q: For integers U and V, when U is divided by V, the remainder is even. Which of the following must be true?
Options:
(A) U is odd
(B) At least one of U and V is odd
(C) The sum U + V is odd
(D) U and V share no common factors other than 1
(E) UV is odd.
a: At least one of U and V is odd The answer is (B).
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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. 55 players took part in that tournament. How many matches were played?
Options:
(A) 90 matches
(B) 95 matches
(C) 99 matches
(D) 85 matches
(E) 87 matches
a: A 54 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 54 matches were played. The answer is (A).
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q: People standing in a straight line are wearing alternating colored shirts. The pattern of shirts begins with red, followed by green, blue, and yellow. This pattern continues (red, green, blue, and yellow) until it ends with a red shirt. If there are more than 4 people in line, which of the following cannot be the number of people in the line?
Options:
(A) 17
(B) 37
(C) 49
(D) 61
(E) 72
a: The correct answer should not take the form: 4x + 1. Hence, it is The answer is (E).
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q: People standing in a straight line are wearing alternating colored shirts. The pattern of shirts begins with red, followed by green, blue, white and yellow. This pattern continues (red, green, blue, white and yellow) until it ends with a blue shirt. If there are more than 5 people in line, which of the following cannot be the number of people in the line?
Options:
(A) 27
(B) 38
(C) 53
(D) 63
(E) 78
a:
The correct answer should not take the form: 5x + 3. Hence, it is The answer is (A).
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