(C) 29
(D) 30
(E) 31
answer: Stream of consciousness: Hint: n^2-5 (n is an integer) is never multiple of 3 (try to prove this), hence 30 is out. The answer is (D).

q: A certain league has three divisions. The respective divisions had 8, 10, and 11 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?
Options:
(A) 51
(B) 52
(C) 54
(D) 56
(E) 57
a: Stream of consciousness: Overall, there can be 57 minuses. Tus, it is The answer is (E).

q: 10 men and 15 women together can complete a work in 8 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
Options:
(A) 127 days
(B) 667 days
(C) 177 days
(D) 187 days
(E) 600 days
a:
Stream of consciousness: 1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/8
15 women's 1 day work = (1/8 - 10/100) = 1/40
1 woman's 1 day work = 1/600
1 woman alone can complete the work in 600 days. The answer is (E).