• 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 ## x/y=5.35 If x and y are positive integers, then what is the tagged by: Mo2men ##### This topic has 1 expert reply and 0 member replies ## x/y=5.35 If x and y are positive integers, then what is the x/y=5.35 and If x and y are positive integers, then what is the value of x? (1) When y is divided by x, the remainder is 20. (2) When x is divided by y, the remainder is 7. OA: D Source: Economist ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1616 messages Followed by: 27 members Upvotes: 470 Mo2men wrote: x/y=5.35 and If x and y are positive integers, then what is the value of x? (1) When y is divided by x, the remainder is 20. (2) When x is divided by y, the remainder is 7. OA: D Source: Economist We are given that x/y = 5.35 and x and y are positive integers. We have to determine the value of x. x/y = 5.35 => x/y = 535/100 = 107/20; after cancelling 535 and 100 by 5. => 107 and 20 would be the multiples of the same common factor. Say the common factor is n, then we have x/y = (107n) / (20n). If we get the value of n, we would get the value of x = 107n. Let's take each statement one by one. (1) When y is divided by x, the remainder is 20. => y = xq + 20 => 20n = (107n)q + 20; where q is the quotient => n(20 - 107q) = 20 Since n is postive quality, (20 - 107q) must be positive. Since q is a non-negative integer, q = 0. => n*(20 - 0) = 20 => 20n = 20 => n = 1. Thus, x = 107n = 107*1 = 107. Sufficient. (2) When x is divided by y, the remainder is 7. => 107n = (20n)q + 7 => n(107 - 20q) = 7 We see that 7, a prime number, is a product of two positive integers n and (107 - 20q). Thus, one between n and (107 - 20q) should be 1 and the other 7, Case 1: Say n = 7 and 107 - 20q = 1 => q = 106/20 = fraction. It's not possible as q is an integer. Case 2: Say n = 1 and 107 - 20q = 7 => q = 100/20 = 5. It's possible as q is an integer. => n = 1. Thus, x = 107n = 107*1 = 107. Sufficient. The correct answer: D Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: New York | Singapore | Doha | Lausanne | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • Free Veritas GMAT Class Experience Lesson 1 Live Free 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 GMAT Exam Know how you'd score today for$0

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

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

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

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

### Top First Responders*

1 fskilnik@GMATH 62 first replies
2 Brent@GMATPrepNow 62 first replies
3 Jay@ManhattanReview 50 first replies
4 GMATGuruNY 35 first replies
5 Rich.C@EMPOWERgma... 25 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik@GMATH

GMATH Teacher

126 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

99 posts
3 Max@Math Revolution

Math Revolution

90 posts
4 Jay@ManhattanReview

Manhattan Review

84 posts
5 Rich.C@EMPOWERgma...

EMPOWERgmat

63 posts
See More Top Beat The GMAT Experts