XAT 2016QA & DI Question 19

Inequality Maximization / MinimizationEasy

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)]?

Answer & solution

  • A

    524

  • B

    693

  • 731

  • D

    970

  • E

    None of the above

Solution

abc – (a + b + c) = a(bc – 1) – b – c .

It is clear that the expression would be maximum when b and c are negative and their modulus are maximum possible.

∴ b = –10 , c = –9.

Now a has to be positive and maximum possible. It has to be 8.

Hence the expression becomes equal to 731.

Hence, option (c).

XAT 2016 QA & DI Q19: a, b, c are integers, |a| ≠ |b| ≠ |c| and –10 ≤ a, b, c ≤ 10. What will be the maximum possi — Solution | TheCATExam