Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 13 Oct 2015, 16:01

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

Kudos [?]: 23 [0], given: 6

If |a| = b is a + b > ab ? [#permalink]  13 Jul 2010, 13:59
3
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

66% (02:13) correct 34% (01:21) wrong based on 275 sessions
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 4164 times ]

_________________

Yogesh Agarwal
yogeshagarwala@gmail.com

CONSIDER AWARDING KUDOS IF MY POST HELPS !!!

Ms. Big Fat Panda
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1922
Concentration: General Management, Nonprofit
Followers: 399

Kudos [?]: 1655 [0], given: 210

Expert's post
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: 29856
Followers: 4925

Kudos [?]: 53970 [4] , given: 8260

4
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: 480
Followers: 4

Kudos [?]: 59 [0], given: 10

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 [?]: 8 [0], given: 6

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 [?]: 2 [0], given: 6

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 [?]: 23 [0], given: 6

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 [?]: 22 [0], given: 4

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

Oops what a catch !!
Even I missed the 0.
Intern
Joined: 05 Mar 2013
Posts: 6
Followers: 0

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

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: 29856
Followers: 4925

Kudos [?]: 53970 [0], given: 8260

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: 1

Kudos [?]: 99 [0], given: 134

Re: If |a| = b is a + b > ab ? [#permalink]  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: 6784
Followers: 369

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

Re: If |a| = b is a + b > ab ? [#permalink]  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.
_________________
Re: If |a| = b is a + b > ab ?   [#permalink] 26 Sep 2014, 05:52
Similar topics Replies Last post
Similar
Topics:
61 If ab ≠ 0, is ab > a/b ? 20 25 May 2014, 11:32
Is a^b > b^a? 3 20 May 2013, 22:31
4 If a is not equal to b, is 1/(a-b) > ab ? 8 27 Feb 2013, 12:17
2 Is a/b > 0 ? 5 27 Feb 2012, 06:19
1 Is a/b > 0? 1 07 Nov 2010, 12:40
Display posts from previous: Sort by