Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 24 May 2017, 09:27

# Live Now:

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x is an integer, then x(x - 1)(x - k) must be evenly divisible by

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

### Hide Tags

Manager
Joined: 25 Mar 2008
Posts: 106
Followers: 1

Kudos [?]: 12 [0], given: 0

If x is an integer, then x(x - 1)(x - k) must be evenly divisible by [#permalink]

### Show Tags

24 Apr 2008, 08:40
2
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

69% (02:14) correct 31% (01:41) wrong based on 75 sessions

### HideShow timer Statistics

If x is an integer, then x(x - 1)(x - k) must be evenly divisible by three when k is any of the following values EXCEPT

A. -4
B. -2
C. -1
D. 2
E. 5

Open discussion of this question is here: if-x-is-an-integer-then-x-x-1-x-k-must-be-evenly-divisible-126853.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Apr 2015, 03:53, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Director
Joined: 05 Jan 2008
Posts: 690
Followers: 5

Kudos [?]: 472 [0], given: 0

Re: If x is an integer, then x(x - 1)(x - k) must be evenly divisible by [#permalink]

### Show Tags

24 Apr 2008, 10:29
Are you sure the question is complete the answer B fails for X=6
_________________

Persistence+Patience+Persistence+Patience=G...O...A...L

SVP
Joined: 24 Aug 2006
Posts: 2130
Followers: 3

Kudos [?]: 144 [0], given: 0

Re: If x is an integer, then x(x - 1)(x - k) must be evenly divisible by [#permalink]

### Show Tags

24 Apr 2008, 11:26
shobuj wrote:
If x is an integer, then x(x – 1)(x – k) must be evenly divisible by three when k is any of the following values EXCEPT
A. -4
B. -2
C. -1
D. 2
E. 5

Answer: (B) -2.

I agree w/prasannar, something's missing from the question. Are you sure the question isn't something like:

X + (X - 1) + (X - k)?

That would yield B as the answer.
-------------------------------

Anyway, if it's the above terms, then just combine to get 3X - 1 - k, eliminate 3X since it's divisible by 3, plug and test with -1 - k to see what isn't divisible by 3.
Manager
Joined: 25 Mar 2008
Posts: 106
Followers: 1

Kudos [?]: 12 [0], given: 0

Re: If x is an integer, then x(x - 1)(x - k) must be evenly divisible by [#permalink]

### Show Tags

24 Apr 2008, 12:31
If x is an integer, then x(x – 1)(x – k) must be evenly divisible by three when k is any of the following values EXCEPT
A. -4
B. -2
C. -1
D. 2
E. 5

guys i have done a little bit about this:

if we put k=-1 we get:

X(x-1)(X+1) rearrange:(x-1)X(X+1)

so it looks like a sequenc,

if we assume that X =2 and put number from the answer then we get:
(x – 1)x(x – k)
k=5 =1.2.-3
k=2 =1.2.0
k=-1 =1.2.3
k=-4 =1.2.6
but when we put
k=-2 =1.2.4 not satisfied

but the stem says that x is and integer and 0 is an integer if we put 0 in this term than anything is divisable by 3, becaz 0 is divisable by 3

now i m also a little bit confused.

thanks
shobuj
SVP
Joined: 24 Aug 2006
Posts: 2130
Followers: 3

Kudos [?]: 144 [0], given: 0

Re: If x is an integer, then x(x - 1)(x - k) must be evenly divisible by [#permalink]

### Show Tags

24 Apr 2008, 12:38
Where did you get the question from?
Current Student
Joined: 28 Dec 2004
Posts: 3363
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 15

Kudos [?]: 297 [0], given: 2

Re: If x is an integer, then x(x - 1)(x - k) must be evenly divisible by [#permalink]

### Show Tags

24 Apr 2008, 12:45
i agree with B..

pick x=2..

1*2*4 isnt divisble by 3...

pick x=5

4*5*7..isnt divisble by 3...
Manager
Joined: 25 Mar 2008
Posts: 106
Followers: 1

Kudos [?]: 12 [0], given: 0

Re: If x is an integer, then x(x - 1)(x - k) must be evenly divisible by [#permalink]

### Show Tags

24 Apr 2008, 12:51
kiddrek i got it from another site and i think that walker can explain me much more better way

and the question is a valid one

but now can u clear me that in this question can we assume x = 0 or not ?

tanks
shobuj
Current Student
Joined: 28 Dec 2004
Posts: 3363
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 15

Kudos [?]: 297 [0], given: 2

Re: If x is an integer, then x(x - 1)(x - k) must be evenly divisible by [#permalink]

### Show Tags

24 Apr 2008, 13:00
haha..ur pushing ur luck..yes for x=0..everything is divisble..

so poorly written question..but suppose it said x is a positive integer..then b would the right answer..

otherwise..Kidrecks stem is also valid..

shobuj wrote:
kiddrek i got it from another site and i think that walker can explain me much more better way

and the question is a valid one

but now can u clear me that in this question can we assume x = 0 or not ?

tanks
shobuj
SVP
Joined: 24 Aug 2006
Posts: 2130
Followers: 3

Kudos [?]: 144 [0], given: 0

Re: If x is an integer, then x(x - 1)(x - k) must be evenly divisible by [#permalink]

### Show Tags

24 Apr 2008, 13:11
shobuj wrote:
kidderek i got it from another site and i think that walker can explain me much more better way

and the question is a valid one

but now can u clear me that in this question can we assume x = 0 or not ?

tanks
shobuj

As the questions reads, we can assume x = 0, negative, any whole number. But as prasannar has said, if x=3 or any number divisible by 3, then the entire product of x(x-1)(x-k) will be divisible by 3, irrespective of the value of k.

That is why I think my divisibility of SUM, X + (X-1) + (X-k), instead of product, makes more sense. It can't just be a coincidence that the answer choice fits too, can it?
Manager
Joined: 25 Mar 2008
Posts: 106
Followers: 1

Kudos [?]: 12 [0], given: 0

Re: If x is an integer, then x(x - 1)(x - k) must be evenly divisible by [#permalink]

### Show Tags

24 Apr 2008, 13:55
hmm
thanks

i pick it from manhattan GMAT forum?

thanks

i will send the link later
thanks
shobuj
Senior Manager
Joined: 29 Jan 2007
Posts: 442
Location: Earth
Followers: 2

Kudos [?]: 63 [0], given: 0

Re: If x is an integer, then x(x - 1)(x - k) must be evenly divisible by [#permalink]

### Show Tags

24 Apr 2008, 18:06
shobuj wrote:
If x is an integer, then x(x – 1)(x – k) must be evenly divisible by three when k is any of the following values EXCEPT
A. -4
B. -2
C. -1
D. 2
E. 5

Answer: (B) -2.

This is what I tried....

for term x(x-1)
pick x = 10 , expression becomes 10*9*(x-k) , this expression is anyway divisible by 3
so 10 is not a good pick to find out k

pick x = 9...again not good pick as 9 itself is divisible by 3

pick 8 , expression becomes...8*7*(x-k)...so (x-k) has to be multiple of 3.

If you try options now...all except B makes (x-k) multiple of 3.

So answer is B.
Manager
Joined: 25 Mar 2008
Posts: 106
Followers: 1

Kudos [?]: 12 [0], given: 0

Re: If x is an integer, then x(x - 1)(x - k) must be evenly divisible by [#permalink]

### Show Tags

24 Apr 2008, 22:54
yes

that what i stated before but my question lies on
what about when x =0

and for this question i think
they
want if x greater than 0 alll digit satisfy the sequence

bcause any threes term sequence is divisable by 3 equence
1,2.3
2,3,4
4,5,6
-1,0,1
-2,-1,0
-3,-2,-1
-1,1,3 diff=2

thanks
shobuj
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15423
Followers: 649

Kudos [?]: 207 [0], given: 0

Re: If x is an integer, then x(x - 1)(x - k) must be evenly divisible by [#permalink]

### Show Tags

27 Apr 2015, 14:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If x is an integer, then x(x - 1)(x - k) must be evenly divisible by   [#permalink] 27 Apr 2015, 14:29
Similar topics Replies Last post
Similar
Topics:
If a is an integer larger than 1, and x=60a, then x must be a multiple 1 28 Sep 2016, 13:55
125 If x is an integer then x(x-1)(x-k) must be evenly divisible 23 25 Jan 2017, 09:02
1 If x is an even integer, is x(x+1)(x+2) divisible by 4? 3 11 May 2011, 21:11
45 If x is an integer, then x(x – 1)(x – k) must be evenly divi 27 05 Oct 2016, 16:33
28 If x is an integer, then x(x - 1)(x - k) must be evenly 12 12 May 2012, 12:38
Display posts from previous: Sort by

# If x is an integer, then x(x - 1)(x - k) must be evenly divisible by

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.