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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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New post Updated on: 03 Apr 2013, 09:42
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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, 09:21.
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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New post 03 Apr 2013, 09:48
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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.

Answer: C.
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New post 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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New post 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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New post 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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New post 01 Sep 2018, 10:12
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

Hence, C is our answer.
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Re: What is the value of a ?  [#permalink]

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New post 01 Sep 2018, 16:23
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 ?   [#permalink] 01 Sep 2018, 16:23
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