Question

p, q and r are three non - negative integers such that p + q + r = 10. The maximum value of pq+ qr + pr + pqr is

• A. $\ge$ 40 and < 50
• B. $\ge$ 50 and < 60
• C. $\ge$ 60 and < 70
• D. $\ge$ 70 and < 80

Answer 1

The correct option is C $\ge$ 60 and < 70

The product of p, q and r will be maximum if p, q and r are as symmetrical as possible. Therefore, the possible combination is (4, 3, 3).
Hence, maximum value of pq + qr + pr + pqr = 4 $\times$ 3 + 4 $\times$ 3 + 3 $\times$ 3 + 4 $\times$ 3 $\times$ 3 = 69. Hence, Option (c) is correct.