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# If x ≠ y, is x = 0? (1) xy = x^2 (2) y ≠ 0

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Math Expert
Joined: 02 Sep 2009
Posts: 58421
If x ≠ y, is x = 0? (1) xy = x^2 (2) y ≠ 0  [#permalink]

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27 Sep 2018, 05:53
00:00

Difficulty:

35% (medium)

Question Stats:

74% (01:04) correct 26% (01:12) wrong based on 82 sessions

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If x ≠ y, is x = 0?

(1) xy = x^2
(2) y ≠ 0

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Re: If x ≠ y, is x = 0? (1) xy = x^2 (2) y ≠ 0  [#permalink]

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27 Sep 2018, 06:27
Bunuel wrote:
If x ≠ y, is x = 0?

(1) xy = x^2
(2) y ≠ 0

Statement (1) xy = x^2 if and only if x=y or x=0. We know x ≠ y, so x must be 0. Sufficient

Statement (2) If y ≠ 0, then x could be 0. But it could also not be 0. Say y = 1 and x = 2. Not Sufficient

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Re: If x ≠ y, is x = 0? (1) xy = x^2 (2) y ≠ 0  [#permalink]

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27 Sep 2018, 10:07
Bunuel wrote:
If x ≠ y, is x = 0?

(1) xy = x^2
(2) y ≠ 0

(1) xy = x^2

This translates into x and y both being equal and the question mentioned that that is not the case. The only other way for this to be possible is when x = 0

SUFFICIENT

(2) y ≠ 0

Does not give anything about x.

INSUFFICIENT

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Re: If x ≠ y, is x = 0? (1) xy = x^2 (2) y ≠ 0  [#permalink]

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27 Sep 2018, 10:26
2
Statement 1)

X^2 = XY

x(x-y)= 0 leading to x = 0

Or x - y = 0 leading to x = y but we know from the question stem that x DOES NOT equal y so x must be equal to zero.

Statement 2) doesn’t provide any additional information.

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Re: If x ≠ y, is x = 0? (1) xy = x^2 (2) y ≠ 0  [#permalink]

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29 Sep 2018, 07:36
Bunuel wrote:
If x ≠ y, is x = 0?

(1) xy = x^2
(2) y ≠ 0

Statement 1:

$$xy = x^2$$

$$xy - x^2 = 0$$

x(y-x) = 0

x=0

or

y=x........not allowed as per the direction of the question.

So, sufficient.

Statement 2: y ≠ 0. No information about x. NOT sufficient.

Re: If x ≠ y, is x = 0? (1) xy = x^2 (2) y ≠ 0   [#permalink] 29 Sep 2018, 07:36
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