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.

Judging by

http://en.wikipedia.org/wiki/Even_and_odd_numbers negative integers can be classified as odd/even. So, our answer is insufficient.

E _________________

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