Last visit was: 19 Jul 2024, 05:20 It is currently 19 Jul 2024, 05:20
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
User avatar
Current Student
Joined: 07 Aug 2011
Status:mba here i come!
Posts: 151
Own Kudos [?]: 1957 [119]
Given Kudos: 48
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 94412
Own Kudos [?]: 642241 [23]
Given Kudos: 86284
Send PM
User avatar
Intern
Intern
Joined: 11 May 2011
Posts: 11
Own Kudos [?]: 84 [19]
Given Kudos: 1
Send PM
General Discussion
User avatar
Intern
Intern
Joined: 11 May 2011
Posts: 11
Own Kudos [?]: 84 [0]
Given Kudos: 1
Send PM
Re: If |a| > |b|, which of the following must be true? [#permalink]
hello MBAhereIcome,

Do consider posting in PS Section ( gmat-problem-solving-ps-140/ ) as this is dedicated for DS questions.


Regards
Raghav.V
avatar
Intern
Intern
Joined: 17 Jul 2010
Posts: 10
Own Kudos [?]: 12 [1]
Given Kudos: 4
Location: United States (AL)
GMAT 1: 720 Q49 V39
Send PM
Re: If |a| > |b|, which of the following must be true? [#permalink]
1
Kudos
A good way to think of this is that a is much further away from zero than b is. a is much "stronger" thanb is. With that you can deduce option 2 as true.

Posted from my mobile device
User avatar
Senior Manager
Senior Manager
Joined: 01 Feb 2011
Posts: 306
Own Kudos [?]: 328 [0]
Given Kudos: 42
Send PM
Re: If |a| > |b|, which of the following must be true? [#permalink]
|a| > |b|

1. ab>0

need not be true . when a>0,b<0 ab<0

2. |a|+b >0

Must be true.

when a , b are of same sign , |a|+b>0

when a is +ve, b is -ve , |a|+b>0 as |a|>|b|

when a is -ve, b is +ve, |a|+b>0

when a is -ve, b is -ve , |a|+b>0 as |a|>|b|


3. a+|b|>0

Need not be true. when a<0,b>0 and |a|>|b|, a+|b|<0

4. |b|/a >0

Need not be true. when a<0,b>0 and |a|>|b|, |b|/a<0

5. |a|b>0

Need not be true. when b<0 ,|a|b<0

Answer is B.
Manager
Manager
Joined: 29 May 2017
Posts: 154
Own Kudos [?]: 20 [0]
Given Kudos: 63
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Send PM
Re: If |a| > |b|, which of the following must be true? [#permalink]
Hello. I dont quite get this question.

1. for |a| we have 2 options ... a or -a
2. for |b| we have 2 options ... b or -b

Option A says ab>0

so if we do a x b ... this will always be >0

a x -b <0,but that is not the same as a x b

he is asking specifically for a x b

Option B says |a| + b>0

this wd mean a + b .... which wd be >0
or
-a + b .... which wd be <0

am i reading the question wrong??
Manager
Manager
Joined: 03 May 2017
Posts: 61
Own Kudos [?]: 55 [0]
Given Kudos: 15
Send PM
Re: If |a| > |b|, which of the following must be true? [#permalink]
Mansoor50 wrote:
Hello. I dont quite get this question.

1. for |a| we have 2 options ... a or -a
2. for |b| we have 2 options ... b or -b

Option A says ab>0

so if we do a x b ... this will always be >0

a x -b <0,but that is not the same as a x b

he is asking specifically for a x b

Option B says |a| + b>0

this wd mean a + b .... which wd be >0
or
-a + b .... which wd be <0

am i reading the question wrong??



Hi Mansoor,

Bunuel has given you a comprehensive solution.

Another approach is to consider 2 different positive integers (absolute values). Now option B is saying add either the negative or positive value of the smaller number to the bigger and the result is positive. This is going to always be true, hence the question is answered. Take 2 and 5 for example, 5+2 and 5-2 are always going to be positive i.e greater than 0.

Best,
Retired Moderator
Joined: 19 Mar 2014
Posts: 815
Own Kudos [?]: 981 [2]
Given Kudos: 199
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Send PM
Re: If |a| > |b|, which of the following must be true? [#permalink]
2
Bookmarks
\(|a| > |b|\)


A. \(ab > 0\)

Not true when one of the numbers is NEGATIVE (Take \(x = -4\) & \(y = 3\))

B. \(|a| + b > 0\)

TRUE for all values (Take \(x = -4\) &\(y = 3\) or \(x = 4\) & \(y = -2\) or \(x = -4\)& \(y -3\))

C. \(a + |b| > 0\)

Not true when when a is NEGATIVE and b is positive (Take \(x = -4\) & \(y = 3\))

D. \(\frac{|b|}{a} > 0\)

Not true when when a is NEGATIVE (Take \(x = -4\) & \(y = 3\))

E. \(|a|*b > 0\)

Not true when when b is NEGATIVE (Take \(x = 4\) & \(y = -3\))

Hence, Answer is B
Manager
Manager
Joined: 29 May 2017
Posts: 154
Own Kudos [?]: 20 [0]
Given Kudos: 63
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Send PM
Re: If |a| > |b|, which of the following must be true? [#permalink]
Thank you all for your replies. And yes, I understand what you are saying.

I realized the mistake i was making: when it wrote ab>0, i assumed that he meant the case when |a|=a ... i thought he wd write -a if |a|=-a.

Whereas in actuality, his references to a or b simply mean whatever the case maybe , ie. 'a' could be +a or -a.

Thanks Everyone!!!!!
Current Student
Joined: 17 Jun 2016
Posts: 473
Own Kudos [?]: 951 [2]
Given Kudos: 206
Location: India
GMAT 1: 720 Q49 V39
GMAT 2: 710 Q50 V37
GPA: 3.65
WE:Engineering (Energy and Utilities)
Send PM
Re: If |a| > |b|, which of the following must be true? [#permalink]
2
Kudos
MBAhereIcome wrote:
If \(|a| > |b|\), which of the following must be true?


A. \(ab > 0\)

B. \(|a| + b > 0\)

C. \(a + |b| > 0\)

D. \(\frac{|b|}{a} > 0\)

E. \(|a|*b > 0\)


Show SpoilerSolution
|a|>|b| so a is a bigger number than b, regardless of their signs. e.g. a=5, b=-2 OR a=-8, b=7.

a) not true if b<0 & a>0
b) TRUE. e.g.|5|-4>0 OR |-8|+7>0
c) incorrect if a<0. the sum will always be negative in this case
d) not true if a<0
e) not true if b<0


Refer to the attached file
Attachments

WhatsApp Image 2017-06-25 at 9.53.09 PM.jpeg
WhatsApp Image 2017-06-25 at 9.53.09 PM.jpeg [ 39.94 KiB | Viewed 25310 times ]

Intern
Intern
Joined: 04 Nov 2018
Posts: 11
Own Kudos [?]: 3 [1]
Given Kudos: 302
Concentration: Finance, General Management
GMAT 1: 700 Q49 V35
GMAT 2: 710 Q48 V40
GPA: 3.83
WE:Sales (Retail)
Send PM
Re: If |a| > |b|, which of the following must be true? [#permalink]
1
Kudos
Not a very foul-proof approach, but definitely time-saving.

I picked two random integers, namely a=-3 and b=2 and checked the answer choices.

Then when I noticed B to be most likely correct, I picked some other numbers and the answer still stand.
VP
VP
Joined: 11 Aug 2020
Posts: 1246
Own Kudos [?]: 208 [0]
Given Kudos: 332
Send PM
Re: If |a| > |b|, which of the following must be true? [#permalink]
If |a|>|b|, which of the following must be true?


A. ab>0
-a and b can have different signs and this would be violated

B. |a|+b>0 CORRECT

C. a+|b|>0
-a can be negative and this would be violated

D. |b|/a>0
-a can be negative here

E. |a|∗b>0
-b can be negative
Director
Director
Joined: 05 Jul 2020
Posts: 584
Own Kudos [?]: 303 [0]
Given Kudos: 151
GMAT 1: 720 Q49 V38
WE:Accounting (Accounting)
Send PM
If |a| > |b|, which of the following must be true? [#permalink]
baldururikson wrote:
Not a very foul-proof approach, but definitely time-saving.

I picked two random integers, namely a=-3 and b=2 and checked the answer choices.

Then when I noticed B to be most likely correct, I picked some other numbers and the answer still stand.

baldururikson, picking numbers might not be the best approach for a must be true question. Definitely works efficiently for a could be true question.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34019
Own Kudos [?]: 852 [0]
Given Kudos: 0
Send PM
Re: If |a| > |b|, which of the following must be true? [#permalink]
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.
GMAT Club Bot
Re: If |a| > |b|, which of the following must be true? [#permalink]
Moderator:
Math Expert
94411 posts