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

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

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New post 24 Nov 2012, 08:56
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62% (00:56) correct 38% (00:43) wrong based on 80 sessions

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

(1) |ab| = ab
(2) |a|/|b| = |a/b|
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Re: a and b are integers such that a*b # 0. Is |a|/|b| = a/b? [#permalink]

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New post 24 Nov 2012, 09:21
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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.
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Re: a and b are integers such that a*b # 0. Is |a|/|b| = a/b? [#permalink]

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New post 14 Aug 2017, 00:44
is the left side of the equation always positive or always non-negative?
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Re: a and b are integers such that a*b # 0. Is |a|/|b| = a/b? [#permalink]

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New post 14 Aug 2017, 01:02
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Bounce1987 wrote:
is the left side of the equation always positive or always non-negative?


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.
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Re: a and b are integers such that a*b # 0. Is |a|/|b| = a/b?   [#permalink] 14 Aug 2017, 01:02
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