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# Is (a − 5)^2 < (b + 5)^2 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 51307
Is (a − 5)^2 < (b + 5)^2 ?  [#permalink]

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24 Apr 2017, 03:27
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Difficulty:

95% (hard)

Question Stats:

47% (02:22) correct 53% (02:14) wrong based on 159 sessions

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Is (a − 5)^2 < (b + 5)^2 ?

(1) a < b
(2) a + b > 5

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Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3327
Location: India
GPA: 3.12
Re: Is (a − 5)^2 < (b + 5)^2 ?  [#permalink]

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24 Apr 2017, 05:14
1
Is (a − 5)^2 < (b + 5)^2 ?
Using trial and error method.
(1) a < b
Lets consider the value a=0,b=1. These values, satisfy the condition
But if we take a=-2,b=-1, the condition does not hold.
Hence, not sufficient.

(2) a + b > 5
Lets consider a=4,b=2, the condition holds good.
However, if a = 15,b = -2, the condition doesn't hold good.
Hence, not sufficient.

On combining both, since one of the number definitely has to be positive,
we can mark the solution sufficient(Option C)
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Re: Is (a − 5)^2 < (b + 5)^2 ?  [#permalink]

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03 Sep 2017, 09:59
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Is (a − 5)^2 < (b + 5)^2 ?  [#permalink]

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03 Sep 2017, 10:48
2
Bunuel wrote:
Is (a − 5)^2 < (b + 5)^2 ?

(1) a < b
(2) a + b > 5

Simplifying the question stem:
$$(a-5)^2-(b+5)^2<0$$ or $$(a-5+b+5)(a-5-b-5)<0$$ or $$(a+b)(a-b-10)<0$$.
Hence the question becomes IS $$a+b<0$$ & $$(a-b-10)>0$$ or $$(a+b)>0$$ & $$(a-b-10)<0$$

Statement 1: $$a<b$$ or $$a-b<0$$ so we can say that $$a-b-10<0$$ (as it is summation of two negative terms)
but we know nothing about $$a$$ & $$b$$ so whether $$a+b<0$$ or $$a+b>0$$ can't be arrived at. For example if $$a=-3$$ & $$b=-1$$, then $$a+b<0$$ as well as $$a-b<0$$ but if $$a=1, b=2$$, then $$a+b>0$$ but $$a-b<0$$. Hence the statement is not sufficient.

Statement 2: this implies that $$a+b>0$$ but we know nothing about $$(a-b)$$, hence can't say that whether $$a-b-10<0$$ or $$a-b-10>0$$. For ex. if $$a=-1, b=7$$ then $$a-b-10<0$$ but if $$a=-1, b=13$$ then $$a-b-10>0$$. Hence insufficient

Combining 1 & 2
we know that $$a-b<0$$, hence $$a-b-10<0$$ and $$a+b>5$$ hence $$a+b>0$$. therefore $$(a+b)(a-b-10)<0$$. Hence sufficient

Option C
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Joined: 27 May 2012
Posts: 639
Re: Is (a − 5)^2 < (b + 5)^2 ?  [#permalink]

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21 Jul 2018, 09:31
Bunuel wrote:
Is (a − 5)^2 < (b + 5)^2 ?

(1) a < b
(2) a + b > 5

Dear Moderator ,
DS Question posted in PS forum, hope you will do the needful. Thank you.
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- Stne

Math Expert
Joined: 02 Sep 2009
Posts: 51307
Re: Is (a − 5)^2 < (b + 5)^2 ?  [#permalink]

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21 Jul 2018, 11:07
stne wrote:
Bunuel wrote:
Is (a − 5)^2 < (b + 5)^2 ?

(1) a < b
(2) a + b > 5

Dear Moderator ,
DS Question posted in PS forum, hope you will do the needful. Thank you.

Moved to DS forum. Thank you.
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Re: Is (a − 5)^2 < (b + 5)^2 ? &nbs [#permalink] 21 Jul 2018, 11:07
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