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

Question

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

reto · Accepted Answer

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

chetan2u · Answer

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

balamoon · Answer

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

lipsi18 · Answer

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,

Bunuel · Answer

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).

OptimusPrepJanielle · Answer

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

RR88 · Answer

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.

JeffTargetTestPrep · Answer

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/

We see that if x = 2, then y = 2/  = 2/-2 = -1.

Answer: D

Arsh4MBA · Answer

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

ablatt4 · Answer

Would try plugging in Y as each of the values here and you will quickly find only y=-1 leads x to being an integer.

D

Advait01 · Answer

I tried it by using Y = X/(2*(1-X))
Here i took X=1 and got Y=0
So C
Can anyone tell me where i went wrong??

Bunuel · Answer

If you plug x = 1 into 2y - x = 2xy, you get 2y - 1 = 2y, which gives -1 = 0, which is obviously false.

If you rearrange the way you did and get y = x/(2 - 2x), plugging x = 1 gives y = 1/0, which is undefined because we cannot divide by 0, not equal 0 as you got.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards