q: Elena's bread recipe calls for 3 ounces of butter for each 4 cups of flour used. She needs to make 4 times the original recipe. If 12 ounces of butter is used, then how many cups of flour are needed?
Options:
(A) 1
(B) 4
(C) 9
(D) 13
(E) 16
a: Number of cups flour needed for 3 ounces of butter = 4
Number of cups flour needed for 1 ounce of butter = 4/3
Number of cups flour needed for 12 ounces of butter = 4/3 * 12 = 16 The answer is (E).
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q: If x, y, and z are positive integers such that x is divisible by y, and y is divisible by z, which of the following is NOT necessarily an integer?
Options:
(A) xy/z
(B) (x + y) /z
(C) xz/y
(D) (x - y) /z
(E) (x + z) /y
a: As per the question, let x = 12, y = 6, and z = 2. Plugging these into the answer choices, only E does not yield an integer. The reason is that (x + z)/y = x/y + z/y, and while x/y must be an integer, z/y is only an integer if y = z. The answer is (E).
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q: For integers U and V, when U is divided by V, the remainder is Zero. Which of the following must be true?
Options:
(A) U and V share no common factors other than 1
(B) UV is odd.
(C) At least one of U and V is odd
(D) The sum U + V is odd
(E) U is odd
a: At least one of U and V is odd The answer is (C).
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q: How many seconds will a train 140 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
Options:
(A) 28 sec
(B) 29 sec
(C) 24 sec
(D) 25 sec
(E) 26 sec
a:
D = 140 + 150 = 290
S = 36 * 5/18 = 10 mps
T = 290/10 = 29 sec The answer is (B).
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