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 350,000 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 the integers a and n are greater than 1 and the product [#permalink]
14 May 2012, 01:41

Bunuel wrote:

subhajeet wrote:

If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a?

(1) a^n = 64

(2) n = 6

Can anyone help me with this question. How is B the correct answer.

Prime factorization would be the best way to attack such kind of questions.

Given: a^n*k=8!=2^7*3^2*5*7. Q: a=?

(1) a^n=64=2^6=4^3=8^2, so a can be 2, 4, or 8. Not sufficient.

(2) n=6 --> the only integer (more than 1), which is the factor of 8!, and has the power of 6 (at least) is 2, hence a=2. Sufficient.

Answer: B.

Dear Bunuel, OA is B but why B? Kindly tell the source from where you get all these number properties/Prime no. properties? If its your Brain then only the explaination for the above will do ! All DS are on Number Properties and i am doing silly mistakes. i opted 'C' Thanx

Re: If the integers a and n are greater than 1 and the product [#permalink]
14 May 2012, 01:48

Expert's post

kashishh wrote:

Bunuel wrote:

subhajeet wrote:

If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a?

(1) a^n = 64

(2) n = 6

Can anyone help me with this question. How is B the correct answer.

Prime factorization would be the best way to attack such kind of questions.

Given: a^n*k=8!=2^7*3^2*5*7. Q: a=?

(1) a^n=64=2^6=4^3=8^2, so a can be 2, 4, or 8. Not sufficient.

(2) n=6 --> the only integer (more than 1), which is the factor of 8!, and has the power of 6 (at least) is 2, hence a=2. Sufficient.

Answer: B.

Dear Bunuel, OA is B but why B? Kindly tell the source from where you get all these number properties/Prime no. properties? If its your Brain then only the explaination for the above will do ! All DS are on Number Properties and i am doing silly mistakes. i opted 'C' Thanx

If the integers a and n are greater than 1 and the product of th [#permalink]
21 Jan 2013, 22:36

This one is a fun question (a good practice of our understanding of factors)!

Analyze the given first before delving into the statements. 8*6*7*5*4*3*2*1 = a^n * R

Statement (1): a^n = 64 8*6*7*5*4*3*2*1 = 64 * R

64 could be 2^6 or 8^2. In 8!, it contains at least 6 factors of 2. In 8!, it also contains 2 factors of 8. Thus, a could be 2 or 8. Thus, INSUFFICIENT.

Statement (2): n = 6 Let us analyze 8! = 8*7*6*5*4*3*2*1. How many prime factors have at least 6 factors in 8!. Let us start with a = 2. YES! Let us then try a=3. NO!

We are certain that 2 has the most number of factors in 8! and it has at least 6. SUFFICIENT. a = 2

Re: If the integers a and n are greater than 1 and the product [#permalink]
22 Jan 2013, 12:22

product of the first 8 integers is: (2^8)(3^2)(5)(7)

Statement 1: a^n = 64. this means a could equal 2,4, or 8 because we don't know what n is. Not sufficient. Statement 2: if n = 6 the only possible value for a is 2 as the product of the first 8 integers does not include any other number raised to the 6th power. Sufficient

Re: If the integers a and n are greater than 1 and the product [#permalink]
10 Aug 2014, 10:34

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. _________________

For my Cambridge essay I have to write down by short and long term career objectives as a part of the personal statement. Easy enough I said, done it...