Jun 29 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Jun 30 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Jul 01 08:00 AM PDT  09:00 AM PDT Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Jul 01 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants.
Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Status: Transforming Educational System
Joined: 21 Sep 2016
Posts: 466
Location: India
Concentration: Nonprofit, Social Entrepreneurship
WE: Education (NonProfit and Government)

If n is an integer, which of the following must be divisible by 3?
[#permalink]
Show Tags
Updated on: 04 Oct 2017, 03:10
Question Stats:
67% (01:34) correct 33% (01:31) wrong based on 474 sessions
HideShow timer Statistics
If n is an integer, which of the following must be divisible by 3? A) n^3 – 4n B) n^3 + 4n C) n^2 +1 D) n^2 1 E) n^2 4
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Originally posted by vivek6199 on 04 Oct 2017, 03:08.
Last edited by Bunuel on 04 Oct 2017, 03:10, edited 1 time in total.
Renamed the topic.




Math Expert
Joined: 02 Sep 2009
Posts: 55804

Re: If n is an integer, which of the following must be divisible by 3?
[#permalink]
Show Tags
04 Oct 2017, 03:13
vivek6199 wrote: If n is an integer, which of the following must be divisible by 3?
A) n^3 – 4n B) n^3 + 4n C) n^2 +1 D) n^2 1 E) n^2 4 Option A: \(n^3 – 4n = n(n^24)=(n2)n(n+2)\). (n2)n(n+2) is the product of three consecutive odd or three consecutive even integers. In any case one of them must be a multiple of 3. Answer: A.
_________________




Manager
Joined: 27 Dec 2016
Posts: 232
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)

Re: If n is an integer, which of the following must be divisible by 3?
[#permalink]
Show Tags
04 Oct 2017, 03:44
vivek6199 wrote: If n is an integer, which of the following must be divisible by 3?
A) n^3 – 4n B) n^3 + 4n C) n^2 +1 D) n^2 1 E) n^2 4 Solved in in one minute, plug in n=2 and n=3. Bunuel has offered the best algebraic approach.
_________________
There's an app for that  Steve Jobs.



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6681
Location: United States (CA)

Re: If n is an integer, which of the following must be divisible by 3?
[#permalink]
Show Tags
06 Oct 2017, 10:58
vivek6199 wrote: If n is an integer, which of the following must be divisible by 3?
A) n^3 – 4n B) n^3 + 4n C) n^2 +1 D) n^2 1 E) n^2 4 Let’s simplify each answer choice: A) n^3 – 4n n(n^2  4) = n(n + 2)(n  2) = (n  2)(n)(n + 2) We see that the expression above is a product of 3 consecutive even integers (if n is even) or the product of 3 consecutive odd integers (if n is odd). In either case, the product will always contain a prime factor of 3, so n^3 – 4n is always divisible by 3. Alternate Solution: If we take n = 1, we see that 1^3 + 4 = 5 is not a multiple of 3; thus, B cannot be the answer. If we take n = 1, we see that 1^2 + 1 = 2 is not a multiple of 3; thus, C cannot be the answer. If we take n = 3, we see that 3^2  1 = 8 is not a multiple of 3; thus, D cannot be the answer. If we take n = 3, we see that n^2  4 = 5 is not a multiple of 3; thus, E cannot be the answer. The only remaining choice is A. Answer: A
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 04 Sep 2017
Posts: 21
Location: United States
Concentration: Finance
GMAT 1: 610 Q36 V36 GMAT 2: 680 Q40 V36
GPA: 3.3
WE: Consulting (Mutual Funds and Brokerage)

Re: If n is an integer, which of the following must be divisible by 3?
[#permalink]
Show Tags
10 Oct 2017, 10:17
I really struggled on this one and feel like I am missing something on this question. Isn't it possible for n to be zero as the question does not suggest otherwise? If you take the algebraic breakdown for A being (n2)n(n+2), isn't it possible to be (2)(0)(2)? I may be missing a math concept here, but I don't believe (2)(0)(2) is divisible by 3.
Can someone help clear this up for me?
Thank you!



Math Expert
Joined: 02 Sep 2009
Posts: 55804

Re: If n is an integer, which of the following must be divisible by 3?
[#permalink]
Show Tags
10 Oct 2017, 10:25
zflodeen wrote: I really struggled on this one and feel like I am missing something on this question. Isn't it possible for n to be zero as the question does not suggest otherwise? If you take the algebraic breakdown for A being (n2)n(n+2), isn't it possible to be (2)(0)(2)? I may be missing a math concept here, but I don't believe (2)(0)(2) is divisible by 3.
Can someone help clear this up for me?
Thank you! ZERO:1. 0 is an integer. 2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even. 3. 0 is neither positive nor negative integer (the only one of this kind). 4. 0 is divisible by EVERY integer except 0 itself. Check below for more: ALL YOU NEED FOR QUANT ! ! !Ultimate GMAT Quantitative MegathreadHope it helps.
_________________



Intern
Joined: 04 Sep 2017
Posts: 21
Location: United States
Concentration: Finance
GMAT 1: 610 Q36 V36 GMAT 2: 680 Q40 V36
GPA: 3.3
WE: Consulting (Mutual Funds and Brokerage)

Re: If n is an integer, which of the following must be divisible by 3?
[#permalink]
Show Tags
10 Oct 2017, 10:37
Bunuel, thank you for clearing that up! I was missing point #4 and suspected that might be the case. I'm trying to dredge up all these old math concepts and appreciate all the insight on these forum posts.



VP
Joined: 09 Mar 2016
Posts: 1274

Re: If n is an integer, which of the following must be divisible by 3?
[#permalink]
Show Tags
26 Jul 2018, 10:22
Bunuel wrote: vivek6199 wrote: If n is an integer, which of the following must be divisible by 3?
A) n^3 – 4n B) n^3 + 4n C) n^2 +1 D) n^2 1 E) n^2 4 Option A: \(n^3 – 4n = n(n^24)=(n2)n(n+2)\). (n2)n(n+2) is the product of three consecutive odd or three consecutive even integers. In any case one of them must be a multiple of 3. Answer: A. pushpitkc, if Bunuel says the product of three consecutive odd or three consecutive even integers. In any case one of them must be a multiple of 3. why cant I say the same of option B ? \(n^3 + 4n = n(n^2+4)=(n+2)n(n+2)\). here is the same product of three consecutive odd or three consecutive even integers. Bunuel used formula \(a^2b^2\) so I just changed the sign onto + \(a^2+b^2\)



Math Expert
Joined: 02 Sep 2009
Posts: 55804

Re: If n is an integer, which of the following must be divisible by 3?
[#permalink]
Show Tags
26 Jul 2018, 10:35
dave13 wrote: Bunuel wrote: vivek6199 wrote: If n is an integer, which of the following must be divisible by 3?
A) n^3 – 4n B) n^3 + 4n C) n^2 +1 D) n^2 1 E) n^2 4 Option A: \(n^3 – 4n = n(n^24)=(n2)n(n+2)\). (n2)n(n+2) is the product of three consecutive odd or three consecutive even integers. In any case one of them must be a multiple of 3. Answer: A. pushpitkc, if Bunuel says the product of three consecutive odd or three consecutive even integers. In any case one of them must be a multiple of 3. why cant I say the same of option B ? \(n^3 + 4n = n(n^2+4)=(n+2)n(n+2)\). here is the same product of three consecutive odd or three consecutive even integers. Bunuel used formula \(a^2b^2\) so I just changed the sign onto + \(a^2+b^2\) Because n^2 + 4 does not equal to (n + 2)(n  2).
_________________



Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3364
Location: India
GPA: 3.12

If n is an integer, which of the following must be divisible by 3?
[#permalink]
Show Tags
26 Jul 2018, 10:46
dave13 wrote: Bunuel wrote: vivek6199 wrote: If n is an integer, which of the following must be divisible by 3?
A) n^3 – 4n B) n^3 + 4n C) n^2 +1 D) n^2 1 E) n^2 4 Option A: \(n^3 – 4n = n(n^24)=(n2)n(n+2)\). (n2)n(n+2) is the product of three consecutive odd or three consecutive even integers. In any case one of them must be a multiple of 3. Answer: A. pushpitkc, if Bunuel says the product of three consecutive odd or three consecutive even integers. In any case one of them must be a multiple of 3. why cant I say the same of option B ? \(n^3 + 4n = n(n^2+4)=(n+2)n(n+2)\). here is the same product of three consecutive odd or three consecutive even integers. Bunuel used formula \(a^2b^2\) so I just changed the sign onto + \(a^2+b^2\) Hey dave13\((a^2  4) = (a^2  2^2) = (a + b)(a  b)\) Let a = 5 > Left hand side is \((5^2  2^2) = 25  4 = 21\)  The righthand side is \((5 + 2)(5  2) = 7*3 = 21\) But try it with your formula  you say \((a^2 + 4) = (a + 2)(a + 2)\) Let a = 3 > Left hand side is \((3^2 + 2^2) = (9 + 4) = 13\)  The righthand side is \((3 + 2)(3 + 2) = 5*5 = 25\) Since these are not equal  your formula must be wrong Hope this clears your confusion. I have merely expanded on Bunuel 's option!
_________________
You've got what it takes, but it will take everything you've got



Senior Manager
Joined: 22 Feb 2018
Posts: 427

Re: If n is an integer, which of the following must be divisible by 3?
[#permalink]
Show Tags
26 Jul 2018, 21:20
vivek6199 wrote: If n is an integer, which of the following must be divisible by 3?
A) n^3 – 4n B) n^3 + 4n C) n^2 +1 D) n^2 1 E) n^2 4 OA: A The product of three consecutive integers is divisible by 3. Three consecutive integers be \(n1, n,n+1\) Product of these three consecutive integers : \((n1)(n)(n+1)=(n^21)n=n^3n\) \(3n\) is also divisible by 3. \((n^3n)(3n)\) i.e \(n^3 – 4n\) would also be divisible by 3.
_________________
Good, good Let the kudos flow through you



Manager
Joined: 29 May 2017
Posts: 128
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability

Re: If n is an integer, which of the following must be divisible by 3?
[#permalink]
Show Tags
31 Oct 2018, 05:11
Bunuel wrote: vivek6199 wrote: If n is an integer, which of the following must be divisible by 3?
A) n^3 – 4n B) n^3 + 4n C) n^2 +1 D) n^2 1 E) n^2 4 Option A: \(n^3 – 4n = n(n^24)=(n2)n(n+2)\). (n2)n(n+2) is the product of three consecutive odd or three consecutive even integers. In any case one of them must be a multiple of 3. Answer: A. how is (n2)(n)(n+2) consecutive? if we take (n3)(n)(n+3), for n as 5 this gives us: 2 x 5 x 8 and as can be seen, is not divisible by 3. But this divisible by 3 if n is even for (n4)(n)(n+4) is divisible by 3 for even or odd n



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9369
Location: Pune, India

Re: If n is an integer, which of the following must be divisible by 3?
[#permalink]
Show Tags
31 Oct 2018, 05:26
Mansoor50 wrote: Bunuel wrote: vivek6199 wrote: If n is an integer, which of the following must be divisible by 3?
A) n^3 – 4n B) n^3 + 4n C) n^2 +1 D) n^2 1 E) n^2 4 Option A: \(n^3 – 4n = n(n^24)=(n2)n(n+2)\). (n2)n(n+2) is the product of three consecutive odd or three consecutive even integers. In any case one of them must be a multiple of 3. Answer: A. how is (n2)(n)(n+2) consecutive? if we take (n3)(n)(n+3), for n as 5 this gives us: 2 x 5 x 8 and as can be seen, is not divisible by 3. But this divisible by 3 if n is even for (n4)(n)(n+4) is divisible by 3 for even or odd n As far as divisibility by 3 is concerned, (n  2) is the same as (n + 1) because if (n  2) is divisible by 3, then so is (n + 1) (which is just (n  2 + 3)). If (n  2) leaves a remainder of 1, so will (n + 1). If (n  2) leaves a remainder of 2, so will (n + 1). By the same concept, (n + 2) is the same as (n  1) So in effect, what we are looking at is this: (n  1)*n*(n + 1)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Re: If n is an integer, which of the following must be divisible by 3?
[#permalink]
31 Oct 2018, 05:26






