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M32-10

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Math Expert
Joined: 02 Sep 2009
Posts: 54369

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17 Jul 2017, 05:26
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Difficulty:

45% (medium)

Question Stats:

47% (00:41) correct 53% (00:39) wrong based on 19 sessions

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What is the value of $$x^2 – y^2$$?

(1) $$|x| = |y|$$

(2) $$x^2 + y^2 = 0$$

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Math Expert
Joined: 02 Sep 2009
Posts: 54369

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17 Jul 2017, 05:27
Official Solution:

What is the value of $$x^2 – y^2$$?

(1) $$|x| = |y|$$

Square: $$x^2 = y^2$$

Re-arrange: $$x^2 – y^2=0$$. Sufficient.

(2) $$x^2 + y^2 = 0$$

We are given that the sum of two non-negative values is 0. This is only possible if both equal 0. Thus, $$x^2 = y^2=0$$ and therefore $$x^2 – y^2=0$$. Sufficient.

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Re M32-10   [#permalink] 17 Jul 2017, 05:27
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M32-10

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