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

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Joined: 02 Sep 2009
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If x = a/2 = 3b, what is the value of a^2 - b^2?  [#permalink]

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17 Oct 2019, 02:08
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Difficulty:

35% (medium)

Question Stats:

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

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If $$x = \frac{a}{2} = 3b$$, what is the value of $$a^2 - b^2$$?

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

(2) $$|x| = 3$$

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

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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

IMO D
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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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