If N is the least positive integer that is divisible by every integer from 3 to 10 inclusive, then N/7 is =
Options:
(A) 360
(B) 720
(C) 2520
(D) 3960
(E) 6720
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The integer should be divisible by: 3, 4, 5, 6, 7, 8, 9 and 10, that is 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5. The least common multiple of these integers is the product of 7, 5, 3^2 and 2^3. Then, N/7 is (7 * 5 * 3^2 * 2^3)/7 = 5*9*8 = 360. So the answer is: (A).
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A train 200 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
Options:
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
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S = (200 + 300)/45 = 500/45 * 18/5 = 40 So the answer is: (D).
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A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 4 days. In how many days can they complete the remaining work?
Options:
(A) 6 days
(B) 2/3 days
(C) 8 days
(D) 3 days
(E) 9 days
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Work done by A in 4 days = 4/5
Remaining work = 1/5
Work done by both A and B in one day = 1/5 + 1/10 = 3/10
Remaining work = 1/5 * 10/3 = 2/3 days. So the answer is: (B).
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