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 a and b are positive even integers, and the least common [#permalink]

Show Tags

11 Oct 2005, 18:32

2

This post received KUDOS

15

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

54% (02:33) correct
46% (07:19) wrong based on 443 sessions

HideShow timer Statistics

If a and b are positive even integers, and the least common multiple of a and b is expressed as a*b/n, which of the following statements could be false?

A. n is a factor of both a and b B. (a*b)/n < ab C. ab is multiple of 2. D. (a*b)/n is a multiple of 2. E. n is a multiple of 4.

If 'a' and 'b' are positive even integers, and the least common multiple of 'a' and 'b' is expressed as ab/n, which of the following could be false? A) n is a factor of both a and b B) ab/n < ab C) ab is a multiple of 2 D) ab/n is a multiple of 2 E) n is a multiple of 4

This question is easier if you know that, for any positive integers a and b:

LCM(a,b) * GCD(a,b) = a*b

So LCM(a,b) = ab/GCD(a,b)

In this question, n is just the GCD of a and b. So we know automatically that n is a factor of a and b... A) must be true. If a and b are both even, they are both divisible by 2, so the smallest possible value for their GCD is 2. That is, n >= 2, so B) must be true If a and b are even, ab is clearly even, and so is the LCM of a and b, so C) and D) must be true. E) is the only one that might be false; E will only be true if both a and b are divisible by 4.

hence E
_________________

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

GIVE VALUE TO OFFICIAL QUESTIONS...

GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabulary-list-for-gmat-reading-comprehension-155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment : http://www.youtube.com/watch?v=APt9ITygGss

If 'a' and 'b' are positive even integers, and the least common multiple of 'a' and 'b' is expressed as ab/n, which of the following could be false? A) n is a factor of both a and b B) ab/n < ab C) ab is a multiple of 2 D) ab/n is a multiple of 2 E) n is a multiple of 4

E) is the only one that might be false; E will only be true if both a and b are divisible by 4.

hence E

Any information is provided such that a and b cannot be a multiple of 4 ( 'a' and 'b' are positive even integers - a can be 4 and b can be 16 or 8) ? I don't think it is valid question.
_________________

Re: If a and b are positive even integers, and the least common [#permalink]

Show Tags

23 Jan 2015, 13:22

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.
_________________

The last poster in this thread (kinjiGC) had some concerns about whether this question was "valid" or not, but I can assure you that it is.

The question is based on Number Property rules that exist in the realm of factors and multiples. Given the restrictions in the prompt, 4 of the answers are ALWAYS TRUE....

For example, since we're told that A and B are POSITIVE EVEN INTEGERS, we know that (A)(B) = (even)(even), so the product will ALWAYS be EVEN. Thus AB is a multiple of 2 and we can eliminate Answer C (since we're asked to find something that is SOMETIMES FALSE - meaning NOT ALWAYS TRUE).

These types of "...must be true..." questions almost always involve Number Properties of some kind, so you can TEST VALUES or use Number Property Rules to get to the correct answer. You'll see a few questions in this general "format" on Test Day and a bunch of questions involving Number Properties in general (especially in DS).

Re: If a and b are positive even integers, and the least common [#permalink]

Show Tags

24 Jan 2015, 13:01

1

This post was BOOKMARKED

If a and b are positive even integers, and the least common multiple of a and b is expressed as a*b/n, which of the following statements could be false?

A. n is a factor of both a and b B. (a*b)/n < ab C. ab is multiple of 2. D. (a*b)/n is a multiple of 2. E. n is a multiple of 4.

If we divide by n and get a multiple of a and of b, then n must be a common factor. Answer A must be true.

If a and b are even integers, dividing by a factor (also an integer) results in something smaller than the product ab. Answer B must be true.

If either a or b is even, then ab must be even. Answer C must be true.

If both are even, the smallest either number can be is 2. Thus, the smallest common factor must be 2. Answer D must be true.

If b is 6 and a is 2, n would be 6, which is not 4. E can be false.

Re: If a and b are positive even integers, and the least common [#permalink]

Show Tags

08 Jun 2016, 21:45

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: If a and b are positive even integers, and the least common [#permalink]

Show Tags

15 Jun 2016, 00:03

1

This post was BOOKMARKED

Using a=2, b=4. LCM (2,4) = 4. This means ab/n can be written as 2*4/2 (because LCM(=4) the least common multiple of 'a' and 'b' is expressed as ab/n, 2*4/2=4=LCM). Thus n=2 (and a=2, b=4) A. n is a factor of both a and b - True. 2 is factor for 2 and 4 B. (a*b)/n < ab - True (4<8) C. ab is multiple of 2. - True (8 is multiple of 2) D. (a*b)/n is a multiple of 2. - True (4 is multiple of 2) E. n is a multiple of 4. False (n=2 is not multiple of 4)

Re: If a and b are positive even integers, and the least common [#permalink]

Show Tags

31 Jul 2016, 05:22

1

This post received KUDOS

manuchadha wrote:

Using a=2, b=4. LCM (2,4) = 4. This means ab/n can be written as 2*4/2 (because LCM(=4) the least common multiple of 'a' and 'b' is expressed as ab/n, 2*4/2=4=LCM). Thus n=2 (and a=2, b=4) A. n is a factor of both a and b - True. 2 is factor for 2 and 4 B. (a*b)/n < ab - True (4<8) C. ab is multiple of 2. - True (8 is multiple of 2) D. (a*b)/n is a multiple of 2. - True (4 is multiple of 2) E. n is a multiple of 4. False (n=2 is not multiple of 4)

Great Explanation ! Thanks !
_________________

Cheers, Shri ------------------------------- GMAT is not an Exam... it is a war .. Let's Conquer !!!

gmatclubot

Re: If a and b are positive even integers, and the least common
[#permalink]
31 Jul 2016, 05:22

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

In early 2012, when I was working as a biomedical researcher at the National Institutes of Health , I decided that I wanted to get an MBA and make the...