|
Author |
Message |
|
TAGS:
|
|
|
Intern
Joined: 24 Oct 2006
Posts: 32
Followers: 0
Kudos [?]:
0
[0], given: 0
|
If x is an integer, then x(x 1)(x k) must be evenly [#permalink]
 14 May 2007, 10:42
Question Stats:
0% (00:00) correct
 0% (00:00) wrong based on 0 sessions
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
Posts: 161
Followers: 1
Kudos [?]:
5
[0], given: 0
|
Answer is -2.
Product of any 3 consequetive numbers is divisible by 3.
|
|
|
|
|
|
Senior Manager
Joined: 03 May 2007
Posts: 281
Followers: 1
Kudos [?]:
7
[0], given: 0
|
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
Joined: 24 Oct 2006
Posts: 32
Followers: 0
Kudos [?]:
0
[0], given: 0
|
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
Posts: 1172
Followers: 5
Kudos [?]:
78
[0], given: 0
|
Re: PS: Divisible by 3 [#permalink]
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 ?
|
|
|
|
|
|
Intern
Joined: 24 Oct 2006
Posts: 32
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Re: PS: Divisible by 3 [#permalink]
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)
|
|
|
|
|
|
Current Student
Joined: 28 Dec 2004
Posts: 3439
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 11
Kudos [?]:
134
[0], given: 2
|
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
Posts: 242
Followers: 1
Kudos [?]:
1
[0], given: 0
|
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
Posts: 222
Followers: 1
Kudos [?]:
2
[0], given: 0
|
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
Joined: 08 Jun 2005
Posts: 1172
Followers: 5
Kudos [?]:
78
[0], given: 0
|
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
sorry to ask again
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
Joined: 30 Mar 2007
Posts: 222
Followers: 1
Kudos [?]:
2
[0], given: 0
|
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.
hope this clears your doubt.
|
|
|
|
|
|
VP
Joined: 08 Jun 2005
Posts: 1172
Followers: 5
Kudos [?]:
78
[0], given: 0
|
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.
hope this clears your doubt.
didn't saw that ! thanks apache 
|
|
|
|
|
|
Current Student
Joined: 28 Dec 2004
Posts: 3439
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 11
Kudos [?]:
134
[0], given: 2
|
today is a new day..and now i get it ...apache ..excellent explanation...
|
|
|
|
|
|
Current Student
Joined: 28 Dec 2004
Posts: 3439
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 11
Kudos [?]:
134
[0], given: 2
|
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
Joined: 15 Jan 2007
Posts: 38
Followers: 0
Kudos [?]:
1
[0], given: 0
|
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.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Similar topics |
Author |
Replies |
Last post |
|
Similar
Topics:
|
 |
|
|
If x is an integer, then x(x 1)(x k) must be evenly
|
sujayb |
2 |
22 Nov 2006, 13:32 |
 |
|
 |
If x is an integer, then x(x 1)(x k) must be evenly
|
ashkrs |
12 |
04 Jan 2008, 21:38 |
|
|
|
|
If x is an integer, then x(x 1)(x k) must be evenly
|
shobuj |
11 |
24 Apr 2008, 08:40 |
|
|
|
|
If x is an integer, then x(x 1)(x k) must be evenly
|
gmatnub |
9 |
29 Jun 2008, 22:06 |
 |
7
|
|
If x is an integer, then x(x - 1)(x - k) must be evenly
|
dimitri92 |
12 |
22 May 2010, 05:15 |
|
|
|
|
|
|
close
