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

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

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Updated on: 27 Mar 2018, 00:54
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Difficulty:

75% (hard)

Question Stats:

18% (02:00) correct 82% (01:43) wrong based on 469 sessions

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

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

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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.

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

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

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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.

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

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

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

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

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22 Apr 2011, 02:34
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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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.

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Posts: 58453
Re: If |a| = b is a + b > ab ?  [#permalink]

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

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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

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

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02 Jun 2016, 05:20
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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27 Mar 2018, 00:22
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Re: If |a| = b is a + b > ab ?   [#permalink] 27 Mar 2018, 00:22
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