It is currently 17 Feb 2018, 23:15

GMAT Club Daily Prep

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If n and mare positive integers, is n^m+2n divisible by 3?

Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4865
GPA: 3.82
If n and mare positive integers, is n^m+2n divisible by 3? [#permalink]

Show Tags

11 Oct 2016, 03:57
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

49% (01:12) correct 51% (00:48) wrong based on 100 sessions

HideShow timer Statistics

If n and mare positive integers, is $$n^m$$+2n divisible by 3?

1)m=3
2)n=1
[Reveal] Spoiler: OA

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Last edited by abhimahna on 14 Oct 2016, 04:45, edited 1 time in total.
Corrected the format
Board of Directors
Status: Aiming MBA
Joined: 18 Jul 2015
Posts: 3067
Location: India
Concentration: Healthcare, Technology
GPA: 3.65
WE: Information Technology (Health Care)
Re: If n and mare positive integers, is n^m+2n divisible by 3? [#permalink]

Show Tags

11 Oct 2016, 05:46
MathRevolution wrote:
If n and mare positive integers, is n^m+2n divisible by 3?

1)m=3
2)n=1

We are given whether [m]n^m+2n [\m] is divisible by 3.

Statement 1 : m = 3.

or I can say [m]n^3+2n [\m] = [m]n(n^2+2) [\m]. This will always be divisible by 3 for any positive integral value of n. Hence, sufficient.

Statement 2 : n =1

or I can say [m]1^m+2 [\m]. Now [m]1^m[\m] will always be equal to 1. So, 1 + 2 = 3. Divisible by 3. Hence , Sufficient.
_________________

How I improved from V21 to V40! ?

How to use this forum in THE BEST way?

Intern
Joined: 01 Jan 2014
Posts: 31
Location: United States
GMAT 1: 690 Q48 V37
GPA: 3.4
Re: If n and mare positive integers, is n^m+2n divisible by 3? [#permalink]

Show Tags

13 Oct 2016, 06:10
abhimahna wrote:
MathRevolution wrote:
If n and mare positive integers, is n^m+2n divisible by 3?

1)m=3
2)n=1

We are given whether [m]n^m+2n [\m] is divisible by 3.

Statement 1 : m = 3.

or I can say [m]n^3+2n [\m] = [m]n(n^2+2) [\m]. This will always be divisible by 3 for any positive integral value of n. Hence, sufficient.

Statement 2 : n =1

or I can say [m]1^m+2 [\m]. Now [m]1^m[\m] will always be equal to 1. So, 1 + 2 = 3. Divisible by 3. Hence , Sufficient.

Can someone clarify what is the question?
Is it (n^m) + 2n or n^(m+2n)??

Last edited by abhimahna on 14 Oct 2016, 04:44, edited 1 time in total.
Corrected the Quote
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4865
GPA: 3.82
Re: If n and mare positive integers, is n^m+2n divisible by 3? [#permalink]

Show Tags

13 Oct 2016, 06:28
==>In the original condition, there are 2 variables, and C is the answer. However, 1) and 2) each becomes yes, so D is the answer, a common CMT 4(B). Especially in the case of 1), if you substitute m=3, you get n^3+2n=n^3-n+3n=(n-1)n(n+1)+3n. Here, (n-1)n(n+1) is the multiple of three consecutive integers, and you always get the multiples of 6, hence yes each time.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Board of Directors
Status: Aiming MBA
Joined: 18 Jul 2015
Posts: 3067
Location: India
Concentration: Healthcare, Technology
GPA: 3.65
WE: Information Technology (Health Care)
Re: If n and mare positive integers, is n^m+2n divisible by 3? [#permalink]

Show Tags

14 Oct 2016, 04:46
mechky wrote:
abhimahna wrote:
MathRevolution wrote:
If n and mare positive integers, is n^m+2n divisible by 3?

1)m=3
2)n=1

We are given whether [m]n^m+2n [\m] is divisible by 3.

Statement 1 : m = 3.

or I can say [m]n^3+2n [\m] = [m]n(n^2+2) [\m]. This will always be divisible by 3 for any positive integral value of n. Hence, sufficient.

Statement 2 : n =1

or I can say [m]1^m+2 [\m]. Now [m]1^m[\m] will always be equal to 1. So, 1 + 2 = 3. Divisible by 3. Hence , Sufficient.

Can someone clarify what is the question?
Is it (n^m) + 2n or n^(m+2n)??

Corrected the format. Please check now.
_________________

How I improved from V21 to V40! ?

How to use this forum in THE BEST way?

Board of Directors
Joined: 17 Jul 2014
Posts: 2723
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: If n and mare positive integers, is n^m+2n divisible by 3? [#permalink]

Show Tags

11 Apr 2017, 09:17
MathRevolution wrote:
If n and mare positive integers, is $$n^m$$+2n divisible by 3?

1)m=3
2)n=1

1.
we can rewrite:
n(n^2 +2)/3
let's try few values.
if n=1, then it is divisible
if n=2, then it is divisible
if n=5, it is divisible
if n=7, it is divisible
so works all the times...sufficient.

2. sufficient alone.

Re: If n and mare positive integers, is n^m+2n divisible by 3?   [#permalink] 11 Apr 2017, 09:17
Display posts from previous: Sort by