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# If the quotient a/b positive, which of the following must be

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If the quotient a/b positive, which of the following must be [#permalink]  03 Sep 2012, 05:49
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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If the quotient a/b positive, which of the following must be true?

(A) a > 0
(B) b > 0
(C) ab > 0
(D) a-b > 0
(E) a+b > 0

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Re: If the quotient a/b positive, which of the following must be [#permalink]  03 Sep 2012, 05:49
SOLUTION

If the quotient a/b positive, which of the following must be true?

(A) a > 0
(B) b > 0
(C) ab > 0
(D) a-b > 0
(E) a+b > 0

\frac{a}{b}>0 means a and b have the same sign, either both are negative or both are positive. Thus, their product will also be positive: ab>0.

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Re: If the quotient a/b positive, which of the following must be [#permalink]  03 Sep 2012, 06:10
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a and be must have the same sign. Either both are positive or both are negative.

When multiplying a*b, the result will therefore be positive.

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Re: If the quotient a/b positive, which of the following must be [#permalink]  05 Sep 2012, 07:14
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I think the best approach in such questions is to plug in numbers Since the question asks about must be true then any numbers should qualify, if a/b is positive then a and b have the same sign so a*b must be positive. (C)
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Re: If the quotient a/b positive, which of the following must be [#permalink]  05 Sep 2012, 19:55
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a/b implies a and b have the same sign.

a<0 AND b<0

or

a>0 AND b>0

A. a>0 does not have to be true, a can be negative
B. b>0 does not have to be true, b can be negative
C. ab>0, has to be true since a AND b have the same sign
D. a-b>0 does not have to be true since a AND b can be negative and the result of a-b can be negative
E. a+b>0 does not have to be true since a AND b can be negative and the result of a+b can be negative

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Re: If the quotient a/b positive, which of the following must be [#permalink]  07 Sep 2012, 03:14
SOLUTION

If the quotient a/b positive, which of the following must be true?

(A) a > 0
(B) b > 0
(C) ab > 0
(D) a-b > 0
(E) a+b > 0

\frac{a}{b}>0 means a and b have the same sign, either both are negative or both are positive. Thus, their product will also be positive: ab>0.

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Re: If the quotient a/b positive, which of the following must be   [#permalink] 07 Sep 2012, 03:14
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