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:

Re: For positive integer k, is the expression (k + 2)(k2 + 4k + [#permalink]

Show Tags

30 Sep 2009, 12:01

1

This post received KUDOS

1

This post was BOOKMARKED

(k+2)(k+3)(k+1).

1) SUFF. if k is divisible by 8 => k+2 is 2 in mod 4; k+3 = 3 in mod 4 and k+1=1 in mod 4. So this multiplication becomes 2x3x1= 6 = 2 in mod 4. Not divisible.

2)INSUFF

(k+1)/3=odd, so k+1 = odd so k is even. if k mod 4 = 0 then this eq. is not divisible by 4. if k mod 4 =2 then eq. is divisible by 4. So we can not know.

A

Last edited by maliyeci on 30 Sep 2009, 13:15, edited 1 time in total.

Re: For positive integer k, is the expression (k + 2)(k2 + 4k + [#permalink]

Show Tags

30 Sep 2009, 12:06

amitgovin wrote:

For positive integer k, is the expression (k + 2)(k2 + 4k + 3) divisible by 4?

(1) k is divisible by 8.

(2) (K + 1)/3 is an odd integer.

IMO A. \((k + 2)(k2 + 4k + 3) = 6K^2+12K+6\)

Statement 1: as K ismultiple of 8, \(6K^2+12K\) is divisible by 8. So \(6K^2+12K+6\) is NOT divisible by 8. Sufficient. Statement 2: As \((K+1)/3\) is an odd integer, K must be a multiple of 3. Insufficient.

Re: For positive integer k, is the expression (k + 2)(k2 + 4k + [#permalink]

Show Tags

30 Sep 2009, 12:09

Aargh! sorry, this question has been frustrating me. I understand 1) however I disagree with 2).

The stem says that K is a positive integer. Given that and the fact that we know that K is even from stem 2) we know that K is at MINIMUM 2. This is where I seem to disagree with your answer (which is apparently the correct one according to the MGMAT). IF k is at minimum 2, then K+2 is 4, thus K+2 is divisible by 4 and that makes the entire expression div by 4.

Re: For positive integer k, is the expression (k + 2)(k2 + 4k + [#permalink]

Show Tags

30 Sep 2009, 13:15

amitgovin wrote:

Aargh! sorry, this question has been frustrating me. I understand 1) however I disagree with 2).

The stem says that K is a positive integer. Given that and the fact that we know that K is even from stem 2) we know that K is at MINIMUM 2. This is where I seem to disagree with your answer (which is apparently the correct one according to the MGMAT). IF k is at minimum 2, then K+2 is 4, thus K+2 is divisible by 4 and that makes the entire expression div by 4.

Tell me why I'm wrong. thanks.

Because there are possibilities other than 2 and they are not divisible. For example 8. But there are possibilites other than 2 and they are divisible. For example 14

Re: For positive integer k, is the expression (k + 2)(k2 + 4k + [#permalink]

Show Tags

30 Sep 2009, 20:11

amitgovin wrote:

Aargh! sorry, this question has been frustrating me. I understand 1) however I disagree with 2).

The stem says that K is a positive integer. Given that and the fact that we know that K is even from stem 2) we know that K is at MINIMUM 2. This is where I seem to disagree with your answer (which is apparently the correct one according to the MGMAT). IF k is at minimum 2, then K+2 is 4, thus K+2 is divisible by 4 and that makes the entire expression div by 4.

Tell me why I'm wrong. thanks.

Hello amitgovin, hwr are ya? well, i can tell you why you are wrong. you made the honest mistake of thinking k+2 is divisible by 4. It has to be k x 2 for it to be divisible by 4. if you test k = 4 in k + 2, you'd get 4 + 2 = 6 and 6 is not divisible by 4. Again if u test k = 6 in k + 2, you'd get 8 which is divisible by 4. So statement 2 is INSUFF. gud?

Re: For positive integer k, is the expression (k + 2)(k2 + 4k + [#permalink]

Show Tags

12 Apr 2010, 12:52

For a product of 2 terms to be div by 4; either product of the factors should be div by 4 (e.g 2x2), or either term should be 0 or any one of the terms should be divisible by 4.

1. K is div by 8: This means that k is even. Thus, the second term (K^2+4k+3) will always be odd and never 0, thus not being div by 4. K being div by 8 also means K is divisible by 4. If we add 2 to any number, whether negative or positive, divisible by 4, the resulting number will not be divisible by 4. Hence, the second term is not div by 4 either. Another scenario is k=0 (0 is div by 8). In that case the(k+2)(K^2+4k+3)= 6 i.e. not div by 4.

Hence statement 1 is sufficient (the term is not div by 4)

2. (k+1)/3 is an odd integer. This means, k is even and k+1 is div by 3. if k=8 or 32, neither (k+2) nor (K^2+4K+3) is div by 4. If k=-34 or 2; (K+2) is div by 4. So, dual cases--hence statement 2 is insufficient.

Re: For positive integer k, is the expression (k + 2)(k2 + 4k + [#permalink]

Show Tags

24 Aug 2014, 05:17

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 positive integer k, is the expression (k + 2)(k2 + 4k + [#permalink]

Show Tags

24 Aug 2014, 06:19

1

This post received KUDOS

Expert's post

amitgovin wrote:

For positive integer k, is the expression (k + 2)(k^2 + 4k + 3) divisible by 4?

(1) k is divisible by 8. (2) (k + 1)/3 is an odd integer.

For positive integer k, is the expression (k + 2)(k^2 + 4k + 3) divisible by 4?

\((k + 2)(k^2 + 4k + 3)=(k+1)(k+2)(k+3)\), so the expression is the product of three consecutive integers.

(1) k is divisible by 8 --> \(k=8n=even\) --> \((k+1)(k+2)(k+3)=odd*even*odd\). Now, \(k+2=8n+2\), though even, is not a multiple of 4 (it's 2 greater than a multiple of 8), therefore the expression is not divisible by 4. Sufficient.

(2) (k + 1)/3 is an odd integer --> \(k+1=3*odd=odd\) --> \(k=even\) --> \((k+1)(k+2)(k+3)=odd*even*odd\). Now, \(k+2=even\) may or may not be divisible by 8, therefore the expression may or may not be divisible by 8. For example, consider \(k=2\) and \(k=6\). Not sufficient.

Post your Blog on GMATClub We would like to invite all applicants who are applying to BSchools this year and are documenting their application experiences on their blogs to...

HBS alum talks about effective altruism and founding and ultimately closing MBAs Across America at TED: Casey Gerald speaks at TED2016 – Dream, February 15-19, 2016, Vancouver Convention Center...