If x is an integer, then x(x 1)(x k) must be evenly : Quant Question Archive [LOCKED]
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 23:28

### 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

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

Author Message
Director
Joined: 23 Sep 2007
Posts: 789
Followers: 5

Kudos [?]: 185 [0], given: 0

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

### Show Tags

29 Jun 2008, 21:06
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
-4
-2
-1
2
5

Any short cut, the OE is not helpful
Senior Manager
Joined: 09 Oct 2007
Posts: 466
Followers: 1

Kudos [?]: 42 [0], given: 1

Re: x(x – 1)(x – k) [#permalink]

### Show Tags

29 Jun 2008, 21:13
I would go for B.

The product may not be divisible by 3 if x-k is not equal to x-2, x-5, x-(-1), x-(-4). Because x or x-1 may not be divisible by 3.
SVP
Joined: 29 Aug 2007
Posts: 2492
Followers: 68

Kudos [?]: 735 [0], given: 19

Re: x(x – 1)(x – k) [#permalink]

### Show Tags

29 Jun 2008, 21:22
gmatnub 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
-4
-2
-1
2
5

Any short cut, the OE is not helpful

make or break the expression into a form such that it is either in a consecutive form or a multiple of 3 as under:
1. x(x – 1)(x + 4) = x(x – 1)(x + 1 +3) = x(x – 1)[(x + 1) +3]
2. x(x – 1)(x + 2)
3. x(x – 1)(x + 1)
4. x(x – 1)(x - 2) = x(x – 1)(x + 1 - 3)
5. x(x – 1)(x - 5) = x(x – 1)(x +1 - 6)

B. except -2, all could be k such that x(x – 1)(x - k) is divisible by 3. in all options except second, the integers are in eith consecutive order or in at least one of them is divisible by 3 but B is not at any case.
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Manager
Joined: 28 May 2008
Posts: 94
Followers: 2

Kudos [?]: 9 [0], given: 0

Re: x(x – 1)(x – k) [#permalink]

### Show Tags

29 Jun 2008, 22:27
I say shortcut for such problems is always trying a couple of numbers and see which one satisfies.
for eg
Take x=5
Just plug in the options. B doesnt satisfy
CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 548

Kudos [?]: 3561 [0], given: 360

Re: x(x – 1)(x – k) [#permalink]

### Show Tags

29 Jun 2008, 22:33
1. x(x – 1)(x – k) is divisible by 3 if x,x-1,x-k is consecutive integers: x(x – 1)(x – 2) for k=2
2. Now, subtraction or addition of 3 to any of members does not change divisibility: -7,-4,-1,2,5,8. -2 is out of the set.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

SVP
Joined: 28 Dec 2005
Posts: 1575
Followers: 3

Kudos [?]: 147 [0], given: 2

Re: x(x – 1)(x – k) [#permalink]

### Show Tags

30 Jun 2008, 10:45
i dont fully get it ... what if x=3 ? thats what i used, and it turned out that if you use that, then for all k values in the question, the product is divisible by 3 :S

I guess for these types of questions, you shouldnt use the value youre dividing by ?
CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 548

Kudos [?]: 3561 [0], given: 360

Re: x(x – 1)(x – k) [#permalink]

### Show Tags

30 Jun 2008, 10:49
pmenon wrote:
i dont fully get it ... what if x=3 ? thats what i used, and it turned out that if you use that, then for all k values in the question, the product is divisible by 3 :S

I guess for these types of questions, you shouldnt use the value youre dividing by ?

Reread the question - must be evenly divisible by three [at any x]

x=3 and k=any - works
x=5 and k=0 - does not work
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Director
Joined: 01 Jan 2008
Posts: 629
Followers: 4

Kudos [?]: 175 [0], given: 1

Re: x(x – 1)(x – k) [#permalink]

### Show Tags

30 Jun 2008, 10:55
gmatnub 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
-4
-2
-1
2
5

Any short cut, the OE is not helpful

my 5 sec solution. x*(x-1)*(x-2) is divisible by 3. x*(x-1)*(x-k) must be divisible by 3 if k = 2(mod 3)

notice that -4, -1, 2, 5 = 2(mod 3). -2 = 1(mod 3) -> B
SVP
Joined: 28 Dec 2005
Posts: 1575
Followers: 3

Kudos [?]: 147 [0], given: 2

Re: x(x – 1)(x – k) [#permalink]

### Show Tags

30 Jun 2008, 11:06
walker wrote:
pmenon wrote:
i dont fully get it ... what if x=3 ? thats what i used, and it turned out that if you use that, then for all k values in the question, the product is divisible by 3 :S

I guess for these types of questions, you shouldnt use the value youre dividing by ?

Reread the question - must be evenly divisible by three [at any x]

x=3 and k=any - works
x=5 and k=0 - does not work

thanks walker, but im still confused. i get the general concept, but having problems applying it. i assume evenly divisible means that the quotient is an even number ? how does this change things ? gah im so confused !
CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 548

Kudos [?]: 3561 [0], given: 360

Re: x(x – 1)(x – k) [#permalink]

### Show Tags

30 Jun 2008, 11:28
pmenon wrote:
thanks walker, but im still confused. i get the general concept, but having problems applying it. i assume evenly divisible means that the quotient is an even number ? how does this change things ? gah im so confused !

the quotient x(x-1)(x-k) div 3 is always even number, because one of the number, x or (x-1), is always even.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Re: x(x – 1)(x – k)   [#permalink] 30 Jun 2008, 11:28
Display posts from previous: Sort by