Is M an even or odd integer?

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

Here we need to understand that multiplication of even with even no. is always even, even with odd no. is also even and odd with odd no. is always odd. Also addition of even with even no. is even, even with odd is odd and odd with odd is even. As per (1), 4m + 3m is even, so either 4m & 3m both are even or both are odd. since 4m is even so 3m is also even. For 3m to be even, m has to be even only. Hence (1) is sufficient. as per (2), 3m2 + 3m3 is even. We know that multiplication of even & even is even and also odd & odd is odd, so square or cube does not change the nature of an integer.

Here both the terms can be either even or odd. If m is even, then the expression becomes even. When m is odd, then also the expression becomes even (both the terms are odd), hence m can be even or odd. hence (2) is not sufficient.