Last visit was: 14 Jun 2024, 03:17 It is currently 14 Jun 2024, 03:17
Close
GMAT Club Daily Prep
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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Difficulty: 555-605 Level,    Number Properties,                      
Show Tags
Hide Tags
User avatar
Retired Moderator
Joined: 25 Apr 2010
Status:battlecruiser, operational...
Posts: 897
Own Kudos [?]: 526 [130]
Given Kudos: 71
Schools: Carey '16
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 93707
Own Kudos [?]: 631622 [41]
Given Kudos: 82302
Send PM
General Discussion
User avatar
Retired Moderator
Joined: 25 Apr 2010
Status:battlecruiser, operational...
Posts: 897
Own Kudos [?]: 526 [1]
Given Kudos: 71
Schools: Carey '16
Send PM
User avatar
Manager
Manager
Joined: 25 Sep 2012
Posts: 204
Own Kudos [?]: 562 [1]
Given Kudos: 242
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Send PM
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
1
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.

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

Answer: B.


If we take \(\sqrt{3}\) = 1.732050807568877
and square it, we still get 2.999999999999
which is not an integer. That's the reason I marked D :( :roll:

Originally posted by b2bt on 30 May 2014, 02:27.
Last edited by b2bt on 30 May 2014, 04:59, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 93707
Own Kudos [?]: 631622 [0]
Given Kudos: 82302
Send PM
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
Expert Reply
b2bt wrote:
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.


If we take \sqrt{3} = 1.732050807568877
and square it, we still get 2.999999999999
which is not an integer. That's the reason I marked D :( :roll:


Writing Mathematical Formulas on the Forum: rules-for-posting-please-read-this-before-posting-133935.html#p1096628 Please read.

\(\sqrt{3}=1.732050807568877293527446341505872366942805253810380628055806...\). It's an irrational number, it goes on forever. Anyway, what's your question?
User avatar
Manager
Manager
Joined: 25 Sep 2012
Posts: 204
Own Kudos [?]: 562 [0]
Given Kudos: 242
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Send PM
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
Quote:

Writing Mathematical Formulas on the Forum: rules-for-posting-please-read-this-before-posting-133935.html#p1096628 Please read.

\(\sqrt{3}=1.732050807568877293527446341505872366942805253810380628055806...\). 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
Math Expert
Joined: 02 Sep 2009
Posts: 93707
Own Kudos [?]: 631622 [0]
Given Kudos: 82302
Send PM
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
Expert Reply
b2bt wrote:
Quote:

Writing Mathematical Formulas on the Forum: rules-for-posting-please-read-this-before-posting-133935.html#p1096628 Please read.

\(\sqrt{3}=1.732050807568877293527446341505872366942805253810380628055806...\). 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.
User avatar
Manager
Manager
Joined: 29 Jul 2015
Posts: 144
Own Kudos [?]: 647 [0]
Given Kudos: 59
Send PM
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
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 ?
Math Expert
Joined: 02 Sep 2009
Posts: 93707
Own Kudos [?]: 631622 [1]
Given Kudos: 82302
Send PM
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
1
Kudos
Expert Reply
kunal555 wrote:
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.
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6012
Own Kudos [?]: 13613 [3]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
2
Kudos
1
Bookmarks
Expert Reply
vwjetty wrote:
Is n an integer?

(1) n^2 is an integer

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


Statement 1: n^2 = Integer

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
Intern
Intern
Joined: 09 Aug 2016
Posts: 42
Own Kudos [?]: 66 [0]
Given Kudos: 8
Send PM
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
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.

Originally posted by Ndkms on 24 Jan 2017, 14:55.
Last edited by Ndkms on 25 Jan 2017, 07:34, edited 1 time in total.
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6012
Own Kudos [?]: 13613 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
Expert Reply
Ndkms wrote:
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 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.
Intern
Intern
Joined: 12 Nov 2014
Posts: 13
Own Kudos [?]: 44 [0]
Given Kudos: 923
Send PM
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
Hi, Bunel how could n2 could be 3 in your assumption. I think it has to be 1,2,4,9 which is sufficient.
Math Expert
Joined: 02 Sep 2009
Posts: 93707
Own Kudos [?]: 631622 [0]
Given Kudos: 82302
Send PM
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
Expert Reply
alice7 wrote:
Hi, Bunel how could n2 could be 3 in your assumption. I think it has to be 1,2,4,9 which is sufficient.


Why cannot n^2 be 3? In this case \(n=\sqrt{3}\) or \(-\sqrt{3}\), so in this case n is an irrational number.

For more on number theory (for example on irrational numbers) check the following link: https://gmatclub.com/forum/math-number- ... 88376.html

Hope it helps.
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3042
Own Kudos [?]: 6449 [0]
Given Kudos: 1646
Send PM
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
Expert Reply
vwjetty wrote:
Is n an integer?

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

(2) \(\sqrt{n}\) is an integer


We need to determine whether n is an integer.

Statement One Alone:

n^2 is an integer.

If n^2 is an integer, n may or may not be an integer. For instance, if n^2 = 4, then n is an integer (since n = 2 or -2). However, if n^2 = 5, then n is not an integer (since n = √5 or -√5). Statement one is not sufficient to answer the question.

Statement Two Alone:

√n is an integer.

In order for √n to be an integer, n must be an integer. This is because n = (√n)^2, and any integer squared is also an integer. Statement two is sufficient to answer the question.

Answer: B
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6012
Own Kudos [?]: 13613 [1]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
1
Bookmarks
Expert Reply
vwjetty wrote:
Is n an integer?

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

(2) \(\sqrt{n}\) is an integer


A proper way to answer any DS question

Check the video solution of this question

Like the youtube video and subscribe to page if you find useful :)

Senior Manager
Senior Manager
Joined: 25 Aug 2020
Posts: 251
Own Kudos [?]: 129 [0]
Given Kudos: 218
Send PM
Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
vwjetty wrote:
Is n an integer?

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

(2) \(\sqrt{n}\) is an integer


Interesting but cunning question :)
Statement 1
( \(\sqrt{2} \))^2 = 2 yet, \(\sqrt{2}\) is not an integer
Conversely, 2^2 =4 and 2 is an integer.

Statement 2
is sufficient by its own.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33550
Own Kudos [?]: 837 [0]
Given Kudos: 0
Send PM
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
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.
GMAT Club Bot
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink]
Moderator:
Math Expert
93707 posts