Find all School-related info fast with the new School-Specific MBA Forum

It is currently 02 Sep 2014, 08:53

Close

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
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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If n is a positive integer, then n(n+1)(n+2) is

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 07 Dec 2005
Posts: 16
Followers: 0

Kudos [?]: 5 [0], given: 0

GMAT Tests User
If n is a positive integer, then n(n+1)(n+2) is [#permalink] New post 10 Jul 2006, 06:56
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

81% (01:54) correct 19% (00:56) wrong based on 328 sessions
If n is a positive integer, then n(n+1)(n+2) is

(A) even only when n is even
(B) even only when n is odd
(C) odd whenever n is odd
(D) divisible by 3 only when n is odd
(E) divisible by 4 whenever n is even
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Oct 2013, 23:52, edited 1 time in total.
RENAMED THE TOPIC.
Manager
Manager
avatar
Joined: 04 Jul 2006
Posts: 57
Followers: 1

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 10 Jul 2006, 07:24
(E)

Assume: n is even, then either n or n+2 is a multiple of 4. Hence, n(n+1)(n+2) is divisible by 4.
Therefore: whenever n is even, the term above is divisble by 4.
2 KUDOS received
VP
VP
User avatar
Joined: 02 Jun 2006
Posts: 1270
Followers: 2

Kudos [?]: 37 [2] , given: 0

GMAT Tests User
 [#permalink] New post 10 Jul 2006, 09:05
2
This post received
KUDOS
(E) divisible by 4 whenever n is even

If n is even => even x odd x even (Prod of two even numbers always divisible by 2x2)
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25253
Followers: 3430

Kudos [?]: 25267 [1] , given: 2702

Re: 224. Arithmetic operation [#permalink] New post 24 Feb 2011, 03:11
1
This post received
KUDOS
Expert's post
Baten80 wrote:
224. If n is a positive integer, then n(n + 1)(n + 2) is
(A) even only when n is even
(B) even only when n is odd
(C) odd whenever n is odd
(D) divisible by 3 only when n is odd
(E) divisible by 4 whenever n is even


n(n + 1)(n + 2) is the product of 3 consecutive integers. The product of 3 consecutive integers is ALWAYS divisible by 2 and 3 (generally the product of k consecutive integers is always divisible by k!, check this: defined-functions-108309.html), so n(n + 1)(n + 2) is always even and always divisible by 3: A, B, C and D are out.

Answer: E.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1691
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 30

Kudos [?]: 288 [0], given: 36

GMAT Tests User Premium Member Reviews Badge
Re: n is a positive integer [#permalink] New post 01 Jul 2011, 00:07
You can use number plugging to do this. Eliminate answers by choosing 1 and 2 as test numbers. I'm not solving it here, perhaps you can give this a try now.
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Current Student
User avatar
Joined: 08 Jan 2009
Posts: 334
GMAT 1: 770 Q50 V46
Followers: 22

Kudos [?]: 81 [0], given: 7

GMAT Tests User
Re: n is a positive integer [#permalink] New post 01 Jul 2011, 00:17
Manhattan NP covers these well.

Will be of the form

Odd, even, odd = even
Even, odd, even = even

Can quickly rule out all but E

Posted from my mobile device Image
_________________

My Debrief

Senior Manager
Senior Manager
avatar
Joined: 29 Jan 2011
Posts: 386
Followers: 0

Kudos [?]: 31 [0], given: 87

GMAT Tests User
Re: n is a positive integer [#permalink] New post 01 Jul 2011, 00:36
pike wrote:
Manhattan NP covers these well.

Will be of the form

Odd, even, odd = even
Even, odd, even = even

Can quickly rule out all but E

Posted from my mobile device Image



Hi Pike,

can you please explain in detail how can you rule out other options without calculating? It will be good to know and might save some time.
Intern
Intern
avatar
Joined: 11 Sep 2010
Posts: 13
Location: India
GMAT 1: 620 Q49 V25
Followers: 0

Kudos [?]: 5 [0], given: 0

Re: n is a positive integer [#permalink] New post 01 Jul 2011, 01:43
siddhans wrote:
How to solve this?

If n is a positive integer, then n(n+1)(n+2) is

A)even only when n is even
B)even only when n is odd
C)odd whenever n is odd
D)divisible by 3 only when n is odd
E)divisible by 4 whenever n is even


n(n+1)(n+2) will always be even as n is a +ve integer so that rules out A, B & C. Atleast one of n, n+1 & n+2 will be even as they are consecutive integers.

even * even is always even e.g 2*4 = 8 or 6*10 = 60 always even
even * odd is always even e.g 2*3 = 6 or 5 * 8 = 40 always even

Either of n, n+1 & n+2 will always be divisible by 3 till the time n is a +ve integer and they are consecutive integers.

Hence that leaves us with E as answer.

Also we can prove it like this way also,
First +ve even integer is 2 and not 0 (0 is neither +ve nor -ve).

so n*n+1*n+2 = 2*3*4 divisible by 4.
or if n=6 then 6*7*8 again divisible by 4.

so is E.
2 KUDOS received
Manager
Manager
User avatar
Joined: 09 Nov 2010
Posts: 63
Location: Paris, FRANCE
Followers: 5

Kudos [?]: 28 [2] , given: 3

Re: n is a positive integer [#permalink] New post 01 Jul 2011, 04:54
2
This post received
KUDOS
ankushjain wrote:
siddhans wrote:
How to solve this?

If n is a positive integer, then n(n+1)(n+2) is

A)even only when n is even
B)even only when n is odd
C)odd whenever n is odd
D)divisible by 3 only when n is odd
E)divisible by 4 whenever n is even


Also we can prove it like this way also,
First +ve even integer is 2 and not 0 (0 is neither +ve nor -ve).

so n*n+1*n+2 = 2*3*4 divisible by 4.
or if n=6 then 6*7*8 again divisible by 4.

so is E.


We can generalize:

If n is even, then n + 2 is also even and n and n + 2 are consecutive even numbers.

2 * 2 = 4, so any two even numbers multiplied together will yield a multiple of 4.

Therefore, any two consecutive even numbers multiplied together will yield a multiple of 4.

THEREFORE, if n is even, n(n + 2) is always a multiple of 4.

But actually, we can go a step further (this may be useful for some future problems):

Every second even number is a multiple of 4. Therefore, given any two consecutive even numbers, one of them will always be a multiple of 4.

4 * 2 is 8, so any multiple of 4 multiplied by another even number will yield a multiple of 8.

Therefore, any two consecutive even numbers multiplied together will yield a multiple of 8.

THEREFORE, if n is even, n(n + 2) is always a multiple of 8.
_________________

Nicholas MOSES

GMAT/Academic Manager
c/o MBA Center Paris

Current Student
avatar
Joined: 26 May 2005
Posts: 571
Followers: 18

Kudos [?]: 108 [0], given: 13

GMAT Tests User
Re: A simple math problem, pls help me explain,thx [#permalink] New post 16 Jul 2011, 01:57
tracyyahoo wrote:
(1) If n is a positive integer, then n(n+1)(n+2) is

a) Even only when n is even
b) Even only when n is odd
c) Odd whenever n is odd
d) Divisible by 3 only when n is odd
e) Divisible by 4 only whenever n is even

Why A isn't correct since I used the plug in to calculate and I know e is correct. why a) isn't correct?


Whats the source?
E is right .
A is wrong becasue even when N is odd, it can be even ,ex: 3*4*5 ( n=3)
Intern
Intern
avatar
Joined: 29 Nov 2010
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: A simple math problem, pls help me explain,thx [#permalink] New post 17 Jul 2011, 02:57
n(n+1)(n+2) will be either

ODD * EVEN * ODD = EVEN
EVEN * ODD * EVEN = EVEN

A says that the result will be even, only when n is even, which we have shown is not the case.
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2047
Followers: 128

Kudos [?]: 906 [0], given: 376

GMAT Tests User
Re: n is a positive integer [#permalink] New post 17 Jul 2011, 03:41
siddhans wrote:
How to solve this?

If n is a positive integer, then n(n+1)(n+2) is

A)even only when n is even
B)even only when n is odd
C)odd whenever n is odd
D)divisible by 3 only when n is odd
E)divisible by 4 whenever n is even


n(n+1)(n+2) is the product of three consecutive integers because n is an integer.

0,1,2
-200,-199,-198
100,101,102
-1,0,1

In any set of three consecutive numbers, there must be at least one odd and one even.

odd,even,odd
OR
even,odd,even

A)even only when n is even
The product of three or more consecutive integers will always be EVEN. To make the product even, we just need one even. It really doesn't matter whether n is even or n+1.

If n is even, say 0
0,1,2. product=0=even

If n is odd, say -1
-1,0,1. product=0=even

Saying that n(n+1)(n+2) will be even ONLY if n=even is NOT correct.

B)even only when n is odd

We just saw that the product will always be even irrespective of whether n is even or odd.

C)odd whenever n is odd

Product will never be odd.

D)divisible by 3 only when n is odd
Rule: Product of n consecutive number will always be divisible be n!

{1,2}: Two numbers. n=2
1*2 will be divisible by 2!=2

{45,46,47,48,49,50}: Six numbers. n=6
45*46*47*48*49*50 will be divisible by 6!=720

Similarly,
3 consecutive numbers: {1,2,3}
1*2*3 will be divisible by 3!=6
If the product is divisible by 6, it must be divisible by its factor, which is 3.

Thus, "n" can be even/odd.
FALSE.

E)divisible by 4 whenever n is even
n=2
2,3,4. Product=24

TRUE.

Ans: "E"
_________________

~fluke

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 03 Jun 2010
Posts: 139
Location: Dubai, UAE
Schools: IE Business School, Manchester Business School, HEC Paris, Rotterdam School of Management, Babson College
Followers: 2

Kudos [?]: 4 [0], given: 4

GMAT ToolKit User
Re: n is a positive integer [#permalink] New post 17 Jul 2011, 04:11
This can be solved easily by process of elimination, it's important to see this as the multiplication of consecutive numbers. Please note the following properties of three Consecutive numbers
They will always be divisible by 3
Irrespective of n, the answer will always be even, because any n multiples by an even number yields an even number.
Hence out of all the options only E makes sense.
And now the icing on the cake, any three consecutive numbers have atleast 2 2's in their prime factors.

Image Posted from GMAT ToolKit
Director
Director
avatar
Joined: 01 Feb 2011
Posts: 770
Followers: 14

Kudos [?]: 82 [0], given: 42

GMAT Tests User
Re: n is a positive integer [#permalink] New post 17 Jul 2011, 13:04
n * n+1 * n+2 is always even irrespective of whether n is odd or even.

Answer choice D would have been good if there is no "Only" in it. product of 3 consecutive integers is always divisible by 3 irrespective of whether n is odd or even.

Answer Choice E.
i.e when n is even =>n+1 is odd => n+2 is even . As we have two even numbers in the product this will always be
divisible by 4.

Answer is E.
Manager
Manager
avatar
Joined: 25 Sep 2010
Posts: 85
Schools: HBS, LBS, Wharton, Kelloggs, Booth
Followers: 0

Kudos [?]: 2 [0], given: 15

Re: n is a positive integer [#permalink] New post 19 Jul 2011, 09:20
Firstly, we can see that n,(n+1) and (n+2) are consecutive integers.
Consecutive integers alternate in an Even-odd fashion. i.e., if n is even, (n+1) is odd, and (n+2) is even. Similarly, when n is odd,(n+1) is even and (n+2) is odd.
In any case, we notice that the product MUST be even. (even*any number = even)
Also,
There is a rule that 'n' consecutive integers are divisible by 'n!'
Here, n=3 => n(n+1)(n+2) div. by 3! = 3.2.1
Let us check the options:
A)even only when n is even --- wrong. Since, it is even when n is both even AND odd.
B)even only when n is odd ----wrong. Same reason as above.
C)odd whenever n is odd ----wrong. Even when n is odd.
D)divisible by 3 only when n is odd ----wrong. div. by 3 when n is even or odd
E)divisible by 4 whenever n is even---Correct. when n is even, (n+1) is odd and (n+2) is even. PRODUCT of two even no.s(here, n & n+2) is ALWAYS div.by 4.
Intern
Intern
avatar
Joined: 17 Jul 2011
Posts: 7
Followers: 1

Kudos [?]: 0 [0], given: 3

Re: A simple math problem, pls help me explain,thx [#permalink] New post 20 Jul 2011, 21:36
I think even E is wrong. Even if n=3, odd, then the product is 3*4*5 and is divisible by 4.
I question the validity of this question!!!
Current Student
User avatar
Joined: 08 Jan 2009
Posts: 334
GMAT 1: 770 Q50 V46
Followers: 22

Kudos [?]: 81 [0], given: 7

GMAT Tests User
Re: A simple math problem, pls help me explain,thx [#permalink] New post 20 Jul 2011, 22:26
Claudia777 wrote:
I think even E is wrong. Even if n=3, odd, then the product is 3*4*5 and is divisible by 4.
I question the validity of this question!!!


Divisible by 4 only whenever n is even

Hence n can't equal 3, as n must be even.
_________________

My Debrief

Intern
Intern
avatar
Joined: 17 Jul 2011
Posts: 7
Followers: 1

Kudos [?]: 0 [0], given: 3

Re: A simple math problem, pls help me explain,thx [#permalink] New post 21 Jul 2011, 05:29
Many thanks. I thougth the problem said " only when n is even" , but it actually said "whenever n is even"...i got it now!
Thanks :-D

On the same note, I found the problem elsewhere and the E. answer was : e) Divisible by 4 whenever n is even ( while here E is e) Divisible by 4 only whenever n is even) Was a bit confusing!!

In any case,I got it now!!:)
Current Student
User avatar
Joined: 08 Jan 2009
Posts: 334
GMAT 1: 770 Q50 V46
Followers: 22

Kudos [?]: 81 [0], given: 7

GMAT Tests User
Re: A simple math problem, pls help me explain,thx [#permalink] New post 21 Jul 2011, 13:48
Claudia777 wrote:
Many thanks. I thougth the problem said " only when n is even" , but it actually said "whenever n is even"...i got it now!
Thanks :-D

On the same note, I found the problem elsewhere and the E. answer was : e) Divisible by 4 whenever n is even ( while here E is e) Divisible by 4 only whenever n is even) Was a bit confusing!!

In any case,I got it now!!:)


Right, but to divide by four, n must be even. So it is E in both questions.
_________________

My Debrief

Intern
Intern
User avatar
Joined: 11 May 2011
Posts: 23
Followers: 0

Kudos [?]: 10 [0], given: 1

Re: consecutive integers product [#permalink] New post 30 Aug 2011, 04:18
This revolves around two principles.

1. if one number in a product of two or more is even then the number is always EVEN

2. A product of three consicutive POSITIVE integers is always divisible by 3.

IF N is even then the least possible product is 2*3*4 which is divisible by 4 . Holds true for any higher even value for N.

a) even only when n is even

even when N is odd the product is even because N+1 is even .


b) even only when n is odd

even when N is even the product is even because (if one number in a product of two or more is even then the number is always EVEN).

c) odd whenever n is odd
THe product of two or more consecutive positive integers is never ODD



d) divisible by 3 only when n is odd

Does not matter if N is even or ODD

Every third poitive integer is divisible by three. Does not matter if N is ODD or EVEN

Example:
1. N= 2 set S= {2,3,4} product is divisible by 3
2. N = 4 set S = {4,5, 6} product is divisible by 3.

Note 3 has a cyclicity of {0,1,2} as reminder for all Positive integers.


e) divisible by 4 whenever n is even

True: if N is even then N and N+2 are necessarily even hence divisible by 4 :

Consider least even positive integer 2

2*3*4 is divisible by 4 {true for all values of N as even because divisibility by 4 means the number must be divisible by 2 twice. In this scenario we would have N and N+2 as even}


Hence option E.

Hope the explanation was helpful.


Regards,
Raghav.V

Consider kudos if my post was helpful. :-D
Re: consecutive integers product   [#permalink] 30 Aug 2011, 04:18
    Similar topics Author Replies Last post
Similar
Topics:
What is the value of n? (1) n(n 1)(n 2 ) = 0 (2) n^2 + n 6 = vageesh 2 11 Jan 2010, 05:50
n is positive integer, is n(n+1)(n+2) divisible by 12? 1) getzgetzu 1 05 May 2006, 23:47
What is the value of n? (1) n(n 1)(n 2 ) = 0 (2) n2 + n 6 = briozeal 1 10 Oct 2005, 16:44
If P = n(n-1)(n-2)...(1) amd n>2, what is the largest Guest 1 11 Sep 2004, 21:06
If P = (n)(n 1)(n 2) . . . (1) and n > 2, what is the Antmavel 6 05 Sep 2004, 16:16
Display posts from previous: Sort by

If n is a positive integer, then n(n+1)(n+2) is

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2    Next  [ 25 posts ] 



GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.