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

1. A. 230
2. B. 225
3. C. 224
4. D. 221

Answer: B

Explanation

To maximize the product of two sums, (p+q)(r+s), where p, q, r, s are distinct single-digit positive numbers, we should select the largest available distinct single-digit positive numbers. These are 1, 2, 3, 4, 5, 6, 7, 8, 9. The four largest distinct single-digit positive numbers are 9, 8, 7, and 6.
Next, to maximize the product of two factors, the factors should be as close to each other in value as possible. We need to group these four numbers into two pairs such that their sums are nearly equal.
Possible groupings and sums:
1. (9+8) = 17, (7+6) = 13. Product = 17 × 13 = 221.
2. (9+7) = 16, (8+6) = 14. Product = 16 × 14 = 224.
3. (9+6) = 15, (8+7) = 15. Product = 15 × 15 = 225.
Comparing these products, the greatest value is 225.