question: A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
Options:
(A) 2 1/0
(B) 2 1/8
(C) 2 1/5
(D) 2 1/3
(E) 2 1/2
answer: Stream of consciousness: Required time = (5 1/4)/3 + (5 1/4)/7 = 2 1/2 hours. The answer is (E).
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question: If x is a positive integer, which of the following could NOT be the square of x?
Options:
(A) 5,008,644
(B) 5,004,169
(C) 4,999,696
(D) 4,995,225
(E) 4,990,752
answer: Stream of consciousness: A perfect square will never end in 2, 3, 7 or 8. (last digit cannot be 2, 3, 7 or 8)
Here E is the odd one out. The answer is (E).
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question: From among the 38 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
Options:
(A) 1360
(B) 1260
(C) 1060
(D) 1160
(E) 1406
answer: Stream of consciousness: There are 38 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 38 ways. When one person is appointed as leader, we are left with 35 students. Out of these 37 teachers, we can select one class representative. So, a class representative can be selected in 37 ways. Hence, the number of ways in which a leader and class representative can be selected = 38 x 37 = 1406 The answer is (E).
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question: Find the mean proportional between 25 & 36?
Options:
(A) A) 59
(B) B) 30
(C) C) 63
(D) D) 65
(E) E) 67
answer:
Stream of consciousness: Formula = ab
A = 25 and B = 36
2536 = 5 6 = 30 The answer is (B).
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