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.