q: A certain league has five divisions. The respective divisions had 6, 7, 8, 9 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) 81
(B) 83
(C) 85
(D) 86
(E) 89
a: Stream of consciousness: Overall, there can be 81 minuses. Tus, it is The answer is (A).
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q: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much?
Look at this series: 95, 10, 75, 20, 55, ... What number should come next?
Options:
(A) 35
(B) 40
(C) 30
(D) 25
(E) 90
a: Stream of consciousness: C
30
This is an alternating addition and subtraction series. In the first pattern, 20 is subtracted from each number to arrive at the next. In the second, 10 is added to each number to arrive at the next. The answer is (C).
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q: Which of the following is equal to (x+2)!/x!?
Options:
(A) x-1
(B) 1+(1/x)
(C) 1
(D) x+1
(E) (x+1) (x+2)
a:
Stream of consciousness: (x + 1)! = (x + 1) (x+2)* x!
(x + 1)!/x! = (x + 1)(x+2) The answer is (E).
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