Algebra

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govind_raj_76: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Tue Apr 20, 2010 7:16 pm; Location: Newark, DE

by govind_raj_76 » Sun Jul 18, 2010 8:09 am

If x is a number such that x^2 - 1 is divisible by 3, which of the following must be true.

a. x must be even.

b. x must be divisible by 3.

c. x must be odd.

d. x cannot be a multiple of 3.

e. x must leave a remainder of 1 when divided by 3.

Please explain how to solve this problem easily.

Govind

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Source: Beat The GMAT — Problem Solving | Sun Jul 18, 2010 8:09 am

aloneontheedge: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Thu Jan 28, 2010 2:07 am; Thanked: 9 times

by aloneontheedge » Sun Jul 18, 2010 8:17 am

govind_raj_76 wrote:If x is a number such that x^2 - 1 is divisible by 3, which of the following must be true.

a. x must be even.

b. x must be divisible by 3.

c. x must be odd.

d. x cannot be a multiple of 3.

e. x must leave a remainder of 1 when divided by 3.

Please explain how to solve this problem easily.

Raj,
x^2 - 1 is divisible by 3 => (x-1)(x+1)/3
plug the values and check For instance x=2,3,4,5,6
which covers all scenarios.
This will show that X cannot be multiple of 3

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