Statement 1: when x is divided by 12, the remainder is 6
given that
$$x=12q+6$$
$$x=6\left(2q+1\right)$$
$$x=2\cdot3\left(2q+1\right)$$
(2q+1) is an odd number, the power of 2 in x will be odd, thus ,x, cannot be a perfect square. Statement 1 is SUFFICIENT

Statement 2: when x is divided by 14, the remainder is 2
Given that x=14p+2. So, x could be 2, 16, 30, ... etc. So, it is not certain that x is a perfect square.

Hence, statement 2 is NOT SUFFICIENT

Answer is Option A because STATEMENT 1 ALONE IS SUFFICIENT and STATEMENT 2 ALONE IS NOT SUFFICIENT