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

 It is currently 20 Jul 2018, 19:19

### 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

# If |a| = b is a + b > ab ?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 19 Feb 2010
Posts: 69
If |a| = b is a + b > ab ?  [#permalink]

### Show Tags

Updated on: 27 Mar 2018, 00:54
1
18
00:00

Difficulty:

75% (hard)

Question Stats:

18% (01:34) correct 82% (01:13) wrong based on 461 sessions

### HideShow timer Statistics

If |a| = b is a + b > ab ?

(1) a = -b
(2) a = -3

I believe its B but the MR says its D.

Attachment:

maths.jpg [ 99.43 KiB | Viewed 6112 times ]

_________________

Yogesh Agarwal
yogeshagarwala@gmail.com

CONSIDER AWARDING KUDOS IF MY POST HELPS !!!

Originally posted by yogeshagarwala on 13 Jul 2010, 14:59.
Last edited by Bunuel on 27 Mar 2018, 00:54, edited 2 times in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 47157
If |a| = b is a + b > ab ?  [#permalink]

### Show Tags

13 Jul 2010, 15:16
7
3
yogeshagarwala wrote:

I believe its B but the MR says its D.

If $$|a|=b$$ is $$a+b>ab$$?

First of all as $$|a|=b$$ ($$b$$ equals to absolute value of some number) then $$b\geq{0}$$, as absolute value is always non-negative.

(1) $$a=-b$$ ($$b=-a$$) --> so $$a\leq{0}$$ and $$LHS=a+b=0$$. But $$RHS=ab\leq{0}$$ thus we can not say for sure that $$a+b>ab$$, because if $$a=b=0$$ then $$a+b=0=ab$$ (so in case $$a=b=0$$, $$a+b$$ is not more than $$ab$$ it equals to $$ab$$). Not sufficient.

(2) $$a=-3$$ --> $$b=3$$ --> $$a+b=0>ab=-9$$. Sufficient.

Hope it's clear.
_________________
##### General Discussion
SVP
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1869
Concentration: General Management, Nonprofit
Re: If |a| = b is a + b > ab ?  [#permalink]

### Show Tags

13 Jul 2010, 15:10
1
Given: $$|a| = b$$

To find: $$Is a+b>ab$$

Statement 1: $$a = -b$$ - Sufficient

$$=> a+b = 0$$

$$ab = (-b)(b) = -b^2 < 0$$

$$0 > ab$$ since ab is negative.

Statement 2: $$a = -3$$ - Sufficient

$$b = |-3| = 3$$

$$=> a+b = 0$$

$$ab = (-3)(3) = -9 < 0$$

$$0 > ab$$ since ab is negative.

Senior Manager
Joined: 25 Feb 2010
Posts: 395
Re: If |a| = b is a + b > ab ?  [#permalink]

### Show Tags

13 Jul 2010, 20:32
1
Waoo

I even came with D, but after looking to "Bunuel" post; I'm not sure what's wrong ?
_________________

GGG (Gym / GMAT / Girl) -- Be Serious

Its your duty to post OA afterwards; some one must be waiting for that...

Manager
Status: one more time
Joined: 05 Jul 2010
Posts: 66
Location: United States
Concentration: Strategy, Entrepreneurship
GMAT 1: 700 Q49 V37
GMAT 2: 740 Q50 V40
GPA: 3.48
WE: Web Development (Computer Software)
Re: If |a| = b is a + b > ab ?  [#permalink]

### Show Tags

13 Jul 2010, 22:46
I think it is D.

Lets take statement 1, a = -b.

Put that value in the equation a+b >ab
then (-b) +b > (-b) (b)
i.e. 0> -b^2
As b^2 is always +ve this equaliton will hold true.
Hence statement 1 is sufficient.

As above explanations say statement B is also sufficient.

Intern
Joined: 11 Oct 2009
Posts: 24
Re: If |a| = b is a + b > ab ?  [#permalink]

### Show Tags

14 Jul 2010, 02:31
Hi Yogesh .. can you please share the access codes for these tests. It will be very nice of you. My email id is sandeepuc@gmail.com.
Manager
Joined: 19 Feb 2010
Posts: 69
Re: If |a| = b is a + b > ab ?  [#permalink]

### Show Tags

14 Jul 2010, 08:47
Bunuel wrote:
yogeshagarwala wrote:

I believe its B but the MR says its D.

If $$|a|=b$$ is $$a+b>ab$$?

First of all as $$|a|=b$$ ($$b$$ equals to absolute value of some number) then $$b\geq{0}$$, as absolute value is always non-negative.

(1) $$a=-b$$ ($$b=-a$$) --> so $$a\leq{0}$$ and $$LHS=a+b=0$$. But $$RHS=ab\leq{0}$$ thus we can not say for sure that $$a+b>ab$$, because if $$a=b=0$$ then $$a+b=0=ab$$ (so in case $$a=b=0$$, $$a+b$$ is not more than $$ab$$ it equals to $$ab$$). Not sufficient.

(2) $$a=-3$$ --> $$b=3$$ --> $$a+b=0>ab=-9$$. Sufficient.

Hope it's clear.

Bravo. This is the very reason I marked B but was shocked to see that MR people had marked it as D. Thanks Bunuel. You made my day.
_________________

Yogesh Agarwal
yogeshagarwala@gmail.com

CONSIDER AWARDING KUDOS IF MY POST HELPS !!!

Current Student
Joined: 31 Mar 2010
Posts: 166
Schools: Tuck Class of 2013
Re: If |a| = b is a + b > ab ?  [#permalink]

### Show Tags

14 Jul 2010, 08:56
yogeshagarwala wrote:
Bunuel wrote:
yogeshagarwala wrote:

I believe its B but the MR says its D.

If $$|a|=b$$ is $$a+b>ab$$?

First of all as $$|a|=b$$ ($$b$$ equals to absolute value of some number) then $$b\geq{0}$$, as absolute value is always non-negative.

(1) $$a=-b$$ ($$b=-a$$) --> so $$a\leq{0}$$ and $$LHS=a+b=0$$. But $$RHS=ab\leq{0}$$ thus we can not say for sure that $$a+b>ab$$, because if $$a=b=0$$ then $$a+b=0=ab$$ (so in case $$a=b=0$$, $$a+b$$ is not more than $$ab$$ it equals to $$ab$$). Not sufficient.

(2) $$a=-3$$ --> $$b=3$$ --> $$a+b=0>ab=-9$$. Sufficient.

Hope it's clear.

Bravo. This is the very reason I marked B but was shocked to see that MR people had marked it as D. Thanks Bunuel. You made my day.

So the trick here is not to consider zero. Probably the owner of the question forgot to say "a and b are both non-zero integers".
Intern
Joined: 06 Sep 2010
Posts: 36
Re: If |a| = b is a + b > ab ?  [#permalink]

### Show Tags

22 Apr 2011, 02:34
Oops what a catch !!
Even I missed the 0.
Intern
Joined: 05 Mar 2013
Posts: 4
Re: If |a| = b is a + b > ab ?  [#permalink]

### Show Tags

26 Apr 2013, 06:55
Bunuel wrote:
yogeshagarwala wrote:

I believe its B but the MR says its D.

If $$|a|=b$$ is $$a+b>ab$$?

First of all as $$|a|=b$$ ($$b$$ equals to absolute value of some number) then $$b\geq{0}$$, as absolute value is always non-negative.

(1) $$a=-b$$ ($$b=-a$$) --> so $$a\leq{0}$$ and $$LHS=a+b=0$$. But $$RHS=ab\leq{0}$$ thus we can not say for sure that $$a+b>ab$$, because if $$a=b=0$$ then $$a+b=0=ab$$ (so in case $$a=b=0$$, $$a+b$$ is not more than $$ab$$ it equals to $$ab$$). Not sufficient.

(2) $$a=-3$$ --> $$b=3$$ --> $$a+b=0>ab=-9$$. Sufficient.

Hope it's clear.

Thanks for the solution.
But I still couldnt understand why are we taking a=0 and b=0 in the 1 st statement. It states a=-b, is it ok to write 0=-0.....
It would be of great help if you can explain. It will help in clearing my doubts.

Math Expert
Joined: 02 Sep 2009
Posts: 47157
Re: If |a| = b is a + b > ab ?  [#permalink]

### Show Tags

26 Apr 2013, 07:48
1
Richa16 wrote:
Bunuel wrote:
yogeshagarwala wrote:

I believe its B but the MR says its D.

If $$|a|=b$$ is $$a+b>ab$$?

First of all as $$|a|=b$$ ($$b$$ equals to absolute value of some number) then $$b\geq{0}$$, as absolute value is always non-negative.

(1) $$a=-b$$ ($$b=-a$$) --> so $$a\leq{0}$$ and $$LHS=a+b=0$$. But $$RHS=ab\leq{0}$$ thus we can not say for sure that $$a+b>ab$$, because if $$a=b=0$$ then $$a+b=0=ab$$ (so in case $$a=b=0$$, $$a+b$$ is not more than $$ab$$ it equals to $$ab$$). Not sufficient.

(2) $$a=-3$$ --> $$b=3$$ --> $$a+b=0>ab=-9$$. Sufficient.

Hope it's clear.

Thanks for the solution.
But I still couldnt understand why are we taking a=0 and b=0 in the 1 st statement. It states a=-b, is it ok to write 0=-0.....
It would be of great help if you can explain. It will help in clearing my doubts.

Yes, it's ok to write 0=-0.
_________________
Senior Manager
Joined: 13 May 2013
Posts: 430
Re: If |a| = b is a + b > ab ?  [#permalink]

### Show Tags

25 Jun 2013, 16:33
1
If |a| = b is a + b > ab

(1) a = -b
(2) a = -3

|a| = b so b MUST be ≥ 0

1.) a = -b
b=-a

So what do we know?

|a|=|b|
b is positive
a is the negative value of b

So,
a + b > ab
a+b = 0
HOWEVER
we are not sure what values a and b are. For example, a and b could be -3 and 3 or a and b could be 0 and 0.
INSUFFICIENT

(2) a = -3
We know that |a|=b, so if a = -3 then b must = 3
a + b > ab
-3+3 > (-3)(3)
0>-9
TRUE

Intern
Joined: 03 Apr 2016
Posts: 16
Re: If |a| = b is a + b > ab ?  [#permalink]

### Show Tags

02 Jun 2016, 05:20
please change the ans to b in oa.
Non-Human User
Joined: 09 Sep 2013
Posts: 7312
Re: If |a| = b is a + b > ab ?  [#permalink]

### Show Tags

27 Mar 2018, 00:22
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.
_________________
Re: If |a| = b is a + b > ab ? &nbs [#permalink] 27 Mar 2018, 00:22
Display posts from previous: Sort by

# Events & Promotions

 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®.