• 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 ## Find the HCF ##### This topic has 2 expert replies and 0 member replies ## Find the HCF Given that the sum of two numbers is ab and their difference is 1/7 of their sum. Find their HCF. A)a+b B)(a-b)/ab C)(12/7)ab D)ab E)(6/7)ab OAE)(6/7)ab ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15313 messages Followed by: 1863 members Upvotes: 13060 GMAT Score: 790 None of the answer choices is correct. I believe that the problem should read as follows: Vikas Mishra wrote: Given that the sum of two numbers is ab and their difference is 1/7 of their sum. Find their HCF. A)a+b B)(a-b)/ab C)(12/7)ab D)ab E)(1/7)ab Since the difference of x and y is equal to 1/7 the sum of x and y, we get: x-y = (1/7)(x+y) 7x-7y = x+y 6x=8y 3x=4y x=(4/3)y. Let y=3, implying that x=4. In this case, ab = the sum of 4 and 3 = 7. Let a=1 and b=7, with the result that ab=7. The HCF (highest common factor) of 4 and 3 is 1. This is our target. Now plug a=1 and b=7 into the answers to see which yields our target of 1. Only E works: (1/7)ab = (1/7) = (1/7)(7) = 1. The correct answer is E. If we test any case in which x = (4/3)y, the HCF will always be (1/7)(x+y). If y=6 and x=8, then the HCF = (1/7)(8+6) = 2. If y=9 and x=12, then the HCF = (1/7)(12+9) = 3. If y=12 and x=16, then the HCF = (1/7)(16+12) = 4. Since ab = the sum of x and y, the OA must be (1/7)ab. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 12 Sep 2012 Posted: 2635 messages Followed by: 116 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 Here's what's happening algebraically. If we know that x - y = (x + y) / 7 then we know 7x - 7y = x + y 6x = 8y 3x = 4y x = (4/3)y The GCF of x and y is thus the GCF of (4/3)y and y. The GCF of any number is also a factor of the difference of the numbers, so it must be a factor of (1/3)y. Since (1/3)y = (1/7) * ((4/3)y + y) = (1/7) * (x + y), we're left with (1/7) * sum, or (1/7) * ab. Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

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

• 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

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

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

### Top First Responders*

1 Ian Stewart 64 first replies
2 Jay@ManhattanReview 53 first replies
3 Brent@GMATPrepNow 52 first replies
4 GMATGuruNY 28 first replies
5 Scott@TargetTestPrep 19 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

200 posts
2 Max@Math Revolution

Math Revolution

93 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

90 posts
4 Ian Stewart

GMATiX Teacher

71 posts
5 Rich.C@EMPOWERgma...

EMPOWERgmat

68 posts
See More Top Beat The GMAT Experts