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# If m and n are positive integers, and if p and q are

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If m and n are positive integers, and if p and q are [#permalink]  20 Dec 2003, 20:56
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If m and n are positive integers, and if p and q are different prime number, do p/q and n/m represent different number?

1. Neither n nor m is a prime number.

2. m is not divisible by q

>>> the correct answer is B >>>
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Joined: 12 Oct 2003
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PLEASE DO NOT INCLUDE THE CORRECT ANSWER IN THE ORIGINAL POST. It kills the fun. I saw an ans in some other post by you too, so ....

Quote:
If m and n are positive integers, and if p and q are different prime number, do p/q and n/m represent different number?

1. Neither n nor m is a prime number.

Case 1: p=2; q=3; n=4; m=6; p/q = n/m
Case 2 n=4; m=5; p/q <> n/m
So insufficient.

Quote:
2. m is not divisible by q

According to (1)Case 1 - we can prove that p/q=n/m. But for this to be true n & m need to be multiple of p & q respectively. Then only the division will lead to an equivalent number. But if, as stated in (2), m is not divisible by q, there is no way that you shall ever get p/q = n/m, because p & q are prime numbers and so the division result can be recreated only by their multiples.

So from 2 we conclude that p/q <> n/m and so it is sufficient.
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