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# What is the value of a ?

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What is the value of a ? [#permalink]

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03 Apr 2013, 09:21
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What is the value of a ?

(1) a ^2 = b^2
(2) b − a = −12
[Reveal] Spoiler: OA

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Last edited by Bunuel on 03 Apr 2013, 09:42, edited 1 time in total.
Edited the question.

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Re: What is the value of a ? [#permalink]

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03 Apr 2013, 09:48
What is the value of a ?

(1) a ^2 = b^2. Clearly insufficient. But from this statement $$b^2-a^2=0$$ --> $$(b-a)(b+a)=0$$ --> $$b-a=0$$ or $$b+a=0$$.

(2) b − a = −12. Also clearly insufficient.

(1)+(2) Since from (2) $$b-a=-12\neq{0}$$, then from (1) $$b+a=0$$. So, we have two equations: $$b-a=-12$$ and $$b+a=0$$. Solving gives $$a=6$$ and $$b=-6$$. Sufficient.

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Re: What is the value of a ? [#permalink]

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03 Apr 2013, 10:01
Thanks Bunuel....your explanation is much more easier than Kaplan's...
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Re: What is the value of a ? [#permalink]

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09 Apr 2013, 22:37
What is the value of a ?

1$$.a^2$$ = $$b^2$$
$$|a|=|b|$$ so or $$a=b$$ or $$a=-b$$, we have no value of b. Not sufficient

2.b - a = -12
Clearly not sufficient.

1+2
$$a-b=12$$, so from statement 1 we can deduce that a=-b ( it cannot be a=b because a-b=b-b=0 and not 12).
$$-b-b=12,b=-6$$ and $$a=6$$. C
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Re: What is the value of a ? [#permalink]

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09 Apr 2013, 23:24
subhendu009 wrote:
What is the value of a ?

1$$.a^2$$ = $$b^2$$
2.b - a = -12

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From F.S 1, we have (a-b)(a+b) = 0. Insufficient.

From F.S 2, we have b-a = -12. Insufficient.

Taking both together, we know that (a-b) is not equal to zero. Thus, (a+b) = 0, and we can get the value for a. Sufficient.

C.
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Re: What is the value of a ? [#permalink]

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14 Oct 2017, 03:53
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Re: What is the value of a ?   [#permalink] 14 Oct 2017, 03:53
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