Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

stmt 1: says that n^2 is an integer. So n could be 4, which n^16 or n could be 5.477 and n^2 would be 30. This gives us two different options so insuff

stmt 2: says that sqrt n is an integer. that means n is the square of an (or integer x integer) which will always give you an integer. suff

Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]

Show Tags

20 Jun 2013, 15:07

Stament 1 : n^2=integer n=+/- sqrt(integer) => Sqrt of integer may or may not be integer depending on whether chose integer is perfect square or not. insufficient

Statement 2: sqrt (n) = integer => Squaring both sides => n= integer^2 = some other integer (as intg*intg=intg) = sufficient

\(\sqrt{3}=1.732050807568877293527446341505872366942805253810380628055806...\). It's an irrational number, it goes on forever. Anyway, what's your question?
_________________

\(\sqrt{3}=1.732050807568877293527446341505872366942805253810380628055806...\). It's an irrational number, it goes on forever. Anyway, what's your question?

How can square of non-integer be an integer? 1.73 is a non- integer and so is its square

\(\sqrt{3}=1.732050807568877293527446341505872366942805253810380628055806...\). It's an irrational number, it goes on forever. Anyway, what's your question?

How can square of non-integer be an integer? 1.73 is a non- integer and so is its square

The square root of 3 is a number which when squared gives 3.
_________________

Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]

Show Tags

21 Jul 2015, 21:29

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.
_________________

Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]

Show Tags

12 Sep 2015, 08:28

Statement 1 says \(n^2\) is an integer. According to the solution, \((\sqrt{2})^2\) is an integer. But \(\sqrt{2}\) is an irrational number which is equal to 1.41421356237 approx. And when we square it we would get 1.9999999 approx. We do not get an integer on squaring an irrational number but rather a value close to an integer. So, if we exclude irrational numbers, we should get integer value for \(\sqrt{n^2}\) For this reason, i marked D. Can someone please explain why is my thinking wrong and why are we taking approximate values ?

Statement 1 says \(n^2\) is an integer. According to the solution, \((\sqrt{2})^2\) is an integer. But \(\sqrt{2}\) is an irrational number which is equal to 1.41421356237 approx. And when we square it we would get 1.9999999 approx. We do not get an integer on squaring an irrational number but rather a value close to an integer. So, if we exclude irrational numbers, we should get integer value for \(\sqrt{n^2}\) For this reason, i marked D. Can someone please explain why is my thinking wrong and why are we taking approximate values ?

The square root of 2 is a number (whatever it is) which when squared gives 2.
_________________

Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]

Show Tags

04 Apr 2016, 14:00

1

This post received KUDOS

Bunuel wrote:

vwjetty wrote:

Is n an integer?

(1) n^2 is an integer

(2) n^(1/2) is an integer

Please explain. Thanks.

Is n an integer?

(1) n^2 is an integer --> not sufficient, as if \(n^2=4\) answer is YES, but if \(n^2=3\) answer is NO. <<<< n will be square root of the value. So it can be an integer or non-integer, depending on the value whether it is a perfect square or not. So, not sufficient.

(2) n^(1/2) is an integer --> \(\sqrt{n}=integer\) --> \(n=integer^2=integer\). Sufficient.

Answer: B.

I have added few more explanation for the 1st option, as i got this question wrong because of that problem. Hope you guys will not repeat the same mistake. #kudos
_________________

i.e. n^2 = 1, 2, 3, 4, 5.... i.e. \(n^2 = 1, \sqrt{2}, \sqrt{3}, 2, \sqrt{5}\).... NOT SIFFICIENT

Statement 2: \(\sqrt{n}\) = 1, 2, 3, 4, 5....

i.e. n = 1, 4, 9, 16, 25... SUFFICIENT

Answer: Option B
_________________

Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html

Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]

Show Tags

24 Jan 2017, 14:55

Bunuel wrote:

vwjetty wrote:

Is n an integer?

(1) n^2 is an integer

(2) n^(1/2) is an integer

Please explain. Thanks.

Is n an integer?

(1) n^2 is an integer --> not sufficient, as if \(n^2=4\) answer is YES, but if \(n^2=3\) answer is NO.

(2) n^(1/2) is an integer --> \(\sqrt{n}=integer\) --> \(n=integer^2=integer\). Sufficient.

Answer: B.

Actually why you dont ROOT both sides in (1)?

Is this because we dont know if integer is negative or not?

I mean n^2 = int and by ROOTING both sides you get n = sqrt(int) which then implies that since n can be any value is not sufficient (?). I find all this smart number approach unnecessary for this question.

Last edited by Ndkms on 25 Jan 2017, 07:34, edited 1 time in total.

(1) n^2 is an integer --> not sufficient, as if \(n^2=4\) answer is YES, but if \(n^2=3\) answer is NO.

(2) n^(1/2) is an integer --> \(\sqrt{n}=integer\) --> \(n=integer^2=integer\). Sufficient.

Answer: B.

Actually why you dont ROOT both sides in (1)?

Is this because we dont know if integer is negative or not?

I mean n^2 = int and by squaring both sides you get n = sqrt(int) which then implies that since n can be any value is not sufficient (?). I find all this smart number approach unnecessary for this question.

Your explanation is fine if you can easily understand n = sqrt(int) and sqrt(int) may or may NOT be an Integer therefore 1st statement is NOT SUFFICIENT

However it's not equally easy for everyone to understand as the natural bias of our mind makes us think that "if n is an integer then n^2 will also be an Integer therefore if n^2 is an Integer then n also must be an Integer"which would lead to incorrect answers.

Being a trainer I keep asking this question to the students and around 70% students get this question wrong who just begin to learn DS

Also, Smart Number approach is definitely a very good approach however the Smart number approach in isolation isn't as good enough in isolation as the Algebraic approach in isolation isn't good enough

I suggest that use of both Smart Number and Algebraic approach is the best way to perform best in any aptitude test.
_________________

Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html

Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]

Show Tags

25 Jan 2017, 07:43

GMATinsight wrote:

Your explanation is fine if you can easily understand n = sqrt(int) and sqrt(int) may or may NOT be an Integer therefore 1st statement is NOT SUFFICIENT

However it's not equally easy for everyone to understand as the natural bias of our mind makes us think that "if n is an integer then n^2 will also be an Integer therefore if n^2 is an Integer then n also must be an Integer"which would lead to incorrect answers.

Being a trainer I keep asking this question to the students and around 70% students get this question wrong who just begin to learn DS

Also, Smart Number approach is definitely a very good approach however the Smart number approach in isolation isn't as good enough in isolation as the Algebraic approach in isolation isn't good enough

I suggest that use of both Smart Number and Algebraic approach is the best way to perform best in any aptitude test.

Imho smart number approach for this question is risky and borderline waste of time.

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...