Question

$\left(\frac{P}{Q}\right)+\left(\frac{R}{S}\right)=x$, where x is an integer. Find the individual values of P,Q,R,S.

1. P,Q,R,S are all prime numbers
2. Q=S, P+R=Q

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Answer 1

The correct option is D Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Using statement (1), we can get several prime numbers which satisfy the condition. We cannot arrive at an unique answer

Using statement (2), we can again get many cases. Hence, this statement also does not individually give an unique answer

Using both statements together, we are looking for an integral sum with prime numbers where Q=S and P+R=Q

One such possible case is $\frac{2}{5}+\frac{3}{5}$ = 1 (where A= 2 or 3 and C=2 or 3). Hence, unique values cannot be obtained. Answer is option (d)