It is currently 18 Oct 2017, 12:18

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
Intern
Joined: 24 Oct 2006
Posts: 31

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

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

Show Tags

14 May 2007, 10:42
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

HideShow timer Statistics

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

(A) -4
(B) -2
(C) -1
(D) 2
(E) 5

Any nice n fast way to solve this? Took way too long for me..

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

Manager
Joined: 28 Aug 2006
Posts: 159

Kudos [?]: 16 [0], given: 0

Show Tags

14 May 2007, 10:55

Product of any 3 consequetive numbers is divisible by 3.

Kudos [?]: 16 [0], given: 0

Senior Manager
Joined: 03 May 2007
Posts: 270

Kudos [?]: 14 [0], given: 0

Show Tags

14 May 2007, 11:00
just plug either -1 or 2 in and you'll see that it's -2
the trick is in word must(meaning it has to work for any number)

Kudos [?]: 14 [0], given: 0

Intern
Joined: 24 Oct 2006
Posts: 31

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

Show Tags

14 May 2007, 11:06
Sergey_is_cool wrote:
just plug either -1 or 2 in and you'll see that it's -2
the trick is in word must(meaning it has to work for any number)

i did start plugging in, both for k and different values for x.. just took too long..

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

VP
Joined: 08 Jun 2005
Posts: 1144

Kudos [?]: 246 [0], given: 0

Re: PS: Divisible by 3 [#permalink]

Show Tags

14 May 2007, 11:49
ani 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

Any nice n fast way to solve this? Took way too long for me..

I don't understand the except part ? if k = -2 and x = 3 then

3*2*5 = 30 which is divisable by 3.

what am I'm doing wrong ?

Kudos [?]: 246 [0], given: 0

Intern
Joined: 24 Oct 2006
Posts: 31

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

Re: PS: Divisible by 3 [#permalink]

Show Tags

14 May 2007, 13:12
KillerSquirrel wrote:
ani 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

Any nice n fast way to solve this? Took way too long for me..

I don't understand the except part ? if k = -2 and x = 3 then

3*2*5 = 30 which is divisable by 3.

what am I'm doing wrong ?

We just need to prove that if k = -2, the expression is NOT divisible by 3 for SOME value of x (when x = 2, for example)

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

Current Student
Joined: 28 Dec 2004
Posts: 3351

Kudos [?]: 319 [0], given: 2

Location: New York City
Schools: Wharton'11 HBS'12

Show Tags

14 May 2007, 13:51
i follow that any 3 consecutiv numbers are divisible by 3..but how come k=-4 doesnt work??

maybe i am brain dead right now..but i am not following the question..

Kudos [?]: 319 [0], given: 2

Manager
Joined: 14 Mar 2007
Posts: 235

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

Show Tags

14 May 2007, 14:48
this is da kind of problem that takes you lots of time to solve if you do not know that 0ddx0dd=Odd so the last term must be odd also and for it comes -2

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

Manager
Joined: 30 Mar 2007
Posts: 213

Kudos [?]: 11 [0], given: 0

Show Tags

14 May 2007, 14:58
let m=x*(x – 1)*(x – k)

m will be surly divisible by 3 is k = 2
coz product of any three consecutive number will always be divisible by three.
1*2*3.....11*12*13........99*100*101

now que asks for what all valuse of k...m will be divisible by 3.
let assume that x and x-1 are not divisible by 3.else for any value to k….m will be divisible.
so we can have x-2 as value divisible by 3.
now subtracting or adding multiple 3 to x-2 will always give a numbers divisible by 3.

x+1, x+4,x-5...so k can be 2,-4,-1,-5..but not -2

Kudos [?]: 11 [0], given: 0

VP
Joined: 08 Jun 2005
Posts: 1144

Kudos [?]: 246 [0], given: 0

Show Tags

14 May 2007, 21:23
apache wrote:
let m=x*(x – 1)*(x – k)

m will be surly divisible by 3 is k = 2
coz product of any three consecutive number will always be divisible by three.
1*2*3.....11*12*13........99*100*101

now que asks for what all valuse of k...m will be divisible by 3.
let assume that x and x-1 are not divisible by 3.else for any value to k….m will be divisible.
so we can have x-2 as value divisible by 3.
now subtracting or adding multiple 3 to x-2 will always give a numbers divisible by 3.

x+1, x+4,x-5...so k can be 2,-4,-1,-5..but not -2

but I can't understand this question

if x=3 won't then the therm x*(x – 1)*(x – k) will be divisable by 3

no matter what k is ?

Kudos [?]: 246 [0], given: 0

Manager
Joined: 30 Mar 2007
Posts: 213

Kudos [?]: 11 [0], given: 0

Show Tags

14 May 2007, 21:54
squirrel,
from my previous post.....let assume that x and x-1 are not divisible by 3.else for any value to k….m will be divisible.

if we assume x or x-1 is divsible by 3 then que stands null and void.
as you rightly pointed that for any value of k ,term will be divisible.

Kudos [?]: 11 [0], given: 0

VP
Joined: 08 Jun 2005
Posts: 1144

Kudos [?]: 246 [0], given: 0

Show Tags

15 May 2007, 04:18
apache wrote:
squirrel,
from my previous post.....let assume that x and x-1 are not divisible by 3.else for any value to k….m will be divisible.

if we assume x or x-1 is divsible by 3 then que stands null and void.
as you rightly pointed that for any value of k ,term will be divisible.

didn't saw that ! thanks apache

Kudos [?]: 246 [0], given: 0

Current Student
Joined: 28 Dec 2004
Posts: 3351

Kudos [?]: 319 [0], given: 2

Location: New York City
Schools: Wharton'11 HBS'12

Show Tags

15 May 2007, 07:48
today is a new day..and now i get it ...apache ..excellent explanation...

Kudos [?]: 319 [0], given: 2

Current Student
Joined: 28 Dec 2004
Posts: 3351

Kudos [?]: 319 [0], given: 2

Location: New York City
Schools: Wharton'11 HBS'12

Show Tags

16 May 2007, 10:10
I dont think this is a valid GMAT question, cause as KS pointed K, K-1 could be divisible by 3...we just dont know..

Kudos [?]: 319 [0], given: 2

Intern
Joined: 15 Jan 2007
Posts: 38

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

Show Tags

16 May 2007, 10:29
fresinha12 wrote:
I dont think this is a valid GMAT question, cause as KS pointed K, K-1 could be divisible by 3...we just dont know..

it is a valid question. agreed x can be 3 but what if x is 5 ? the question asks about the whole expression ! and remember x * (x+1) * (x+2) can always be divided by 3.

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

16 May 2007, 10:29
Display posts from previous: Sort by