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

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Intern
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If x is an integer, then x(x 1)(x k) must be evenly [#permalink]  14 May 2007, 09:42
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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..
Manager
Joined: 28 Aug 2006
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Product of any 3 consequetive numbers is divisible by 3.
Senior Manager
Joined: 03 May 2007
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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)
Intern
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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..
VP
Joined: 08 Jun 2005
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Re: PS: Divisible by 3 [#permalink]  14 May 2007, 10:49
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 ?

Intern
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Re: PS: Divisible by 3 [#permalink]  14 May 2007, 12:12
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)
Current Student
Joined: 28 Dec 2004
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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..
Manager
Joined: 14 Mar 2007
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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
Manager
Joined: 30 Mar 2007
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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
VP
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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 ?
Manager
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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.
VP
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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
Current Student
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today is a new day..and now i get it ...apache ..excellent explanation...

Current Student
Joined: 28 Dec 2004
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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..
Intern
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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.
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