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

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If x is an integer, then x(x 1)(x k) must be evenly [#permalink] New post 22 Nov 2006, 12:32
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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


Explanations pls.


Ans : B
Senior Manager
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 [#permalink] New post 22 Nov 2006, 17:06
b.

pick a number so that x(x-1) is not divisible by 3. for exampe 2.
then plugin the different values for k
a) 2*1*6 divisible
b) 2*1*4 not
c) 2*1*3 is
d) 2*1*0 is (0 is divisible by any integer except 0)
e) 2*1*(-3) is

so th answer is b.
the reason for this choice is if x(x-1) already divisible by 3. multiplying it by x-k will not change that...so gives us no information
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[#permalink] New post 22 Nov 2006, 17:43
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


x + x-1 + x - k = 3x-1+k

A 3x-1+4=3x+3 divisible by 3
B 3x -1 +2 = 3x +1
C 3x-1+1 = 3x divisible by 3
D 3x -1 -2 = 3x -3 divisible by 3
E 3x -1 -5 = 3x -6 divisible by 3
B   [#permalink] 22 Nov 2006, 17:43
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