Discussion
For integers \(a\), \(b\) and \(c\), what would be the minimum and maximum values respectively of \(a + b + c\) if \(\log|a| + \log|b| + \log|c| = 0\)?
Answer: A
The minimum and maximum are -3 and 3.
\(\log|a| + \log|b| + \log|c| = \log|abc| = 0\), so \(|abc| = 1\). For integers this forces |a| = |b| = |c| = 1, so each of a, b and c is +1 or -1.
The sum is smallest when all three are -1, giving -3, and largest when all three are +1, giving 3. The other options leave out these extremes: -1 and 1 are sums with mixed signs, and 1 and 3 ignores that the values can be negative, since the logarithm is taken of the absolute value.
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