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:

If x is the product of the positive integers from 1 to 8, in [#permalink]

Show Tags

21 Jan 2013, 15:11

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

15% (low)

Question Stats:

78% (02:10) correct
22% (01:58) wrong based on 125 sessions

HideShow timer Statistics

If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2^i * 3^k * 5^m * 7^p, then i + k + m + p =

A. 4 B. 7 C. 8 D. 11 E. 12

The OG Guide and MGMAT Guide both have different solutions, a bit long. Can someone tell me if I'm doing this incorrectly.

If I'm plugging #'s in, I'm getting 2+3+4+5, = 14, but not all can be added, because not all are prime, and some numbers are repeated right, so if I take the sum of all primes in 2+3+4+5, without repeats I'll get 1+3+2+5, then I get 11? is this correct? I know 1 is not prime, and the first 2, and 4 share the same primes, so do I use 1 as a digit for 2, and use 2 as a prime # for 4? to end up with 1+3+2+5?

Re: If x is the product of the positive integers from 1 to 8, in [#permalink]

Show Tags

21 Jan 2013, 15:29

Expert's post

If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2^i * 3^k * 5^m * 7^p, then i + k + m + p =

A. 4 B. 7 C. 8 D. 11 E. 12

Given that \(x=8!=2^7*3^2*5*7\). Hence, \(x=2^7*3^2*5^1*7^1=2^i * 3^k * 5^m * 7^p\), since i, k, m, and p are positive integers, then we can equate the exponents, so we have that \(i=7\), \(k=2\), \(m=1\), and \(p=1\).

Re: If x is the product of the positive integers from 1 to 8, in [#permalink]

Show Tags

21 Jan 2013, 20:56

Expert's post

laythesmack23 wrote:

If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2^i * 3^k * 5^m * 7^p, then i + k + m + p =

A. 4 B. 7 C. 8 D. 11 E. 12

The OG Guide and MGMAT Guide both have different solutions, a bit long. Can someone tell me if I'm doing this incorrectly.

If I'm plugging #'s in, I'm getting 2+3+4+5, = 14, but not all can be added, because not all are prime, and some numbers are repeated right, so if I take the sum of all primes in 2+3+4+5, without repeats I'll get 1+3+2+5, then I get 11? is this correct? I know 1 is not prime, and the first 2, and 4 share the same primes, so do I use 1 as a digit for 2, and use 2 as a prime # for 4? to end up with 1+3+2+5?

You cannot plug in numbers. You need to find the values of i, k, m and p.

x = 1*2*3*4*5*6*7*8 = 8!

\(x = 2^i*3^k*5^m*7^p\)

To get the value of i, you need to find the number of 2s in x i.e. 8! (including the 2s you get in 4, 6 and 8). You can quickly count - one from 2, two from 4, one from 6 and three from 8 = total seven 2s are there in 8!

To get the value of k, you need to find the number of 3s in 8!. There are two 3s in 8! (one from 3 and another from 6) It is easy to see that there is only one 5 and one 7 in 8!.

If x is the product of the positive integers from 1 to 8, in [#permalink]

Show Tags

11 Aug 2013, 01:44

If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m and p are positive integers such that \(x = 2^i3^k5^m7^p\), then i + k + m + p = A 4 B 7 C 8 D 11 E 12 _________________

Re: If x is the product of the positive integers from 1 to 8, in [#permalink]

Show Tags

11 Aug 2013, 01:48

Expert's post

Stiv wrote:

If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m and p are positive integers such that \(x = 2^i3^k5^m7^p\), then i + k + m + p = A 4 B 7 C 8 D 11 E 12

Merging similar topics. Please refer to the solutions above. _________________

Re: If x is the product of the positive integers from 1 to 8, in [#permalink]

Show Tags

11 Aug 2013, 01:51

Stiv wrote:

If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m and p are positive integers such that \(x = 2^i3^k5^m7^p\), then i + k + m + p = A 4 B 7 C 8 D 11 E 12

\(X= 1*2*3*4*5*6*7*8\) OR =\(1*2*3*2^2*5*(2*3)*7*2^3\) =\(1*2^7*3^2*5*7\) THEREFORE \(i + k + m + p = 7+2+1+1 = 11\)

HENCE D _________________

When you want to succeed as bad as you want to breathe ...then you will be successfull....

Re: If x is the product of the positive integers from 1 to 8, in [#permalink]

Show Tags

21 May 2016, 14:02

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. _________________

http://blog.ryandumlao.com/wp-content/uploads/2016/05/IMG_20130807_232118.jpg The GMAT is the biggest point of worry for most aspiring applicants, and with good reason. It’s another standardized test when most of us...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...