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.

A, B, and C are all sufficient to find the SD of the original set.

The official answer to this question needs to be updated. Options A, B, and C are all sufficient to determine the SD of Set A.