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2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin

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Bunuel
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2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin [#permalink] New post   24 Jun 2015, 00:04
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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



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D
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Re: 2y - x = 2xy and x ≠ 0. If x and y are integers, which of the fo [#permalink] New post   24 Jun 2015, 06:46
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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.


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.

Answer D
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Re: 2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin [#permalink] New post   24 Jun 2015, 00:48
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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.


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 followin [#permalink] New post   24 Jun 2015, 07:50
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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

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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Re: 2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin [#permalink] New post   24 Jun 2015, 09:53
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

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Re: 2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin [#permalink] New post   29 Jun 2015, 05:54
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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



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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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2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin [#permalink] New post   01 Jul 2015, 01:05
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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
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Re: 2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin [#permalink] New post   17 Apr 2017, 05:22
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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Re: 2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin [#permalink] New post   20 Apr 2017, 16:42
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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.

Answer: D
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2y - x = 2xy and x ≠ 0. If x and y are integers, which of the followin [#permalink] New post   27 Aug 2017, 23:54
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
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Re: 2y - x = 2xy and x 0. If x and y are integers, which of the followin [#permalink] New post   11 Dec 2023, 06:53
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