# Q. If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p + q)(r+s)?

(a) 230

(b) 225

(c) 224

(d) 221

Correct Answer: (b) 225

#### Question from UPSC Prelims 2023 CSAT

**Explanation : **

## Greatest Value of Expression (p + q)(r+s)

The greatest value of (p + q)(r + s) will be achieved when p, q, r, and s are the largest distinct single digit positive numbers.

The largest distinct single digit positive numbers are 9, 8, 7 and 6.

So, the greatest value of (p + q)(r + s) is (9 + 8)(7 + 6) = 17 * 13 = 221.

However, if we rearrange the numbers as (9 + 7)(8 + 6), we get a larger value: 16 * 14 = 224.

But, the largest value is obtained when we rearrange the numbers as (9 + 6)(8 + 7) = 15 * 15 = 225.

So, the correct answer is (b) 225.