Join us for MBA Spotlight – The Top 20 MBA Fair      Schedule of Events | Register

It is currently 06 Jun 2020, 06:31

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

If N is a positive integer, is N^3/4 an integer?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Director
Director
avatar
V
Joined: 18 Feb 2019
Posts: 783
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
If N is a positive integer, is N^3/4 an integer?  [#permalink]

Show Tags

New post Updated on: 10 Jun 2019, 22:50
10
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

62% (01:55) correct 38% (01:53) wrong based on 131 sessions

HideShow timer Statistics

If N is a positive integer, is (N^3)/4 an integer?

I. N^2 + 3 is a prime number.
II. N is the number of odd factors of 6.

Originally posted by kiran120680 on 09 Jun 2019, 09:18.
Last edited by kiran120680 on 10 Jun 2019, 22:50, edited 1 time in total.
GMAT Tutor
avatar
P
Joined: 24 Jun 2008
Posts: 2122
Re: If N is a positive integer, is N^3/4 an integer?  [#permalink]

Show Tags

New post 09 Jun 2019, 10:40
2
1
Strange question. If n is even, n^3 will be divisible by 2^3, so it will definitely be divisible by 2^2, and n^3/4 will be an integer. If n is odd, then n^3 won't even be divisible by 2, so n^3/4 certainly won't be an integer. So the question is just asking "is n even?"

Using Statement 1, n^2 + 3 can never equal 2 (since then n^2 would be negative, which is impossible). So if n^2 + 3 is a prime, n^2 + 3 must be an odd prime, and n^2 must be even, so n is even, and Statement 1 is sufficient.

Statement 2 unambiguously tells us the numerical value of n, so it has to be sufficient; there's no reason to spend any time actually working out what n is. So the answer is D.
_________________
GMAT Tutor in Montreal

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Intern
Intern
avatar
B
Joined: 07 Jun 2019
Posts: 14
Re: If N is a positive integer, is N^3/4 an integer?  [#permalink]

Show Tags

New post 10 Jun 2019, 08:30
The 2nd condition tells me N = 2 and it is sufficient clearly.
But I don't get why the 1st condition is sufficient.
I can see that N must be even but I don't understand how it helps to get an answer.
I would appreciate if anyone gives me any explanation.
Intern
Intern
avatar
S
Joined: 03 Aug 2009
Posts: 24
Re: If N is a positive integer, is N^3/4 an integer?  [#permalink]

Show Tags

New post 08 Aug 2019, 04:53
Lilyj, let me try to help you

\(\frac{N^{3}}{4}\) to be an integer, N has to even. Why? because \(Odd*Odd*Odd = Odd\). If n is even \(=> N^{2}\) is even.

Statement 1 says that \(N^{2} + 3\) is a prime number. All prime numbers, except 2, are odd.
Let \(N^{2} + 3 = X\). If \(X=2 => N^{2} + 3 = 2=> N^{2} = -1\), which is impossible as original statement says that N is a positive integer. Therefore, X has to be odd.
3 is Odd => \(N^{2}+Odd = Odd\). The only way previous equation to hold true is for \(N^{2}\) to be Even (Even+Odd=Odd).

As we needed to prove that \(N^{2}\) is even, statement 1 is sufficient.

Hope this helps.
Intern
Intern
avatar
B
Joined: 03 Oct 2016
Posts: 1
Re: If N is a positive integer, is N^3/4 an integer?  [#permalink]

Show Tags

New post 18 Aug 2019, 03:09
kiran120680 wrote:
If N is a positive integer, is (N^3)/4 an integer?

I. N^2 + 3 is a prime number.
II. N is the number of odd factors of 6.


Pl explain what does statement II means?
Intern
Intern
avatar
B
Joined: 16 Jul 2019
Posts: 1
Re: If N is a positive integer, is N^3/4 an integer?  [#permalink]

Show Tags

New post 18 Aug 2019, 11:20
Can anyone please explain what does second statement mean?

Posted from my mobile device
Intern
Intern
avatar
S
Joined: 11 Jun 2019
Posts: 34
Location: India
Re: If N is a positive integer, is N^3/4 an integer?  [#permalink]

Show Tags

New post 18 Aug 2019, 11:53
Hi,
2nd statement says N= number of odd factors of 6. Now we know that 6 has 4 factors (1,2,3,6) out of which 2 are odd. Hence N=2.which is sufficient to answer the question

Posted from my mobile device
Senior Manager
Senior Manager
avatar
P
Joined: 27 Feb 2014
Posts: 277
Location: India
Concentration: General Management, International Business
GMAT 1: 570 Q49 V20
GPA: 3.97
WE: Engineering (Education)
Re: If N is a positive integer, is N^3/4 an integer?  [#permalink]

Show Tags

New post 19 Aug 2019, 01:43
kiran120680 wrote:
If N is a positive integer, is (N^3)/4 an integer?

I. N^2 + 3 is a prime number.
II. N is the number of odd factors of 6.


is (N^3)/4 an integer OR Is N divisible by 2?

(1) N^2 + 3 is a prime number, only possible when N=2. Sufficient.

(2) N is the number of odd factors of 6, there are 2 factors of 6 which are odd. Sufficient.

D is correct.
_________________
Inspired by great content in some best books on GMAT, I have created my own YouTube channel-QUANT MADE EASY! I would love some support and feedback. Please hit subscribe and check it out!

https://www.youtube.com/channel/UCvdY0kJNbnJzPEOsT5PMFRQ
GMAT Club Bot
Re: If N is a positive integer, is N^3/4 an integer?   [#permalink] 19 Aug 2019, 01:43

If N is a positive integer, is N^3/4 an integer?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne