GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Oct 2019, 16:15

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 a and n are integers, and a^2 = 24n, then n must be

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

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
User avatar
Joined: 21 Oct 2013
Posts: 411
If a and n are integers, and a^2 = 24n, then n must be  [#permalink]

Show Tags

New post 29 Jun 2014, 09:47
1
11
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (01:28) correct 34% (01:39) wrong based on 239 sessions

HideShow timer Statistics

If a and n are integers, and a^2 = 24n, then n must be divisible by which of the following?

A. 2
B. 4
C. 12
D. 18
E. 24

OE
\(a^2\)=24n = 2·2·2·3·n to 2·2·2·3·2·3.
Intern
Intern
avatar
Joined: 28 Mar 2014
Posts: 19
Location: India
GPA: 3
WE: Business Development (Retail Banking)
Re: If a and n are integers, and a^2 = 24n, then n must be  [#permalink]

Show Tags

New post 29 Jun 2014, 10:06
a^2 = 24 n = 2^2 * 2 *3 * n. Since a & n are integers n should must contain at least one 2 and one 3. Option choice i) gives 2. Therefore i) is correct
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58396
Re: If a and n are integers, and a^2 = 24n, then n must be  [#permalink]

Show Tags

New post 29 Jun 2014, 12:35
goodyear2013 wrote:
If a and n are integers, and a^2 = 24n, then n must be divisible by which of the following?

A. 2
B. 4
C. 12
D. 18
E. 24

OE
\(a^2\)=24n = 2·2·2·3·n to 2·2·2·3·2·3.


Similar questions to practice:
if-n-is-a-positive-integer-and-n-2-is-divisible-by-96-then-127364.html
if-n-is-a-positive-integer-and-n-2-is-divisible-by-72-then-90523.html
a-certain-clock-marks-every-hour-by-striking-a-number-of-tim-91750.html
if-m-and-n-are-positive-integer-and-1800m-n3-what-is-108985.html
if-x-and-y-are-positive-integers-and-180x-y-100413.html
n-is-a-positive-integer-and-k-is-the-product-of-all-integer-104272.html
if-x-is-a-positive-integer-and-x-2-is-divisible-by-32-then-88388.html
if-n-and-y-are-positive-integers-and-450y-n-92562.html
if-5400mn-k-4-where-m-n-and-k-are-positive-integers-109284.html
if-n-and-y-are-positive-integers-and-450y-n-92562.html
if-n-and-y-are-positive-integers-and-450y-n-92562.html

Hope this helps.
_________________
Manager
Manager
avatar
Joined: 07 Dec 2009
Posts: 86
GMAT Date: 12-03-2014
GMAT ToolKit User
If a and n are integers, and a^2 = 24n, then n must be  [#permalink]

Show Tags

New post 07 Jul 2014, 14:47
hi,

shouldn't the answer be E ?

since a is an integer we need atleast one more 2 and 3. only with option E we get a= Integer.

With option a we will have a^2 = (2^3)*3*2. this way a is not an Integer... Where am I going wrong ?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58396
Re: If a and n are integers, and a^2 = 24n, then n must be  [#permalink]

Show Tags

New post 07 Jul 2014, 15:10
1
bhatiavai wrote:
hi,

shouldn't the answer be E ?

since a is an integer we need atleast one more 2 and 3. only with option E we get a= Integer.

With option a we will have a^2 = (2^3)*3*2. this way a is not an Integer... Where am I going wrong ?


The question asks about divisibility of n, not a.

If a and n are integers, and a^2 = 24n, then n must be divisible by which of the following?

A. 2
B. 4
C. 12
D. 18
E. 24

\(a^2 = 24n=4*6n\);
\(a = 2*\sqrt{6n}\).

From above the least positive value of n is 6 and if it is 6, then it's divisible only by option A (2).

Answer: A.

Hope it's clear.
_________________
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1747
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If a and n are integers, and a^2 = 24n, then n must be  [#permalink]

Show Tags

New post 07 Jul 2014, 21:35
\(a^2 = 24n\)

\(a^2 = 2^2 * 6 n\)

Least value of n to make "a" a perfect square is 6

Answer = A = 2
_________________
Kindly press "+1 Kudos" to appreciate :)
Intern
Intern
avatar
Joined: 30 Oct 2015
Posts: 9
GPA: 3.89
WE: Analyst (Consulting)
Re: If a and n are integers, and a^2 = 24n, then n must be  [#permalink]

Show Tags

New post 14 Nov 2015, 11:12
The biggest hint here but just be the answer choices. All of the answers are even, and thus also divisible by 2. Choice A is the only exclusive answer.
Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 357
Re: If a and n are integers, and a^2 = 24n, then n must be  [#permalink]

Show Tags

New post 30 Nov 2016, 09:33
If we break down 24 to show its prime factorization --> (2^3)(3) --> We see that we are missing 2 and 3 in order to great a perfect square.

2x3=6 = n

Since a is an integer, 6 is only divisible by 2 (it will give you an integer, not a fraction)

A.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13382
Re: If a and n are integers, and a^2 = 24n, then n must be  [#permalink]

Show Tags

New post 31 Oct 2018, 23:06
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: If a and n are integers, and a^2 = 24n, then n must be   [#permalink] 31 Oct 2018, 23:06
Display posts from previous: Sort by

If a and n are integers, and a^2 = 24n, then n must be

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





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