Question 14

a, b, c are integers, |a| ≠ |b| ≠|c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc - (a + b + c)]?

Solution

|a| ≠ |b| ≠|c| and -10 ≤ a, b, c ≤ 10

Expression : $$[abc - (a + b + c)]$$

For maximum value, two of a,b and c should be negative, as all three negative will make abc negative.

Thus, max value will occur if $$a = -10 , b = -9 , c = 8$$

=> Max value = $$[(-10 \times -9 \times 8) - (-10 -9 + 8)]$$

= $$720 + 11 = 731$$

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