Author 
Message 
Director
Joined: 23 Sep 2007
Posts: 783

If x is an integer, then x(x 1)(x k) must be evenly [#permalink]
Show Tags
29 Jun 2008, 22:06
This topic is locked. If you want to discuss this question please repost 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

Re: x(x – 1)(x – k) [#permalink]
Show Tags
29 Jun 2008, 22:13
I would go for B.
The product may not be divisible by 3 if xk is not equal to x2, x5, x(1), x(4). Because x or x1 may not be divisible by 3.



SVP
Joined: 29 Aug 2007
Posts: 2473

Re: x(x – 1)(x – k) [#permalink]
Show Tags
29 Jun 2008, 22:22
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.
_________________
Verbal: http://gmatclub.com/forum/newtotheverbalforumpleasereadthisfirst77546.html Math: http://gmatclub.com/forum/newtothemathforumpleasereadthisfirst77764.html Gmat: http://gmatclub.com/forum/everythingyouneedtoprepareforthegmatrevised77983.html
GT



Manager
Joined: 28 May 2008
Posts: 94

Re: x(x – 1)(x – k) [#permalink]
Show Tags
29 Jun 2008, 23:27
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: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: x(x – 1)(x – k) [#permalink]
Show Tags
29 Jun 2008, 23:33
1. x(x – 1)(x – k) is divisible by 3 if x,x1,xk 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 musthave app especially if you aim at 700+  PrepGame



SVP
Joined: 28 Dec 2005
Posts: 1558

Re: x(x – 1)(x – k) [#permalink]
Show Tags
30 Jun 2008, 11:45
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: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: x(x – 1)(x – k) [#permalink]
Show Tags
30 Jun 2008, 11:49
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 musthave app especially if you aim at 700+  PrepGame



Director
Joined: 01 Jan 2008
Posts: 622

Re: x(x – 1)(x – k) [#permalink]
Show Tags
30 Jun 2008, 11:55
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*(x1)*(x2) is divisible by 3. x*(x1)*(xk) 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: 1558

Re: x(x – 1)(x – k) [#permalink]
Show Tags
30 Jun 2008, 12:06
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: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: x(x – 1)(x – k) [#permalink]
Show Tags
30 Jun 2008, 12:28
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(x1)(xk) div 3 is always even number, because one of the number, x or (x1), is always even.
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  PrepGame




Re: x(x – 1)(x – k)
[#permalink]
30 Jun 2008, 12:28






