• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If x and y are positive, what is the value of y ? ##### This topic has 2 expert replies and 1 member reply ### Top Member ## If x and y are positive, what is the value of y ? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If x and y are positive, what is the value of y ? (1) xy is the square of an integer. (2) 600 percent of x equals 200 percent of y. OA E Source: Magoosh ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: If x and y are positive, what is the value of y ? (1) xy is the square of an integer. (2) 600 percent of x equals 200 percent of y. Source: Magoosh $x,y\,\, > 0\,\,$ $? = y$ LetÂ´s go straight to (1+2). Our BIFURCATION will guarantee that the correct answer is (E) immediately! $$\left( {1 + 2} \right)\,\,\,\,\left\{ \matrix{ \,xy = {M^2}\,,\,\,M\,\,{\mathop{\rm int}} \hfill \cr \,6x = 2y\,\,\, \Rightarrow \,\,\,y = 3x \hfill \cr} \right.\,\,\,\,\,\left( * \right)\,\,\,\,\,\,\,\,\,\left[ {\, \Rightarrow \,\,\,\,\,\,3{x^2} = {M^2}\,\,,\,\,\,M\,\,{\mathop{\rm int}} \,} \right]$$ $$\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {\sqrt 3 ,3\sqrt 3 } \right)\,\,\,\, \Rightarrow \,\,\,\,\,\left( * \right)\,\,\,{\rm{ok}}\,\,\,\, \Rightarrow \,\,\,\,\,y = 3\sqrt 3 \,\,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {2\sqrt 3 ,6\sqrt 3 } \right)\,\,\,\, \Rightarrow \,\,\,\,\,\left( * \right)\,\,\,{\rm{ok}}\,\,\,\, \Rightarrow \,\,\,\,\,y = 6\sqrt 3 \,\, \hfill \cr} \right.$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 966 messages Followed by: 2 members Top Reply What is the value of y? Statement 1 xy is the square of an integer. xy gives a perfect square if x and y are two integers it could be any positive number $$1,2,3,4,5$$ e.t.c if x and y are integers it will $$\ 1,4,9,16,25$$ $$\ 1,4,9,16,25$$ e.t.c . However, this doesn't mean that x=y $$\sin ce\ 4\cdot1=4,\ 2\cdot8=16\ e.t.c$$ $$hence\ Statement\ 1\ is\ INSUFFICIENT$$ Statement 2 $$600\%\ of\ \ x=200\%\ of\ y$$ $$\frac{600}{100}\cdot x=\frac{200}{100}\cdot y$$ $$y=3x$$ , This leaves with an unknown variable, hence $$statement\ 2\ is\ INSUFFICIENT$$ Statement 1 and 2 together if x and y are non integers then it could be any pair of number leaving us with many solutions. since the value of y is not definite. $$statement\ 1\ and\ \ 2 together\ are\ INSUFFICIENT$$ $$answer\ is\ option\ E$$ ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12827 messages Followed by: 1247 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorDC wrote: If x and y are positive, what is the value of y ? (1) xy is the square of an integer. (2) 600 percent of x equals 200 percent of y. Target question: What is the value of y? Given: x and y are positive Statement 1: xy is the square of an integer. There are several values of x and y that satisfy this condition. Here are two: Case a: x = 1 and y = 1. Here xy = (1)(1) = 1, which is the square of an integer. In this case y = 1 Case b: x = 2 and y = 2. Here xy = (2)(2) = 4, which is the square of an integer. In this case y = 2 Since we cannot answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: 600 percent of x equals 200 percent of y. So, 6x = 2y Divide both sides by 2 to get: 3x = y There are several values of x and y that satisfy this condition. Here are two: Case a: x = 1 and y = 3. In this case y = 3 Case a: x = 2 and y = 6. In this case y = 6 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that xy is the square of an integer. Statement 2 tells us that 3x = y Take statement 1 and replace y with 3x to get: x(3x) is the square of an integer. In other words, 3xÂ² is the square of an integer. There are several values of x that satisfy this condition. Here are two: Case a: x = âˆš3. This means 3xÂ² = 3(âˆš3)Â² = 9, and 9 is the square of an integer. From statement 2, if x = âˆš3, then y = 3âˆš3. Case b: x = 4âˆš3. This means 3xÂ² = 3(4âˆš3)Â² = 36, and 36 is the square of an integer. From statement 2, if x = 4âˆš3, then y = 12âˆš3. Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT Answer: E Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Get 300+ Practice Questions
25 Video lessons and 6 Webinars for FREE

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

### Top First Responders*

1 Jay@ManhattanReview 71 first replies
2 Brent@GMATPrepNow 67 first replies
3 GMATGuruNY 43 first replies
4 Ian Stewart 27 first replies
5 Scott@TargetTestPrep 18 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

221 posts
2 Max@Math Revolution

Math Revolution

93 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

90 posts
4 Jay@ManhattanReview

Manhattan Review

73 posts
5 GMATGuruNY

The Princeton Review Teacher

66 posts
See More Top Beat The GMAT Experts