We are given the set $$A=\{p, q, r, s, t\}$$; we need to check from the options that which of them is sufficient to find the standard deviation of set $$A$$

(A) S.D. of the set $$\{p+100, q+100, r+100, s+100, t+100\}$$ - is sufficient as if each term of a set of numbers is increased/decreased by a certain value, the standard deviation remains same. So, the standard deviation of the new set would be same as that of the original set.

(B) S.D. of the set $$\{100 \mathrm{p}, 100 \mathrm{q}, 100 \mathrm{r}, 100 \mathrm{~s}, 100 \mathrm{t}\}$$ - is sufficient as if each term of a set of numbers is multiplied by a certain value, the standard deviation also gets multiplied by the same number. For example if the standard deviation of the new set is $$x$$, the standard deviation of the original set should have been $$\mathrm{x} / 100$$.

(C) S.D. of the set $$\{p+100,2 q+100,3 r+100,4 s+100,5 t+100\}$-$ is insufficient to find the standard deviation of the original set as the increase in each term is not same.

(D) S.D. of the set $$\frac{p}{2}, \frac{q}{3}, \frac{r}{4}, \frac{s}{5}, \frac{t}{6}$$ - is insufficient to find the standard deviation of the original set as the increase in each term is not the same.

Hence only statements (A) \& (B) are sufficient, so are correct.