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# What is x - y?

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Math Expert
Joined: 02 Sep 2009
Posts: 49206
What is x - y?  [#permalink]

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25 Sep 2017, 23:52
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Difficulty:

45% (medium)

Question Stats:

62% (00:58) correct 38% (01:20) wrong based on 47 sessions

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What is x - y?

(1) x^2 - y^2 = 0
(2) The average of x^2 and y^2 is equal to the product of x and y.

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What is x - y?  [#permalink]

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25 Sep 2017, 23:59
What is x - y?

(1) x^2 - y^2 = 0
This could be possible for value x=y=1 and x=1, y=-1
The value for the expression x-y is different for both the combinations(Insufficient)

(2) The average of x^2 and y^2 is equal to the product of x and y.
If the average of $$x^2 and y^2$$ is equal to the the product of x,y
$$\frac{x^2 + y^2}{2} = xy => x^2 + y^2 = 2xy => x^2 + y^2 - 2xy = 0 => (x - y)^2 = 0$$

This is possible if and only if y = x. Hence, this statement alone is sufficient(Option B)
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What is x - y? &nbs [#permalink] 25 Sep 2017, 23:59
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