GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 May 2019, 00:23 ### 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. ### Request Expert Reply # If |a| > |b|, which of the following must be true?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager  Status: mba here i come!
Joined: 07 Aug 2011
Posts: 202
If |a| > |b|, which of the following must be true?  [#permalink]

### Show Tags

7
30 00:00

Difficulty:   25% (medium)

Question Stats: 73% (01:27) correct 27% (01:31) wrong based on 619 sessions

### HideShow timer Statistics

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. $$|a|*b > 0$$

Spoiler: :: Solution
|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

_________________
press +1 Kudos to appreciate posts

Originally posted by MBAhereIcome on 30 Aug 2011, 03:32.
Last edited by Bunuel on 24 Jun 2017, 14:35, edited 3 times in total.
Renamed the topic and edited the question.
##### Most Helpful Community Reply
Intern  Joined: 11 May 2011
Posts: 18
Re: If |a| > |b|, which of the following must be true?  [#permalink]

### Show Tags

8
2
Hello,

lets take each one given |a| > |b|

a) ab > 0

Not allways . If a,b are both negative then true, either positive then fails.

b) |a|+b > 0

Since we know that absolute value of a is greater than absolute value of b , we can for sure say that |a| > b

The above would fail only if |a| = |b| or |b| > |a| so B is the answer because -- given |a| > |b|

c) a+|b| > 0

Not always consider a = -7 and b = -5 (given |a| > |b|)

-7 + 5 = -2 <0 hence not possible ;

d) |b|/a > 0

not always if a is positive then true, if a is negative then false because for all values of {b} except zero |B| is always positive

e) |a|*b > 0

not always if b is positive then true, if b is negative then false because for all values of {a} except zero |a| is always positive

Hope my explanation was helpful. OA is B

Regards
Raghav.V

Consider Kudos if you think my explanation was helpful ##### General Discussion
Intern  Joined: 11 May 2011
Posts: 18
Re: If |a| > |b|, which of the following must be true?  [#permalink]

### Show Tags

hello MBAhereIcome,

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

Regards
Raghav.V
Intern  Joined: 17 Jul 2010
Posts: 14
Location: United States (AL)
GMAT 1: 720 Q49 V39 Re: If |a| > |b|, which of the following must be true?  [#permalink]

### Show Tags

1
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
Director  Joined: 01 Feb 2011
Posts: 646
Re: If |a| > |b|, which of the following must be true?  [#permalink]

### Show Tags

|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  B
Joined: 29 May 2017
Posts: 128
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: If |a| > |b|, which of the following must be true?  [#permalink]

### Show Tags

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??
Math Expert V
Joined: 02 Sep 2009
Posts: 55271
If |a| > |b|, which of the following must be true?  [#permalink]

### Show Tags

1
2
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??

$$|a| = a$$, when $$a \geq 0$$ and $$|a| = -a$$, when $$a\leq 0$$. You cannot simply plug a or -a if you don't know which case you have.

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. $$|a|*b > 0$$

$$|a| > |b|$$ means that a is further from 0 than b is. So, we can have one of the following 4 cases:

1. ----a----b----0---------------
2. ----a---------0----b----------
3. ---------b----0---------a-----
4. --------------0----b----a-----

A. $$ab > 0$$ --> Not true for cases in which a and b have different signs (cases 2 and 3). Discard.

B. $$|a| + b > 0$$ --> true for all cases.

C. $$a + |b| > 0$$ --> not true for cases in which a is negative (cases 1 and 2). Discard.

D. $$\frac{|b|}{a} > 0$$ --> not true for cases in which a is negative (cases 1 and 2). Discard.

E. $$|a|*b > 0$$ --> not true for cases in which b is negative (cases 1 and 3). Discard.

Answer: B.

Hope it helps.
_________________
Manager  B
Joined: 03 May 2017
Posts: 91
Re: If |a| > |b|, which of the following must be true?  [#permalink]

### Show Tags

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 P
Joined: 19 Mar 2014
Posts: 931
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: If |a| > |b|, which of the following must be true?  [#permalink]

### Show Tags

$$|a| > |b|$$

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
_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Manager  B
Joined: 29 May 2017
Posts: 128
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: If |a| > |b|, which of the following must be true?  [#permalink]

### Show Tags

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!!!!!
Retired Moderator P
Joined: 17 Jun 2016
Posts: 503
Location: India
GMAT 1: 720 Q49 V39 GMAT 2: 710 Q50 V37 GPA: 3.65
WE: Engineering (Energy and Utilities)
Re: If |a| > |b|, which of the following must be true?  [#permalink]

### Show Tags

1
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. $$|a|*b > 0$$

Spoiler: :: Solution
|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 [ 39.94 KiB | Viewed 5858 times ]

_________________
Intern  B
Joined: 04 Nov 2018
Posts: 13
Concentration: Finance, General Management
GPA: 3.83
WE: Sales (Retail)
Re: If |a| > |b|, which of the following must be true?  [#permalink]

### Show Tags

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.
_________________
- GMAT Prep #1 CAT (Apr 2019) : 640 (Q48, V31)

Still not there.

If you're reading this, we've got this. Re: If |a| > |b|, which of the following must be true?   [#permalink] 23 Mar 2019, 00:15
Display posts from previous: Sort by

# If |a| > |b|, which of the following must be true?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

#### MBA Resources  