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# If x ≠ y, is x + y = xy?

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Math Expert
Joined: 02 Sep 2009
Posts: 47184
If x ≠ y, is x + y = xy?  [#permalink]

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11 Nov 2017, 09:39
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Difficulty:

35% (medium)

Question Stats:

73% (00:56) correct 27% (01:41) wrong based on 45 sessions

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If x ≠ y, is x + y = xy?

(1) $$(1 - x)(1 - y) = 1$$

(2) $$x^2 - y^2 = x^2y - xy^2$$

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Math Expert
Joined: 02 Aug 2009
Posts: 6280
Re: If x ≠ y, is x + y = xy?  [#permalink]

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11 Nov 2017, 09:59
Bunuel wrote:
If x ≠ y, is x + y = xy?

(1) $$(1 - x)(1 - y) = 1$$

(2) $$x^2 - y^2 = x^2y - xy^2$$

(1) $$(1 - x)(1 - y) = 1$$.
$$-x-y+1+xy=1...........xy=x+y$$
suff

(2) $$x^2 - y^2 = x^2y - xy^2$$.
$$(x-y)(x+y)=xy(x-y)..................(x-y)(x+y-xy)=0$$
so either x=y or xy=x+y
since x ≠ y, xy=x+y
suff

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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If x ≠ y, is x + y = xy?  [#permalink]

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11 Nov 2017, 10:19
1
1) 1-y-x+xy=1
xy=1-1+x+y
=> xy=x+y -> sufficient
2)(x-y)(x+y)=xy(x-y)
=> x+y=xy -> sufficient
=> D
If x ≠ y, is x + y = xy? &nbs [#permalink] 11 Nov 2017, 10:19
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