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bryan88: Master | Next Rank: 500 Posts; Posts: 120; Joined: Mon Nov 07, 2011 10:54 pm; Location: Delhi; Thanked: 5 times

by bryan88 » Sun May 13, 2012 6:39 am

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

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Source: Beat The GMAT — Problem Solving | Sun May 13, 2012 6:39 am

Birottam Dutta: Master | Next Rank: 500 Posts; Posts: 342; Joined: Wed Jul 08, 2009 8:50 amFollowed by: 19 members; Thanked: 214 times; GMAT Score:740

by Birottam Dutta » Sun May 13, 2012 7:50 am

Assume values of x and solve.

Answer is B (-2).

By assuming values, you should be able to find the answer within a minute.

Folks please check this out
https://www.youtube.com/watch?v=H7p56NzAVKc

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun May 13, 2012 9:30 pm

bryan88 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

The product of 3 integers is divisible by 3 if at least one multiple is divisible by 3. Now, to find if at least one integer out of x, (x - 1), and (x - k) is divisible by 3 these numbers must have different remainders on division by 3, which means that one of them should have remainder of 1, another one should have remainder of 2 and the last one should have remainder of 0.

If k = -2 then (x - 1)x(x + 2) = (x - 1)x(x - 1 + 3), which means that (x - 1) and (x + 2) will have the same remainder on division by 3. So, for k = -2 we are not sure if (x - 1)x(x - k) is divisible by 3.

The correct answer is B.

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