Find all School-related info fast with the new School-Specific MBA Forum

It is currently 24 May 2016, 03:33
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the prime numbers p and t are the only prime factors of

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

Hide Tags

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9607
Followers: 465

Kudos [?]: 120 [0], given: 0

Premium Member
Re: If the prime numbers p and t are the only prime factors of [#permalink]

Show Tags

New post 17 Aug 2014, 08:59
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Manager
Manager
User avatar
Joined: 22 Feb 2009
Posts: 230
Followers: 5

Kudos [?]: 93 [0], given: 148

GMAT ToolKit User
Re: If the prime numbers p and t are the only prime factors of [#permalink]

Show Tags

New post 17 Aug 2014, 15:39
Bunuel wrote:
phoenixgmat wrote:
I would appreciate some help with:

If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of p²t?
1) m has more than 9 positive factors.
2) m is a multiple of p³

some explanations to both statements would be great!
thx a lot


We are told that \(p\) and \(t\) are the ONLY prime factors of m. It could be expressed as \(m=p^x*t^y\), where \(x\) and \(y\) are integers \(\geq{1}\).

Question: is \(m\) a multiple of \(p^2*t\). We already know that \(p\) and \(t\) are the factors of \(m\), so basically question asks whether the power of \(p\), in our prime factorization denoted as \(x\), more than or equal to 2: so is \(x\geq{2}\).

(1) m has more than 9 positive factors:

Formula for counting the number of distinct factors of integer \(x\) expressed by prime factorization as: \(n=a^x*b^y*c^z\), is \((x+1)(y+1)(z+1)\). This also includes the factors 1 and \(n\) itself.

We are told that \((x+1)(y+1)>9\) (as we know that \(m\) is expressed as \(m=p^x*t^y\))
But it's not sufficient to determine whether \(x\geq{2}\). (\(x\) can be 1 and \(y\geq{4}\) and we would have their product \(>9\), e.g. \((1+1)(4+1)=10\).) Not sufficient.

(2) m is a multiple of p^3
This statement clearly gives us the value of power of \(p\), which is 3, \(x=3>2\). So \(m\) is a multiple of \(p^2t\). Sufficient.

Answer: B.


I could answer the question in 1.5 min. But I have never known the formula for counting the number of distinct factors of a integer. Thanks a ton, Bunuel :-D :-D :-D
_________________

.........................................................................
+1 Kudos please, if you like my post

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9607
Followers: 465

Kudos [?]: 120 [0], given: 0

Premium Member
Re: If the prime numbers p and t are the only prime factors of [#permalink]

Show Tags

New post 20 Sep 2015, 00:43
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If the prime numbers p and t are the only prime factors of   [#permalink] 20 Sep 2015, 00:43

Go to page   Previous    1   2   [ 23 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
9 Experts publish their posts in the topic A Wagstaff prime is a prime number p such that p = pratikshr 17 06 Aug 2014, 04:02
9 Experts publish their posts in the topic A Pierpont prime is any prime number p such that p guerrero25 7 25 Jan 2014, 07:36
2 Experts publish their posts in the topic Is the prime number p equal to 3 joylive 3 11 Nov 2012, 08:56
2 A number n has the prime factors a, b, and c, and only these actleader 3 06 Nov 2012, 22:59
11 Experts publish their posts in the topic If the prime numbers p and t are the only prime factors of gulatin2 10 19 Aug 2009, 11:55
Display posts from previous: Sort by

If the prime numbers p and t are the only prime factors of

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


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.