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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: If p is the product of the integers from 1 to 30, inclusive, what is t [#permalink]

Show Tags

09 Aug 2009, 13:02

I can see that any of these numbers is ok. so I just pick 18.

P = 30! = 30x29x28x......x4x3x2x1

if 3K is a factor of p, it means that we can divide p by 3K and the result is an integer. there is a "3" in the expression of p, and all numbers shown are also there.

Re: If p is the product of the integers from 1 to 30, inclusive, what is t [#permalink]

Show Tags

09 Aug 2009, 22:22

Agree with Economist. But from the list, the best answer would be 18. Since all the prime factors of 18*3(2*3*3*3) would be in the product number. OA pls!
_________________

GMAT offended me. Now, its my turn! Will do anything for Kudos! Please feel free to give one.

Re: If p is the product of the integers from 1 to 30, inclusive, what is t [#permalink]

Show Tags

11 Aug 2009, 03:04

1

This post received KUDOS

tarek99 wrote:

If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3k is a factor of p? A. 10 B. 12 C. 14 D. 16 E. 18

please show the fastest way to solve this. thanks

Well ..I think question should read as 3^k ....i.e, If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

Re: If p is the product of the integers from 1 to 30, inclusive, what is t [#permalink]

Show Tags

11 Aug 2009, 03:32

1

This post received KUDOS

age wrote:

tarek99 wrote:

If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3k is a factor of p? A. 10 B. 12 C. 14 D. 16 E. 18

please show the fastest way to solve this. thanks

Well ..I think question should read as 3^k ....i.e, If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

Then C ..14 will be correct..

I agree. If C is the OA, then the questions should read as 3^k giving 14 as the answer.

Although if its not 3^k, then another interpretation of 3k could be 300 + k instead of 3*k, because 3*k makes the question silly. This means that when k=10, we get 310 and not 3*10 = 30

Thus proceeding with the "300 + k" assumption, we get: P = 30!

Option A: 310 => 310 = 2 * 5 * 31 => 31 is a prime and is not present in 30! Thus 310 is not a factor of P => A is Eliminated

Option B: 312 => 312 = 2^3 * 3 * 13 Thus 312 is a factor of P => B is the correct answer !

Option C: 314 => 314 = 2 * 157 => 157 is a prime and is not present in 30! Thus 314 is not a factor of P => C is Eliminated

Option D: 316 => 316 = 2^2 * 79 => 79 is a prime and is not present in 30! Thus 316 is not a factor of P => D is Eliminated

Option E: 318 => 310 = 2 * 3 * 53 => 53 is a prime and is not present in 30! Thus 318 is not a factor of P => E is Eliminated

Re: If p is the product of the integers from 1 to 30, inclusive, what is t [#permalink]

Show Tags

29 Sep 2014, 06:27

tarek99 wrote:

If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3k is a factor of p? A. 10 B. 12 C. 14 D. 16 E. 18

please show the fastest way to solve this. thanks

Can we change 3k to 3^K . A minor correction to make this question correct.

If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p ?

(A) 10 (B) 12 (C) 14 (D) 16 (E) 18

Finding the number of powers of a prime number k, in the n!.

The formula is: \(\frac{n}{k}+\frac{n}{k^2}+\frac{n}{k^3}\) ... till \(n>k^x\)

For example: what is the power of 2 in 25! (the highest value of m for which 2^m is a factor of 25!) \(\frac{25}{2}+\frac{25}{4}+\frac{25}{8}+\frac{25}{16}=12+6+3+1=22\). So the highest power of 2 in 25! is 22: \(2^{22}*k=25!\), where k is the product of other multiple of 25!.

Back to the original question: If p is the product of integers from 1 to 30, inclusive, what is the greatest integer k for which \(3^k\) is a factor of p?

A. 10 B. 12 C. 14 D. 16 E. 18

Given \(p=30!\).

Now, we should check the highest power of 3 in 30!: \(\frac{30}{3}+\frac{30}{3^2}+\frac{30}{3^3}=10+3+1=14\). So the highest power of 3 in 30! is 1.

Campus visits play a crucial role in the MBA application process. It’s one thing to be passionate about one school but another to actually visit the campus, talk...

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...