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
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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly 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 See our Youtube demo
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 Answer D. 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
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 Answer D. 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^3n+3n=(n1)n(n+1)+3n. Here, (n1)n(n+1) is the multiple of three consecutive integers, and you always get the multiples of 6, hence yes each time. Answer: D
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly 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 See our Youtube demo



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 Answer D. 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
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. answer is D.




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






