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:

Positive integer n divisible by 4 and 21 [#permalink]
19 Jul 2009, 09:00

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct
0% (00:00) wrong based on 3 sessions

This question and answer explanation is from a Manhattan GMAT practice test. I don't understand why they don't take into account the 7 as one of the prime factors. Can anyone explain this? Thanks for your help.

If positive integer n is divisible by both 4 and 21, then n must be divisible by which of the following?

8 - 2, 2, 2

12 - 2, 2, 3

18, 2, 3, 3

24 - 2, 2, 2, 3

48- , 2, 2, 2, 2,

If n is divisible by both 4 and 21, its prime factors include 2, 2, 3, and 7. Therefore, any integer that can be constructed as the product of these prime factors is also a factor of n. In this case, 12 is the only integer that can definitively be constructed from the prime factors of n, since 12 = 2 x 2 x 3.

Re: Positive integer n divisible by 4 and 21 [#permalink]
19 Jul 2009, 10:08

You are confused.

Read the question again, carefully.

If you still don't get it, here it is -

Now, prime factors :

4= 2, 2. 21=3,7.

'n' is divisible by 4 & 21. Consider, Y is divisor after dividing 'n' by 4 & 21. Let's write 'n' as

n = 4 x 21 x Y = 2 x 2 x 3 x 7 x Y.

Now, question asks for a number that divides 'n'. If there is a number that divides 'n' for sure, it must not have any additional prime factors than (2,2,3,7). Consider the possibility that Y might even be 1, so we don't consider Y here.

All other options except '12'=2 x 2 x 3, have those additional prime factors.

This is complete logic. Quick way to solve the problem -

Divide 4 x 21 by each option given. The one which gives integer divisor, is your answer. _________________

Re: Positive integer n divisible by 4 and 21 [#permalink]
23 Jul 2009, 03:31

In Other way, the first number,apart from 0, is LCM of 4 and 21. This is 84. so out of the following only 12 divides it. Thanks.

nss123 wrote:

This question and answer explanation is from a Manhattan GMAT practice test. I don't understand why they don't take into account the 7 as one of the prime factors. Can anyone explain this? Thanks for your help.

If positive integer n is divisible by both 4 and 21, then n must be divisible by which of the following?

8 - 2, 2, 2

12 - 2, 2, 3

18, 2, 3, 3

24 - 2, 2, 2, 3

48- , 2, 2, 2, 2,

If n is divisible by both 4 and 21, its prime factors include 2, 2, 3, and 7. Therefore, any integer that can be constructed as the product of these prime factors is also a factor of n. In this case, 12 is the only integer that can definitively be constructed from the prime factors of n, since 12 = 2 x 2 x 3.

The correct answer is B.

gmatclubot

Re: Positive integer n divisible by 4 and 21
[#permalink]
23 Jul 2009, 03:31

I´ve done an interview at Accepted.com quite a while ago and if any of you are interested, here is the link . I´m through my preparation of my second...

It has been a good week so far. After the disappointment with my GMAT score, I have started to study again, re-schedule the new test date and talked with...

It’s here. Internship season. The key is on searching and applying for the jobs that you feel confident working on, not doing something out of pressure. Rotman has...