question: If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)?
Options:
(A) -f(x)
(B) f(x)
(C) 2*f(x)
(D) 1/f(x)
(E) 2/f(x)
answer: Stream of consciousness: If x = 2 then f(x) = 8/15 and f(1/x) = -8/15 which is equal to -f(x) The answer is (A).
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question: The speed of a boat in still water is 70kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
(A) 22 kmph
(B) 40 kmph
(C) 78 kmph
(D) 50 kmph
(E) 23 kmph
answer: Stream of consciousness: Speed downstream = 70 + 20 = 90 kmph
Speed upstream = 70 - 20 = 50 kmph The answer is (D).
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question: In a bucket there are 3 blue balls and 2 red balls. What is the probability of drawing at least one blue ball when drawing two consecutive balls randomly?
Options:
(A) 9/10
(B) 16/20
(C) 2/5
(D) 3/5
(E)
answer: Stream of consciousness: P(at least one blue) = 1 - P(no blue, so 2 red) = 1- 2/5*1/4 = 9/10. The answer is (A).
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question: In a race of 600 metres, A can beat B by 60 metres and in a race of 500 metres, B can beat C by 50 metres. By how many metres will A beat C in a race of 400 metres?
Options:
(A) 76 metres
(B) 80 metres
(C) 70 metres
(D) 84 metres
(E) None
answer:
Stream of consciousness: A runs B runs C runs
600 metres race 600m 540 m
500 metres race 500 m 450m
Combing ratio A runs B runs C runs
300metres - 2700meters - 2430metres
Unitary A runs B runs C runs
Method 400mtres - 360 metres - 324 metres
? A beats C by 400-324 = 76 metres. The answer is (A).
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