question: The number N is 5,2H4, where H represents the ten's digit. If N is divisible by 3, what is the value of H?
Options:
(A) 2
(B) 3
(C) 5
(D) 4
(E) 9
answer: Stream of consciousness: Integer is divisible by 3 - Sum of digits is divisible by 3 The answer is (D).
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question: If a man can cover 18 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
(A) 243 km
(B) 162 km
(C) 1767 km
(D) 1887 km
(E) 177 km
answer: Stream of consciousness: 18 m/s = 18 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 18 * 18/5 * 15/4 km = 243 km. The answer is (A).
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question: In b is a positive integer smaller than 200 and (14b)/60 is an integer, then b has how many different positive prime factors?
Options:
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
answer: Stream of consciousness: 7b/30 tells us that b is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3. The answer is (B).
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question: If A takes x days to do a work then B takes 2x days to do the same work then with in how many day's A will alone complete this work ?
Options:
(A) 27
(B) 23
(C) 24
(D) 25
(E) 26
answer:
Stream of consciousness: 1/x+1/2x = 1/18 = > 3/2x = 1/18 = > x = 27 days. Hence, A alone can finish the work in 27 days. The answer is (A).
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