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# If x and y are positive integers, what is the value of x/y?

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Math Expert
Joined: 02 Sep 2009
Posts: 51214
If x and y are positive integers, what is the value of x/y?  [#permalink]

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11 Jun 2015, 02:57
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Difficulty:

35% (medium)

Question Stats:

69% (00:52) correct 31% (01:44) wrong based on 160 sessions

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If x and y are positive integers, what is the value of x/y?

(1) x^2 = 2xy – y^2
(2) 2xy = 8

Kudos for a correct solution.

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Joined: 12 Nov 2014
Posts: 63
Re: If x and y are positive integers, what is the value of x/y?  [#permalink]

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11 Jun 2015, 03:06
3
2
Stmt 1: x^2 = 2xy – y^2
x^2 - 2xy + y^2 = 0
(x-y)^2 = 0; x -y = 0; x =y
x/y = 1. Suff

Stmt 2: 2xy = 8
xy =4
No info can be deduced about x/y . Not suff

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Re: If x and y are positive integers, what is the value of x/y?  [#permalink]

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11 Jun 2015, 23:48
Bunuel wrote:
If x and y are positive integers, what is the value of x/y?

(1) x^2 = 2xy – y^2
(2) 2xy = 8

Kudos for a correct solution.

1:
$$x^2=2xy-y^2$$
$$x^2 - 2xy + y^2 = 0$$
$$(x-y)^2 = 0$$
$$x-y = 0$$
$$x=y$$
$$x/y=1$$ sufficient.

2:
$$2xy =8$$
$$xy=4$$
If $$x=1, y=4, x/y=1/4$$ but if $$x=4, y=1, x/y=4$$ so not sufficient.
Joined: 24 Oct 2012
Posts: 170
Re: If x and y are positive integers, what is the value of x/y?  [#permalink]

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16 Jun 2015, 09:23
Bunuel wrote:
If x and y are positive integers, what is the value of x/y?

(1) x^2 = 2xy – y^2
(2) 2xy = 8

Kudos for a correct solution.

Statement 1 :
X^2 = 2XY - Y^2
(X-Y)^2 = 0
X = Y

hence X/Y = 1, for all values of X and Y.
Statement 1 is sufficient

Statement 2:
XY = 4
multiple combination satisfy this condition
X =1, Y = 4 - > X/Y = 1/4
X = 2, Y = 2 -> X/Y = 1
X = 4, Y = 1 -> X/Y = 4

Hence Statement 2 is not sufficient.

Hence Option A is correct
Current Student
Joined: 12 Aug 2015
Posts: 2627
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If x and y are positive integers, what is the value of x/y?  [#permalink]

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29 Apr 2017, 16:49
We need x/y

Statement 1 => x^2=2xy-y^2
x^2+y^2-2xy=0
(x-y)^2=0
x-y=0
x=y

Hence x/y=1

Sufficient
Statement 2 =>
2xy=8
xy=4

(1,4)=> 1/4
(4,1)=> 4

Hence not sufficient

SMASH THAT A.

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Re: If x and y are positive integers, what is the value of x/y?  [#permalink]

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23 Nov 2018, 23:24
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Re: If x and y are positive integers, what is the value of x/y? &nbs [#permalink] 23 Nov 2018, 23:24
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# If x and y are positive integers, what is the value of x/y?

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