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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: \(ab>0\).

Re: If the quotient a/b positive, which of the following must be [#permalink]

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05 Sep 2012, 06:14

1

This post received KUDOS

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]

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05 Sep 2012, 18:55

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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

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: \(ab>0\).

Answer: C.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: If the quotient a/b positive, which of the following must be [#permalink]

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14 Jun 2013, 18:23

Hi Bunuel, what if a=0;b=2. we have a/b as positive as a result ab = 0. C fails.(:D is this some kind of miss in the question or Am i missing my basics here)

Tx

Bunuel wrote:

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: \(ab>0\).

Answer: C.

Kudos points given to everyone with correct solution. Let me know if I missed someone.

Hi Bunuel, what if a=0;b=2. we have a/b as positive as a result ab = 0. C fails.(:D is this some kind of miss in the question or Am i missing my basics here)

Tx

Bunuel wrote:

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: \(ab>0\).

Answer: C.

Kudos points given to everyone with correct solution. Let me know if I missed someone.

If a=0 and b=2, then a/b=0. 0 is neither positive nor negative.

Re: If the quotient a/b positive, which of the following must be [#permalink]

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29 Jun 2014, 05:28

Hello from the GMAT Club BumpBot!

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Re: If the quotient a/b positive, which of the following must be [#permalink]

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26 Aug 2015, 04:23

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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09 May 2016, 12:35

\(\frac{a}{b}\) is positive means \(\frac{a}{b}\) > 0

This means that both a and b are either negative or both a and b are positive So quotient \(\frac{a}{b}\) will always be positive ab > 0 correct answer - C

Re: If the quotient a/b positive, which of the following must be [#permalink]

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10 May 2016, 06:26

Bunuel wrote:

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

We are given that a divided by b is positive (or greater than zero). We know that in division when a quotient is positive, the two numbers being divided are either both negative or both positive.

This is also the case in multiplication; that is, to get a product that is positive, we must multiply two positive numbers or two negative numbers. Thus the only answer choice that MUST be positive is C, ab > 0.
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