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Re: is it an integer? [#permalink]
06 Aug 2009, 21:59

1

This post received KUDOS

A

Statement 1: if u take N=5 and any value for M it will always hold true that is (10^M + N)/3 an integer; becoz 10^M ( let M = any value) will always leave a reminder of 1....and 1+5 = 6 which is divisable by 3 ....sufficient

Statement 2 : if MN is even ...this means (M,N) can be both even or odd (except both being odd at a time)....if taken an example....

Re: is it an integer? [#permalink]
06 Aug 2009, 22:13

1

This post received KUDOS

Expert's post

Let's consider 10^M

at M>=0: 10^M = {1, 10, 100, 1000....} or 3k+1 at M<0: 10^M is a fraction and our expression is not an integer.

Now, let's see our statements:

1) N=5 at M>=0: (3k+1 + 5) /3 = k+2 - an integer at M<0: a fraction. insufficient

2) MN is even a) at M=2, N=5 our expression is an integer b) at M=-2, N=-5 our expression in a fraction insufficient

1)&2) N=5 & MN is even --> N=5, M is even For all even M>=0 we will get an integer. Now we have interesting question: Could negative numbers be even or odd? if yes, we can choose M=-2, N=5 and get a fraction. if no, M cannot be negative and two statements are sufficient.

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