If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p + q)(r +…
If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p + q)(r + s)?
230
225
224
221
Solution
To maximize the product of two sums using four distinct single-digit positive numbers, use the largest digits 9, 8, 7, 6. The total $9 + 8 + 7 + 6 = 30$ is split into two sums; the product is maximized when the sums are as equal as possible: $15 \times 15$. Pair $(9+6) = 15$ and $(8+7) = 15$, giving $15 \times 15 = 225$.