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

It is currently 20 May 2019, 10:52

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 the least common multiple of a positive integer x ,4^3 and 6^5 is 6

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

Hide Tags

 
Manager
Manager
User avatar
Joined: 04 Aug 2013
Posts: 96
Location: India
Schools: McCombs '17
GMAT 1: 670 Q47 V35
GPA: 3
WE: Manufacturing and Production (Pharmaceuticals and Biotech)
If the least common multiple of a positive integer x ,4^3 and 6^5 is 6  [#permalink]

Show Tags

New post 04 Dec 2014, 02:46
1
18
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

50% (02:08) correct 50% (02:18) wrong based on 122 sessions

HideShow timer Statistics

If the least common multiple of a positive integer x ,4^3 and 6^5 is 6^6. Then x can take how many values?

A 1
B 6
C 7
D 30
E 36
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55188
Re: If the least common multiple of a positive integer x ,4^3 and 6^5 is 6  [#permalink]

Show Tags

New post 04 Dec 2014, 04:17
4
2
anceer wrote:
If the least common multiple of a positive integer x ,4^3 and 6^5 is 6^6. Then x can take how many values?

A 1
B 6
C 7
D 30
E 36


If the least common multiple of a positive integer x, 4^3 and 6^5 is 6^6. Then x can take how many values?

A. 1
B. 6
C. 7
D. 30
E. 36

We are given that \(6^6=2^{6}*3^{6}\) is the least common multiple of the following three numbers:

x;
\(4^3=2^6\);
\(6^5 = 2^{5}*3^5\);

First notice that \(x\) cannot have any other primes other than 2 or/and 3, because LCM contains only these primes.

Now, since the power of 3 in LCM is higher than the powers of 3 in either the second number or in the third, than \(x\) must have \(3^{6}\) as its multiple (else how \(3^{6}\) would appear in LCM?).

Next, \(x\) can have 2 as its prime in ANY power ranging from 0 to 6, inclusive (it cannot have higher power of 2 since LCM limits the power of 2 to 6).

Thus, \(x\) could take total of 7 values.

Answer: C.
_________________
General Discussion
Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 274
Re: If the least common multiple of a positive integer x ,4^3 and 6^5 is 6  [#permalink]

Show Tags

New post 04 Dec 2014, 03:53
2
anceer wrote:
If the least common multiple of a positive integer x ,4^3 and 6^5 is 6^6. Then x can take how many values?

A 1
B 6
C 7
D 30
E 36


\(4^3=2^6\), \(6^5= 2^5.3^5\)

now if the power of 3 in x is less than 6, then l.c.m will have \(3^5\)in it.
if the power of 3 in x is more than 6, then l.c.m will have a term more than \(3^6\).

thus x must have \(3^6\) in it, and x cannot have any prime number other than 2 and 3. why ?? because in that case l.c.m won't be \(6^6\).
Also, maximum power of 2 that x can contain is 6. thus power of 2 in x can vary from 2^0 to 2^6. this gives us 7 possible cases. which are \(2^0.3^6,2^1.3^6,2^2.3^6,2^3.3^6,2^4,3^6,2^5.3^6,2^6.3^6\)

hence answer is C
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 10959
Re: If the least common multiple of a positive integer x ,4^3 and 6^5 is 6  [#permalink]

Show Tags

New post 06 Apr 2019, 02:26
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 the least common multiple of a positive integer x ,4^3 and 6^5 is 6   [#permalink] 06 Apr 2019, 02:26
Display posts from previous: Sort by

If the least common multiple of a positive integer x ,4^3 and 6^5 is 6

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.