If the quotient a/b positive, which of the following must be : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 22 Jan 2017, 04:38

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 36596
Followers: 7093

Kudos [?]: 93419 [0], given: 10563

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

### Show Tags

03 Sep 2012, 04:49
Expert's post
7
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

84% (01:29) correct 16% (00:41) wrong based on 843 sessions

### HideShow timer Statistics

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

Practice Questions
Question: 32
Page: 156
Difficulty: 550
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36596
Followers: 7093

Kudos [?]: 93419 [0], given: 10563

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

### Show Tags

03 Sep 2012, 04:49
Expert's post
2
This post was
BOOKMARKED
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: $$ab>0$$.

_________________
Intern
Joined: 28 Aug 2012
Posts: 46
Location: Austria
GMAT 1: 770 Q51 V42
Followers: 3

Kudos [?]: 43 [1] , given: 3

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

### Show Tags

03 Sep 2012, 05:10
1
KUDOS
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.

Manager
Joined: 28 Feb 2012
Posts: 115
GPA: 3.9
WE: Marketing (Other)
Followers: 0

Kudos [?]: 42 [1] , given: 17

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

### Show Tags

05 Sep 2012, 06:14
1
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)
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Intern
Joined: 30 Apr 2010
Posts: 21
Followers: 0

Kudos [?]: 16 [4] , given: 2

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

### Show Tags

05 Sep 2012, 18:55
4
KUDOS
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

Math Expert
Joined: 02 Sep 2009
Posts: 36596
Followers: 7093

Kudos [?]: 93419 [0], given: 10563

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

### Show Tags

07 Sep 2012, 02:14
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: $$ab>0$$.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
_________________
Intern
Joined: 28 Aug 2012
Posts: 6
Followers: 0

Kudos [?]: 0 [0], given: 14

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

### Show Tags

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: $$ab>0$$.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
Math Expert
Joined: 02 Sep 2009
Posts: 36596
Followers: 7093

Kudos [?]: 93419 [0], given: 10563

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

### Show Tags

14 Jun 2013, 23:56
p111 wrote:
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: $$ab>0$$.

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.

For more check here: math-number-theory-88376.html#p666609

Hope it helps.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13497
Followers: 577

Kudos [?]: 163 [0], given: 0

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

### Show Tags

29 Jun 2014, 05:28
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 47

Kudos [?]: 1935 [0], given: 193

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

### Show Tags

10 Jul 2014, 01:35
For $$\frac{a}{b} > 0$$, I took help of numbers:

$$\frac{6}{3} = 2 & \frac{-6}{-3} = 2$$

Checking all options:

A: a>0 ............ Fail for a = -6; b = -3

B: b>0 ............... Fail for a = -6; b = -3

C: ab>0 ................ OK for both (6*3 = 18 & -6 * -3 = 18)

D: a-b > 0 ........... Fail for a = -6; b = -3

E: a+b > 0 ........... Fail for a = -6; b = -3

_________________

Kindly press "+1 Kudos" to appreciate

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13497
Followers: 577

Kudos [?]: 163 [0], given: 0

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

### Show Tags

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Director
Joined: 24 Nov 2015
Posts: 564
Location: United States (LA)
Concentration: General Management, Marketing
GMAT 1: 700 Q49 V36
GRE 1: 328 Q167 V161
Followers: 11

Kudos [?]: 25 [0], given: 222

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

### Show Tags

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
Senior Manager
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 464
Followers: 22

Kudos [?]: 193 [0], given: 2

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

### Show Tags

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.
_________________

Jeffrey Miller
Jeffrey Miller

Manager
Joined: 11 Jul 2016
Posts: 86
Followers: 0

Kudos [?]: 10 [0], given: 83

### Show Tags

04 Sep 2016, 07:47

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

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

Regards,
MoM
BSchool Forum Moderator
Joined: 18 Jul 2015
Posts: 951
Location: India
GMAT 1: 670 Q50 V32
GMAT 2: 700 Q50 V34
GPA: 3.65
WE: Brand Management (Health Care)
Followers: 25

Kudos [?]: 235 [0], given: 33

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

### Show Tags

04 Sep 2016, 09:21
Manonamission wrote:

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

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

Regards,
MoM

a/b positive means both a and b MUST of same sign. Hence, ab>0. Answer is C
_________________

Thanks.

Re: If the quotient a/b positive, which of the following must be   [#permalink] 04 Sep 2016, 09:21
Similar topics Replies Last post
Similar
Topics:
If |ab| > ab, which of the following must be true? 2 19 Jan 2017, 19:22
2 If ab > 0, which of the following must be negative? 7 25 Jun 2015, 02:30
24 |a|=|b|, which of the following must be true : 14 28 Oct 2012, 11:06
81 If x and y are positive, which of the following must be 34 13 Oct 2009, 11:10
84 If x and y are positive, which of the following must be 46 08 Aug 2009, 06:57
Display posts from previous: Sort by