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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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Updated on: 03 Apr 2013, 08:42
1
00:00

Difficulty:

25% (medium)

Question Stats:

72% (01:13) correct 28% (01:18) wrong based on 184 sessions

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What is the value of a ?

(1) a ^2 = b^2
(2) b − a = −12

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Originally posted by atalpanditgmat on 03 Apr 2013, 08:21.
Last edited by Bunuel on 03 Apr 2013, 08:42, 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, 08:48
2
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, 09:01
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, 21:37
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, 22:24
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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01 Sep 2018, 09:12
Harshgmat wrote:
What is the value of a ?

a) $$a^2 = b^2$$

b) b - a = -12

Statement 1: $$a^2 = b^2$$
This implies, a=+b or -b
Insufficient.

Statement 2: b - a = -12
Clearly inssuficient.

Statement 1 and 2 Together:

Case 1: a=+b
b-b=-12
0=-12
Absurd Result.

Case 2: a=-b
b+b=-12
b=-6

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

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01 Sep 2018, 15:23
Harshgmat wrote:
What is the value of a ?

a) $$a^2 = b^2$$

b) b - a = -12

To prove that each statement alone is insufficient, we present a BIFURCATION (algebraic, in this case):

$$? = a$$

$$\left( 1 \right)\,\,{a^2} = {b^2}$$

$$Take\,\,\left\{ \begin{gathered} {a^2} = {b^2} = 0\,\,\,\,\, \Rightarrow \,\,\,\,? = 0 \hfill \\ {a^2} = {b^2} = 1\,\,\,\,\, \Rightarrow \,\,\,\,? \ne 0\,\,\,\,\,\,\,\,\left( {a = \pm \,1} \right) \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{INSUF}}{\text{.}}$$

$$\left( 2 \right)\,\,a\, - b = 12$$

$$Take\,\,\left\{ \begin{gathered} b = 0\,\,\,\,\, \Rightarrow \,\,\,\,? = 12 \hfill \\ b = 1\,\,\,\, \Rightarrow \,\,\,\,? \ne 12\,\,\,\,\,\,\,\,\left( {a = \,13} \right) \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{INSUF}}{\text{.}}$$

$$\left( {1 + 2} \right)\,\,\,\,\,\left\{ \begin{gathered} {a^2} - {b^2} = 0\,\,\,\,\, \hfill \\ a - b = 12 \hfill \\ \end{gathered} \right. \Rightarrow \,\,\,\,\,\,\left\{ \begin{gathered} \left( {a + b} \right)\left( {a - b} \right) = 0 \hfill \\ a - b = 12 \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \begin{gathered} a + b = 0 \hfill \\ a - b = 12 \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,2a = 12\,\,\,\,\,\, \Rightarrow \,\,\,\,\,a\,\,{\text{unique}} \Rightarrow \,\,\,\,\,\,{\text{SUF}}{\text{.}}\,$$

The above follows the notations and rationale taught in the GMATH method.
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Re: What is the value of a ? &nbs [#permalink] 01 Sep 2018, 15:23
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