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

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Math Expert
Joined: 02 Sep 2009
Posts: 58428
If x ≠ y, is x + y − xy = 0? (1) (1 − x)(1 − y) = 1 (2) (x + y)(x − y  [#permalink]

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30 Oct 2018, 04:18
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Difficulty:

35% (medium)

Question Stats:

70% (01:32) correct 30% (02:22) wrong based on 48 sessions

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If x ≠ y, is x + y − xy = 0?

(1) (1 − x)(1 − y) = 1
(2) (x + y)(x − y) = xy(x − y)

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Joined: 12 Sep 2015
Posts: 4017
Re: If x ≠ y, is x + y − xy = 0? (1) (1 − x)(1 − y) = 1 (2) (x + y)(x − y  [#permalink]

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30 Oct 2018, 08:02
Top Contributor
Bunuel wrote:
If x ≠ y, is x + y − xy = 0?

(1) (1 − x)(1 − y) = 1
(2) (x + y)(x − y) = xy(x − y)

Given: x ≠ y

Target question: Is x + y − xy = 0?

Statement 1: (1 − x)(1 − y) = 1
Use FOIL to expand left side: 1 - y - x + xy = 1
Subtract 1 from both sides to get: -y - x + xy = 0
Multiply both sides by -1 to get: (-1)(-y - x + xy) = (-1)(0)
Simplify: y + x - xy = 0
PERFECT
The answer to the target question is YES, x + y − xy DOES equal 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: (x + y)(x − y) = xy(x − y)
Since we're told x ≠ y, we know that (x - y) ≠ 0, which means we can safely divide both sides by (x -y)
When we do so, we get: x + y = xy
Subtract xy from both sides to get: x + y - xy = 0
PERFECT
The answer to the target question is YES, x + y − xy DOES equal 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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

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31 Oct 2018, 03:17
Bunuel wrote:
If x ≠ y, is x + y − xy = 0?

(1) (1 − x)(1 − y) = 1
(2) (x + y)(x − y) = xy(x − y)

Given

x + y - xy = 0

x + y = xy

Statement 1:

(1 − x)(1 − y) = 1

1 - y -x + xy = 1

- y - x + xy =0

xy = x + y.

Sufficient.

Statement 2:

(x + y ) ( x - y ) = xy ( x - y)

x + y = xy

Sufficient .

Re: If x ≠ y, is x + y − xy = 0? (1) (1 − x)(1 − y) = 1 (2) (x + y)(x − y   [#permalink] 31 Oct 2018, 03:17
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