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Math Expert V
Joined: 02 Sep 2009
Posts: 58390
2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 68% (02:08) correct 32% (02:19) wrong based on 305 sessions

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2y - x = 2xy and x ≠ 0. If x and y are integers, which of the following could equal y?

(A) 2
(B) 1
(C) 0
(D) -1
(E) - 2

Kudos for a correct solution.

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Math Expert V
Joined: 02 Aug 2009
Posts: 7961
Re: 2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin  [#permalink]

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1
Bunuel wrote:
2y - x = 2xy and x ≠ 0. If x and y are integers, which of the following could equal y?

(A) 2
(B) 1
(C) 0
(D) -1
(E) - 2

Kudos for a correct solution.

2y - x = 2xy ...
separate out x and y terms and find value of x in terms of y...
x=2y/(1+2y)..
now we know that x and y are int, so 2y/(1+2y) should be an int..
denominator is even and numerator is odd and next consecutive number..
in this case the values which should be checked are 0 and 1, since two consecutive numbers are involved ..
when y=0, x=0... which goes against the question.
when y=1, x=2/3.. no
when x=-1,x=-2/(1-2)=2.. this is what we are looking for...
we can also substitute value and check..
ans D
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Re: 2y - x = 2xy and x ≠ 0. If x and y are integers, which of the fo  [#permalink]

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1
Bunuel wrote:
2y - x = 2xy and x ≠ 0. If x and y are integers, which of the following could equal y?

(A) 2
(B) 1
(C) 0
(D) -1
(E) - 2

Kudos for a correct solution.

Plug in the answer choices in the equation from the question stem.

A) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE
B) y = 1 >>> 2 - x = 2x >>> Same, POE
C) y = 0 >>> -x = 0 >>> x can not equal 0
D) y = -1 >>> -2 - x = -2x >>> Holds true for x = 2, no need to check E. This is the answer.

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Manager  B
Joined: 26 Dec 2011
Posts: 115
Schools: HBS '18, IIMA
Re: 2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin  [#permalink]

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2
2y - x = 2xy and x ≠ 0. If x and y are integers, which of the following could equal y?

(A) 2
(B) 1
(C) 0
(D) -1
(E) - 2

Solution -
2y - x = 2xy, solving this equation interms of y -> y=x/2(1-x)

To get integer y, x must be 2 because of 2 in the denominator of above equation. Other values of x will lead y to decimal.

So for x=2, value of y=-1. ANS D.

Thanks

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Manager  B
Joined: 26 Dec 2012
Posts: 144
Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)
Re: 2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin  [#permalink]

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Rearranging the above equation we get
X= 2Y/(1+2Y)
As we know that X=not 0 and an integer, so by putting Y= 0,1,2,-2 X is not an integer . But only for Y=-1 X is an integer .

Hence answer is D

Thanks,
Math Expert V
Joined: 02 Sep 2009
Posts: 58390
Re: 2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin  [#permalink]

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Bunuel wrote:
2y - x = 2xy and x ≠ 0. If x and y are integers, which of the following could equal y?

(A) 2
(B) 1
(C) 0
(D) -1
(E) - 2

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

First, solve for x in terms of y, so that you can test values of y in the answer choices.

2y - x = 2xy;
x = 2y/(2y + 1)

Ordinarily, this result would not be enough for you to reach an answer. However, you know that both x and y must be integers. Therefore, you should find which integer value of y generates an integer value for x.

Now, test the possibilities for y, using the answer choices. The case y = 0 produces x = 0, but this outcome is disallowed by the condition that x ≠ 0 . The only other case that produces an integer value for x is = - 1, yielding x = 2.

Thus, the answer is (D).
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SVP  B
Joined: 06 Nov 2014
Posts: 1873
2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin  [#permalink]

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2y - x = 2xy and x ≠ 0. If x and y are integers, which of the following could equal y?

This equation can be rearranged to solve for x. x=2y/(2y+1). Then we can substitute the values for y in the answer choices. Only Choice D produces an integer for x.

(A) 2 x is a fraction
(B) 1 x is a fraction
(C) 0 x=0
(D) -1 x=2
(E) - 2 x is a fraction
Manager  S
Joined: 18 Oct 2016
Posts: 134
Location: India
WE: Engineering (Energy and Utilities)
Re: 2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin  [#permalink]

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Option D

x & y are integers such that 2y - x = 2xy & x # 0.

y = ?
x = 2y/(1+2y). Substitute y from options to find the one which gives integer as result.
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Target Test Prep Representative G
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Affiliations: Target Test Prep
Joined: 04 Mar 2011
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Re: 2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin  [#permalink]

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Bunuel wrote:
2y - x = 2xy and x ≠ 0. If x and y are integers, which of the following could equal y?

(A) 2
(B) 1
(C) 0
(D) -1
(E) - 2

Let’s first get all terms containing the variable y on one side of the equation, and then pull out the common factor 2y from those terms. Then we can easily solve for y itself.

2y - x = 2xy

2y - 2xy = x

2y(1 - x) = x

y = x/[2(1 - x)]

We see that if x = 2, then y = 2/[2(1 - 2)] = 2/-2 = -1.

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Manager  B
Joined: 19 Jul 2017
Posts: 83
Location: India
Concentration: General Management, Strategy
GPA: 3.5
2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin  [#permalink]

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x=2y/(1+2y)
Only when y=-1 get and Integer value x=2.
When y=0 ; x=0
when y=1,2,-2 x getting fractional value
Hence Option D
Non-Human User Joined: 09 Sep 2013
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Re: 2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin  [#permalink]

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_________________ Re: 2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin   [#permalink] 02 Oct 2018, 20:44
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