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lvb9th
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E...with Paul providing so many examples...need anyone say more.

Vivek.
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anandnk
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a) 4 * a/b is an integer. if a/b = 0.25 4*a/b = 1 which is an integer but a/b is not an integer. If a/b = 1 then 4*a/b = 4 which is an integer.
So Insufficient.

b) if 4 *b/a is an integer then fractional part of b/a could be 0.5 or 0.25
for example 2.5 *4 = 10 but 1/2.5 is not an integer

combine both of them
a/b = 0.25 and b/a = 4 or a/b = 1 or b/a = 1
So cannot be determined.
Answer is E.
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lvb9th
Is a/b an ineger?

(1) 4a/b is an ineger
(2) 4b/a is an integer


Is a = 0 (mod b) ?

(1) 4a = 0 (mod b)
(2) 4b = 0 (mod a)

1. 4a = 0 (mod b)
2a = 0 (mod b/2) or a = 0 (mod b/4)
We dont know whether b is multiple of 2 or of 4.

2. 4b = 0 (a)
2b = 0 (mod a/2) or b = 0 (mod a/4)
We dont know about a either.

Combining (1) and (2): (2) does not tell whether b is a multiple of 2 or of 4.

Answer is E.



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