If |a| = b is a + b > ab ? : GMAT Data Sufficiency (DS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 10 Dec 2016, 17:24

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

Author Message
TAGS:

Hide Tags

Manager
Joined: 19 Feb 2010
Posts: 81
Followers: 2

Kudos [?]: 34 [1] , given: 6

If |a| = b is a + b > ab ? [#permalink]

Show Tags

13 Jul 2010, 13:59
1
KUDOS
12
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

56% (02:13) correct 44% (01:23) wrong based on 441 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.
[Reveal] Spoiler: OA

Attachments

maths.jpg [ 99.43 KiB | Viewed 5485 times ]

_________________

Yogesh Agarwal
yogeshagarwala@gmail.com

CONSIDER AWARDING KUDOS IF MY POST HELPS !!!

Last edited by Bunuel on 02 Jun 2016, 07:13, edited 1 time in total.
Edited the question.
Ms. Big Fat Panda
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1922
Concentration: General Management, Nonprofit
Followers: 443

Kudos [?]: 1958 [1] , given: 210

Re: If |a| = b is a + b > ab ? [#permalink]

Show Tags

13 Jul 2010, 14:10
1
KUDOS
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.

Math Expert
Joined: 02 Sep 2009
Posts: 35951
Followers: 6866

Kudos [?]: 90120 [7] , given: 10418

Re: If |a| = b is a + b > ab ? [#permalink]

Show Tags

13 Jul 2010, 14:16
7
KUDOS
Expert's post
2
This post was
BOOKMARKED
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.
_________________
Senior Manager
Joined: 25 Feb 2010
Posts: 481
Followers: 4

Kudos [?]: 82 [1] , given: 10

Re: If |a| = b is a + b > ab ? [#permalink]

Show Tags

13 Jul 2010, 19:32
1
KUDOS
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: 72
Location: United States
Concentration: Strategy, Entrepreneurship
GMAT 1: 700 Q49 V37
GMAT 2: 740 Q50 V40
GPA: 3.48
WE: Web Development (Computer Software)
Followers: 0

Kudos [?]: 10 [0], given: 6

Re: If |a| = b is a + b > ab ? [#permalink]

Show Tags

13 Jul 2010, 21:46
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: 26
Followers: 0

Kudos [?]: 3 [0], given: 6

Re: If |a| = b is a + b > ab ? [#permalink]

Show Tags

14 Jul 2010, 01:31
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: 81
Followers: 2

Kudos [?]: 34 [0], given: 6

Re: If |a| = b is a + b > ab ? [#permalink]

Show Tags

14 Jul 2010, 07:47
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: 167
Schools: Tuck Class of 2013
Followers: 2

Kudos [?]: 25 [0], given: 4

Re: If |a| = b is a + b > ab ? [#permalink]

Show Tags

14 Jul 2010, 07:56
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: 45
Followers: 0

Kudos [?]: 5 [0], given: 0

Re: If |a| = b is a + b > ab ? [#permalink]

Show Tags

22 Apr 2011, 01:34
Oops what a catch !!
Even I missed the 0.
Intern
Joined: 05 Mar 2013
Posts: 6
Followers: 0

Kudos [?]: 2 [0], given: 11

Re: If |a| = b is a + b > ab ? [#permalink]

Show Tags

26 Apr 2013, 05:55
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: 35951
Followers: 6866

Kudos [?]: 90120 [1] , given: 10418

Re: If |a| = b is a + b > ab ? [#permalink]

Show Tags

26 Apr 2013, 06:48
1
KUDOS
Expert's post
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: 472
Followers: 3

Kudos [?]: 156 [0], given: 134

Re: If |a| = b is a + b > ab ? [#permalink]

Show Tags

25 Jun 2013, 15:33
1
This post was
BOOKMARKED
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

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12908
Followers: 563

Kudos [?]: 158 [0], given: 0

Re: If |a| = b is a + b > ab ? [#permalink]

Show Tags

26 Sep 2014, 05:52
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 Legend
Joined: 09 Sep 2013
Posts: 12908
Followers: 563

Kudos [?]: 158 [0], given: 0

Re: If |a| = b is a + b > ab ? [#permalink]

Show Tags

28 May 2016, 07:37
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.
_________________
Intern
Joined: 03 Apr 2016
Posts: 20
Followers: 2

Kudos [?]: 6 [0], given: 1219

Re: If |a| = b is a + b > ab ? [#permalink]

Show Tags

02 Jun 2016, 04:20
please change the ans to b in oa.
Re: If |a| = b is a + b > ab ?   [#permalink] 02 Jun 2016, 04:20
Similar topics Replies Last post
Similar
Topics:
3 Is A^B > B^A? 3 12 Jun 2016, 08:04
33 If ab ≠ 0, is |a-b| > |a+b|? 18 06 May 2016, 07:46
2 Is a^b > b^a? 4 20 May 2013, 22:31
2 Is a/b > 0 ? 6 27 Feb 2012, 06:19
2 Is a/b > 0? 3 07 Nov 2010, 12:40
Display posts from previous: Sort by