ichha148 wrote:

If \(M\) and \(N\) are integers, is \(\frac{10^M + N}{3}\) an integer?

1. \(N = 5\)

2. \(MN\) is even

(C) 2008 GMAT Club - m25#7

The question is: (10^m + n)/3= k? where k is an integer.

1. N = 5 is not suff. If m is a +ve integer, k is always an integer.

If m is a -ve integer, k is always a -ve integer. NSF.

2. MN = 2p where p is an integer. In this case, either m or n is even (either -ve or +ve or 0) integer.

If m = 1 and n = 2, k is an integer.

If m = -1 and n = 2, k is not an integer.

If m = 2 and n = 1, k is not an integer.

NSF....

1 and 2: m is even, and n is 5.

When m is -ve even and n = 5, k never be an integer.

When m is +ve even and n = 5, k is always an integer. Still NSF.

E.

ichha148 wrote:

MN is even in 2nd and N =5 , so that means M can not be 0 or -ve , infact M needs to be even , so MN can be even i.e. M can be 2 , 4 ,6 etc .

now any even value of 10^ M + 5 is divisible by 3 and I am getting C , however that is not mentioned as correct answer , can some one please point out my mistake or solve this question

In st 2: Either m or n is even or both can be even. That includes 0 or -ve integers.

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