a and b are integers such that a*b # 0. Is |a|/|b| = a/b?

Question

a and b are integers such that ab ≠ 0. Is |a|/|b| = a/b?

(1) |ab| = ab
(2) |a|/|b| = |a/b|

GMATNinja · Answer

First, let's figure out what the question is really asking. The left side of the equation is always positive, so the answer to the question is "yes" if both variables are positive or if both variables are negative. The answer is "no" if the two variables have different signs.

So the restated question is: "do a and b have the same sign?"

Statement 1: again, the left side of the equation is always positive, and this statement is true whenever the variables a & b have the same sign. It answers the question perfectly. -- sufficient

Statement 2: this statement is always true for nonzero values of ab. We could have any combination of positives and negatives, and this equation would still be true. So a & b could both be positive, they could both be negative, or we could have one positive and one negative. -- not sufficient

The answer is A.

Bounce1987 · Answer

is the left side of the equation always positive or always non-negative?

Bunuel · Answer

Generally absolute value of a number is non-negative, so it's positive or 0 but here we are given that ab ≠ 0, which implies that neither of the variables is 0, so in this cases |a|/|b| is positive only.

Hope it's clear.

a and b are integers such that a*b # 0. Is |a|/|b| = a/b?

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