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Algebra

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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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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