GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 24 May 2020, 18:01

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.

Close

Request Expert Reply

Confirm Cancel

If n is the product of three consecutive intergers, and n is divisible

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 25 Jul 2013
Posts: 5
If n is the product of three consecutive intergers, and n is divisible  [#permalink]

Show Tags

New post 12 Feb 2016, 02:51
6
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (01:44) correct 40% (01:55) wrong based on 100 sessions

HideShow timer Statistics

If n is the product of three consecutive integers, and n is divisible by 7, which of the following is not necessarily a divisor of n ?


(A) 6

(B) 14

(C) 21

(D) 28

(E) 42

can you explain why???
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64068
Re: If n is the product of three consecutive intergers, and n is divisible  [#permalink]

Show Tags

New post 12 Feb 2016, 03:23
3
3
tjkim88 wrote:
If n is the product of three consecutive integers, and n is divisible by 7, which of the following is not necessarily a divisor of n ?


(A) 6

(B) 14

(C) 21

(D) 28

(E) 42

can you explain why???


The product of k consecutive integers is always divisible by k! (factorial of k).

So, according to the above, the product of 3 consecutive integers is divisible by 3! = 6. Since n is also divisible by 7, then it must be divisible by the LCM of 6 and 7, which is 42. Therefore n is divisible by 6, 14, 21 and 42. By POE the correct answer must be D.

Answer: D.
_________________
General Discussion
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8584
Re: If n is the product of three consecutive intergers, and n is divisible  [#permalink]

Show Tags

New post 12 Feb 2016, 03:03
2
3
tjkim88 wrote:
If n is the product of three consecutive integers, and n is divisible by 7, which of the following is not necessarily a divisor of n ?


(A) 6

(B) 14

(C) 21

(D) 28

(E) 42

can you explain why???


Hi,
first you have to see the minimum value and ways..
1) 5*6*7= 2*3*5*7
2) 6*7*8= 2^4*3*7
3) 7*8*9..=2^3*7*9..

what is the common in the three terms..
2*3*7..

lets find the choice which contains any term beyond these three..
(A) 6
2*3= so Always

(B) 14
2*7= again always

(C) 21
3*7= again always

(D) 28
2*2*7..
may be there, may not be there
CORRECT

(E) 42
2*3*7= again always

ans D
hope it helps
_________________
Intern
Intern
avatar
B
Joined: 25 Jul 2013
Posts: 5
Re: If n is the product of three consecutive intergers, and n is divisible  [#permalink]

Show Tags

New post 12 Feb 2016, 03:21
chetan2u wrote:
tjkim88 wrote:
If n is the product of three consecutive integers, and n is divisible by 7, which of the following is not necessarily a divisor of n ?


(A) 6

(B) 14

(C) 21

(D) 28

(E) 42

can you explain why???


Hi,
first you have to see the minimum value and ways..
1) 5*6*7= 2*3*5*7
2) 6*7*8= 2^4*3*7
3) 7*8*9..=2^3*7*9..

what is the common in the three terms..
2*3*7..

lets find the choice which contains any term beyond these three..
(A) 6
2*3= so Always

(B) 14
2*7= again always

(C) 21
3*7= again always

(D) 28
2*2*7..
may be there, may not be there
CORRECT

(E) 42
2*3*7= again always

ans D
hope it helps


thx a lot I completely understand it !
VP
VP
avatar
D
Joined: 07 Dec 2014
Posts: 1252
Re: If n is the product of three consecutive intergers, and n is divisible  [#permalink]

Show Tags

New post 25 Mar 2017, 12:01
tjkim88 wrote:
If n is the product of three consecutive integers, and n is divisible by 7, which of the following is not necessarily a divisor of n ?


(A) 6

(B) 14

(C) 21

(D) 28

(E) 42

can you explain why???


28 divides only if the sequence includes a multiple of 4
it works for 6,7,8 and 7,8,9, but not for 5,6,7
D
Manager
Manager
avatar
B
Joined: 30 Jun 2019
Posts: 208
Re: If n is the product of three consecutive intergers, and n is divisible  [#permalink]

Show Tags

New post 12 Mar 2020, 14:30
n = (x)(x+1)(x+2)

if we know that this is divisible by 7, then we need to rationalize the other prime factors

at a minimum, we have (1)(2)(3) which means we have at least one 2 and one 3 as prime factors FOR SURE.
7*1 = 7 given
7*2 = 14
7*3 = 21
7*2*3 = 42

We are not guaranteed a 2nd 2 which is what is needed for 28 -->7*2*2 = 28
So 28 is the answer.
GMAT Club Bot
Re: If n is the product of three consecutive intergers, and n is divisible   [#permalink] 12 Mar 2020, 14:30

If n is the product of three consecutive intergers, and n is divisible

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne