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2y  x = 2xy and x ≠ 0. If x and y are integers, which of the followin
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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 Kudos for a correct solution.
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Re: 2y  x = 2xy and x ≠ 0. If x and y are integers, which of the followin
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24 Jun 2015, 00:48
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/(12)=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
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24 Jun 2015, 06:46
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 >>> 4x = 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
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24 Jun 2015, 07:50
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(1x) 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 Kudos Please.
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Re: 2y  x = 2xy and x ≠ 0. If x and y are integers, which of the followin
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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
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29 Jun 2015, 05:54
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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2y  x = 2xy and x ≠ 0. If x and y are integers, which of the followin
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01 Jul 2015, 01:05
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
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17 Apr 2017, 05:22
Option Dx & 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
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20 Apr 2017, 16:42
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
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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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