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

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

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New post Updated on: 26 Mar 2018, 23:54
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If |a| = b is a + b > ab ?

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


I believe its B but the MR says its D.

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Originally posted by yogeshagarwala on 13 Jul 2010, 13:59.
Last edited by Bunuel on 26 Mar 2018, 23:54, edited 2 times in total.
Edited the question.
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If |a| = b is a + b > ab ?  [#permalink]

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New post 13 Jul 2010, 14:16
7
3
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: If |a| = b is a + b > ab ?  [#permalink]

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New post 13 Jul 2010, 14:10
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.

So the answer is D.
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Re: If |a| = b is a + b > ab ?  [#permalink]

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New post 13 Jul 2010, 19:32
1
Waoo

I even came with D, but after looking to "Bunuel" post; I'm not sure what's wrong ?
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Re: If |a| = b is a + b > ab ?  [#permalink]

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

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

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

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

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New post 22 Apr 2011, 01:34
Oops what a catch !!
Even I missed the 0.
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Re: If |a| = b is a + b > ab ?  [#permalink]

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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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Posts: 50544
Re: If |a| = b is a + b > ab ?  [#permalink]

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New post 26 Apr 2013, 06:48
1
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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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]

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New post 25 Jun 2013, 15:33
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

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

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New post 02 Jun 2016, 04:20
please change the ans to b in oa.
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Re: If |a| = b is a + b > ab ?  [#permalink]

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Re: If |a| = b is a + b > ab ? &nbs [#permalink] 26 Mar 2018, 23:22
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