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:

For any positive integer n, the length of n is defined as [#permalink]
29 Jan 2012, 16:15

3

This post received KUDOS

11

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

68% (01:45) correct
32% (01:02) wrong based on 366 sessions

For any positive integer n, the length of n is defined as number of prime factors whose product is n, For example, the length of 75 is 3, since 75=3*5*5. How many two-digit positive integers have length 6?

A. 0 B. 1 C. 2 D. 3 E. 4

I need to understand the concept behind solving this question please.

Re: 2 digit positive integers with length 6 [#permalink]
29 Jan 2012, 16:21

9

This post received KUDOS

Expert's post

14

This post was BOOKMARKED

enigma123 wrote:

For any positive integer n, the length of n is defined as number of prime factors whose product is n, For example, the length of 75 is 3, since 75=3*5*5. How many two-digit positive integers have length 6?

A. 0 B. 1 C. 2 D. 3 E. 4

I need to understand the concept behind solving this question please.

Basically the length of the integer is the sum of the powers of its prime factors.

Length of six means that the sum of the powers of primes of the two-digit integer must be 6. First we can conclude that 5 can not be a factor of this integer as the smallest integer with the length of six that has 5 as prime factor is 2^5*5=160 (length=5+1=6), not a two-digit integer.

The above means that the primes of the two-digit integers we are looking for can be only 2 and/or 3. \(n=2^p*3^q\), \(p+q=6\).

Let's start with the highest value of \(p\): \(n=2^6*3^0=64\) (length=6+0=6); \(n=2^5*3^1=96\) (length=5+1=6);

\(n=2^4*3^2=144\) (length=4+2=6) not good as 144 is a three digit integer.

Re: For any positive integer n, the length of n is defined as [#permalink]
08 Mar 2013, 15:13

Try the smallest possible value first: In this case it is 2^6 which equals 64.

If we replace the last 2 with 3, then we have 2^5*3 = 96

From here we can positively assume that any other number will have more than 2 digits. So the answer is (C) 2 numbers that have length 6 and are only 2 digits.

Re: For any positive integer n, the length of n is defined as [#permalink]
09 Mar 2014, 00:18

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. _________________

Re: For any positive integer n, the length of n is defined as [#permalink]
19 Apr 2014, 23:45

Length of a number = Total number of prime factors of the number.

Any composite number can be represented as a product of prime numbers as shown below:

N= 2^x * 3^y * 5^z * 7^a ...so on

Since our requirement is a two digit number, we shall raise maximum power for smallest prime factor.

N= 2^6 = 64 has Length 6

N= 2^5 * 3 = 96 has length 6

N=2^4 * 3^2 = 144 is a three digit number and so on the other combinations would reveal 3 digit numbers.

Hence there are only 2 numbers _________________

Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

Re: For any positive integer n, the length of n is defined as [#permalink]
30 May 2015, 02:39

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. _________________

Hello everyone! Researching, networking, and understanding the “feel” for a school are all part of the essential journey to a top MBA. Wouldn’t it be great... ...

Are you interested in applying to business school? If you are seeking advice about the admissions process, such as how to select your targeted schools, then send your questions...