Given that:
- group X has 6 students
- group X has 3 boys
- group X has 3 girls
- all boys in X are j years old
- all girls in X are k years old

Group Y has 4 students
- group Y has 1 boy
- group Y has 3 girls
- all boys in group Y are j years old
- all girls in group Y are k years old

Target question => What is the variance of the ages in group Y?

Statement 1 => The standard deviation of X is 0
Standard deviation can only be 0 only if all the data/values are identical
Therefore j = k
For group Y with 4 students and j = k
Assuming j = 2
$$mean=\frac{2+2+2+2}{4}=\frac{8}{4}=2$$
$$variance\ =\frac{\left(data\ value-mean\right)^2}{data\ set}$$
$$=\frac{\left(2-2\right)^2}{4}=\frac{0^2}{4}=\frac{0}{4}=0$$
So variance = 0 when standard deviation = 0 and data values are identical. Statement 1 is SUFFICIENT

Statement 2 => j = k
data value are identical variance will be = 0. This is the same as statement 1 hence, statement 2 IS SUFFICIENT

Since each statement alone IS SUFFICIENT,
Answer = D