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If x = a/2 = 3b, what is the value of a^2 - b^2?

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If x = a/2 = 3b, what is the value of a^2 - b^2?  [#permalink]

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New post 17 Oct 2019, 02:08
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  35% (medium)

Question Stats:

71% (01:32) correct 29% (01:03) wrong based on 23 sessions

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If x = a/2 = 3b, what is the value of a^2 - b^2?  [#permalink]

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New post 17 Oct 2019, 03:20
Bunuel wrote:
If \(x = \frac{a}{2} = 3b\), what is the value of \(a^2 - b^2\)?


(1) \(\frac{x^3}{27} = -1\)

(2) \(|x| = 3\)



Asked: If \(x = \frac{a}{2} = 3b\), what is the value of \(a^2 - b^2\)?
\(a = 2x; b = \frac{x}{3};\)
\(a^2 - b^2 = 4x^2 - \frac{x^2}{9} = \frac{35x^2}{9}\)

(1) \(\frac{x^3}{27} = -1\)
\(\frac{x}{3} = -1\)
x = -3
\(a^2 - b^2 = 4x^2 - \frac{x^2}{9} = \frac{35x^2}{9} = \frac{35(-3)^2}{9} = 35\)
SUFFICIENT

(2) \(|x| = 3\)
\(a^2 - b^2 = 4x^2 - \frac{x^2}{9} = \frac{35x^2}{9} = \frac{35*3^2}{9} = 35\)
SUFFICIENT

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If x = a/2 = 3b, what is the value of a^2 - b^2?   [#permalink] 17 Oct 2019, 03:20
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