• 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 ## Is n an integer? tagged by: Vincen ##### This topic has 1 expert reply and 0 member replies ## Is n an integer? Is n an integer? $$(1)\ \ \ 3n^2\ is\ an\ integer.$$ $$(2)\ \ \frac{\sqrt{n}}{3}\ is\ an\ \ integer.$$ Experts, is not sufficient the statement (1)? Why not? Also, how can I use the statement (2) to get an answer? Can you clarify this for me? Thanks in advanced. ### GMAT/MBA Expert Legendary Member Joined 20 Jul 2017 Posted: 503 messages Followed by: 10 members Upvotes: 86 GMAT Score: 770 Statement 1 Let's try an example where 3n^2 is an integer: we'll let $$3n^2=1$$ Solving for n gives $$n^2=\frac{1}{3}$$ $$n=\frac{1}{\sqrt{3}}$$ This is not an integer. Insufficient. Statment 2 We know $$\frac{\sqrt{n}}{3}=integer$$ Multiplying an integer by another integer will always give an integer, so if we multiply both sides by 3 $$\sqrt{n}=3\left(integer\right)$$ $$\sqrt{n}=integer$$ Squaring an integer is that same as multiplying that integer by itself. So again, we're multiplying an integer by an integer, which will always give an integer. So if we square both sides $$n=integer^2$$ $$n=integer$$ So n will always be an integer. Sufficient. _________________ Erika John - Content Manager/Lead Instructor https://gmat.prepscholar.com/gmat/s/ Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/ Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog • 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

• FREE GMAT Exam
Know how you'd score today for \$0

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

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

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 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

• Get 300+ Practice Questions

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

### Top First Responders*

1 Brent@GMATPrepNow 69 first replies
2 fskilnik@GMATH 54 first replies
3 Jay@ManhattanReview 48 first replies
4 GMATGuruNY 35 first replies
5 Rich.C@EMPOWERgma... 31 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

128 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

101 posts
3 Max@Math Revolution

Math Revolution

92 posts
4 Jay@ManhattanReview

Manhattan Review

86 posts
5 Rich.C@EMPOWERgma...

EMPOWERgmat

78 posts
See More Top Beat The GMAT Experts