Question

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

Accepted Answer

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

Algebra: Optimization of Integer Expression

Explanation

Practise this under exam conditions