For integers a, b and c, what would be the minimum and maximum values respectively of a + b + c if log|a| + log|b| + log|c| = 0? A. -3 and 3 B. -1 and 1 C. -1 and 3 D. 1 and 3

GATE 2018 · General Aptitude · Logarithms · medium

Answer: Minimum = -3, Maximum = 3. Answer: A. -3 and 3

1. Convert log sum to product condition: log(|a|*|b|*|c|) = 0 implies |a|*|b|*|c| = 10^0 = 1
2. Determine individual values from the integer constraint: The only factorisation of 1 into positive integers is 1*1*1, so |a| = |b| = |c| = 1, meaning each of a, b, c is either +1 or -1.
3. Find minimum and maximum sums: Maximum: all three = +1, so a + b + c = 3. Minimum: all three = -1, so a + b + c = -3.