February 17, 2019 February 17, 2019 07:00 AM PST 09:00 AM PST Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT. February 18, 2019 February 18, 2019 10:00 PM PST 11:00 PM PST We don’t care what your relationship status this year  we love you just the way you are. AND we want you to crush the GMAT!
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52906

2y  x = 2xy and x ≠ 0. If x and y are integers, which of the followin
[#permalink]
Show Tags
23 Jun 2015, 23:04
Question Stats:
69% (02:07) correct 31% (02:20) wrong based on 286 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Aug 2009
Posts: 7334

Re: 2y  x = 2xy and x ≠ 0. If x and y are integers, which of the followin
[#permalink]
Show Tags
23 Jun 2015, 23:48
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
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentageincreasedecreasewhatshouldbethedenominator287528.html
GMAT Expert



Retired Moderator
Joined: 29 Apr 2015
Posts: 838
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: 2y  x = 2xy and x ≠ 0. If x and y are integers, which of the fo
[#permalink]
Show Tags
24 Jun 2015, 05:46
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
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.



Manager
Joined: 26 Dec 2011
Posts: 114

Re: 2y  x = 2xy and x ≠ 0. If x and y are integers, which of the followin
[#permalink]
Show Tags
24 Jun 2015, 06:50
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.
_________________
Thanks, Kudos Please



Manager
Joined: 26 Dec 2012
Posts: 146
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]
Show Tags
24 Jun 2015, 08:53
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
Thanks,



Math Expert
Joined: 02 Sep 2009
Posts: 52906

Re: 2y  x = 2xy and x ≠ 0. If x and y are integers, which of the followin
[#permalink]
Show Tags
29 Jun 2015, 04:54
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).
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



SVP
Joined: 06 Nov 2014
Posts: 1877

2y  x = 2xy and x ≠ 0. If x and y are integers, which of the followin
[#permalink]
Show Tags
01 Jul 2015, 00:05
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



Manager
Joined: 18 Oct 2016
Posts: 139
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]
Show Tags
17 Apr 2017, 04:22
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.
_________________
Press Kudos if you liked the post!
Rules for posting  PLEASE READ BEFORE YOU POST



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827

Re: 2y  x = 2xy and x ≠ 0. If x and y are integers, which of the followin
[#permalink]
Show Tags
20 Apr 2017, 15:42
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
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 19 Jul 2017
Posts: 85
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]
Show Tags
27 Aug 2017, 22:54
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



NonHuman User
Joined: 09 Sep 2013
Posts: 9836

Re: 2y  x = 2xy and x ≠ 0. If x and y are integers, which of the followin
[#permalink]
Show Tags
02 Oct 2018, 19:44
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: 2y  x = 2xy and x ≠ 0. If x and y are integers, which of the followin
[#permalink]
02 Oct 2018, 19:44






