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Algebra: Optimization of Integer Expression

XAT 2016 · Quantitative Ability & Data Interpretation · Hard · Quantitative Ability

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

  1. A.

    524

  2. B.

    693

  3. C.

    731

  4. D.

    970

  5. E.

    None of the above

Answer

C

Explanation

To maximize abc−(a+b+c)abc - (a+b+c), abcabc should be as large positive as possible, which requires two negative integers and one positive integer with maximum magnitudes. Choose a=−10,b=−9,c=8a = -10, b = -9, c = 8. abc=(−10)(−9)(8)=720abc = (-10)(-9)(8) = 720. a+b+c=−10−9+8=−11a + b + c = -10 - 9 + 8 = -11. abc−(a+b+c)=720−(−11)=731abc - (a+b+c) = 720 - (-11) = 731.

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