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

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If |a| = b is a + b > ab ? [#permalink] New post 13 Jul 2010, 13:59
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A
B
C
D
E

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  25% (medium)

Question Stats:

70% (01:53) correct 30% (01:21) wrong based on 120 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

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Re: Please Solve [#permalink] New post 13 Jul 2010, 14:10
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.

So the answer is D.
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Re: Please Solve [#permalink] New post 13 Jul 2010, 14:16
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Expert's post
yogeshagarwala wrote:
Please solve:

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.

Answer: B.

Hope it's clear.
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Re: Please Solve [#permalink] New post 13 Jul 2010, 19:32
Waoo

I even came with D, but after looking to "Bunuel" post; I'm not sure what's wrong ?
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Re: Please Solve [#permalink] New post 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.

B is answer.
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Re: Please Solve [#permalink] New post 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.
Thanks in advance.
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Re: Please Solve [#permalink] New post 14 Jul 2010, 07:47
Bunuel wrote:
yogeshagarwala wrote:
Please solve:

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.

Answer: B.

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.
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Re: Please Solve [#permalink] New post 14 Jul 2010, 07:56
yogeshagarwala wrote:
Bunuel wrote:
yogeshagarwala wrote:
Please solve:

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.

Answer: B.

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".
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Re: Please Solve [#permalink] New post 22 Apr 2011, 01:34
Oops what a catch !!
Even I missed the 0.
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Re: Please Solve [#permalink] New post 26 Apr 2013, 05:55
Bunuel wrote:
yogeshagarwala wrote:
Please solve:

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.

Answer: B.

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.

Thanks in advance
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Re: Please Solve [#permalink] New post 26 Apr 2013, 06:48
Expert's post
Richa16 wrote:
Bunuel wrote:
yogeshagarwala wrote:
Please solve:

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.

Answer: B.

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.

Thanks in advance


Yes, it's ok to write 0=-0.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If |a| = b is a + b > ab ? [#permalink] New post 25 Jun 2013, 15:33
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

Answer = b
Re: If |a| = b is a + b > ab ?   [#permalink] 25 Jun 2013, 15:33
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