q: K-numbers are positive integers with only 2's as their digits. For example, 2, 22, and 222 are K-numbers. The K-weight of a number n is the minimum number of K-numbers that must be added together to equal n. For example, the K-weight of 50 is 5, because 50 = 22 + 22 + 2 + 2 + 2. What is the K-weight of 650?
Options:
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
a: 650 = 2*222 + (22*9) + 4*2
K weight of 600 = 2 +9+2 = 13 The answer is (D).
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q: Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 1/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
Options:
(A) 3/140
(B) 1/280
(C) 27/280
(D) 3/35
(E) 7/56
a: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*1/8*5/7 + 1/5*7/8*2/7 + 4/5*1/8*2/7 = 27/280. The answer is (C).
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q: A train 150 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform?
Options:
(A) 33
(B) 87
(C) 350
(D) 88
(E) 277
a: D = 72 * 5/18 = 25 = 500 150 = 350 The answer is (C).
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q: Right triangle ABC is the base of the prism in the figure above. If AB=AC=2 and the height of the prism is 3, what is the volume of the prism?
Options:
(A) 1
(B) 3/2
(C) 2
(D) 3
(E) 6
a:
Volume of prism = Area of base * height = 1/2* (square root of 2) * (square root of 2)*3 = 3 The answer is (D).
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