q: X can finish a work in 21 days. Y can finish the same work in 15 days. Y worked for 5 days and left the job. how many days does X alone need to finish the remaining work?
Options:
(A) 12
(B) 13
(C) 16
(D) 14
(E) 18
a: Work done by X in 1 day = 1/21
Work done by Y in 1 day = 1/15
Work done by Y in 5 days = 5/15 = 1/3
Remaining work = 1 1/3 = 2/3
Number of days in which X can finish the remaining work = (2/3) / (1/21) = 14 The answer is (D).
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q: A man rows his boat 105 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
(A) 5 kmph
(B) 7 kmph
(C) 12 kmph
(D) 8 kmph
(E) 1 kmph
a: Speed downstream = d/t = 105/(2 1/2) = 42 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (42 - 18)/2 = 12 kmph The answer is (C).
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q: A train 500 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
Options:
(A) 32
(B) 28
(C) 49
(D) 64
(E) 21
a: S = (500 + 300)/45 = 800/45 * 18/5 = 64 The answer is (D).
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q: During a particular baseball game, the probability of a team's pitcher throwing a strike on each throw is 2/5. What is the least number of times that the pitcher should pitch the ball that will increase the probability of getting a strike at least once to more than 50%.
Options:
(A) 3
(B) 2
(C) 1
(D) 4
(E) 5
a:
Rule of Subtraction: P(A) = 1 - P(A')
Rule of Multiplication: P(A B) = P(A) P(B)
The probability that the pitcher throws a strike at least once in 2 guesses is 1- (3/5)^2 = 1 - 9/25 = 16/25 > 50%. The answer is (B).
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