Data Sufficiency

colakumarfanta wrote:Q. Is (x-1)*(x + 1) divisible by 2 ?
a) x is not divisible by 3
b)(x-1) is divisible by 2

Target question: Is (x-1)(x+1) divisible by 2?
or
Target question: Is (x-1)(x+1) even?

Statement 1: x is not divisible by 3
Several possible cases here.
case a: x=1 --> (x-1)(x+1) = (1-1)(1+1) = 0, which is divisible by 2
case b: x=2 --> (x-1)(x+1) = (2-1)(2+1) = 3, which is not divisible by 2
Since we cannot definitively answer the target question, statement 1 is INSUFFICIENT

Statement 2: (x-1) is divisible by 2
If (x-1) is divisible by 2, then x-1 is even
If x-1 is even, then x is odd
If x is odd, then x+1 is even
So, (x-1)(x+1) = (even)(even) = even
Since we can definitively answer the target question, statement 2 is SUFFICIENT

The answer is B

Cheers,
Brent

colakumarfanta wrote:Q. Is (x-1)*(x + 1) divisible by 2 ?
a) x is not divisible by 3
b)(x-1) is divisible by 2

Got a PM to reply on this thread.

(1) If x = 4, then (x - 1)(x + 1) = 3 * 5 = 15, not divisible by 2.
If x = 5, then (x - 1)(x + 1) = (4)(6) = 24, divisible by 2.
No definite answer; NOT sufficient.

(2)(x - 1) is divisible by 2.
So, definitely (x - 1)(x + 1) will always be divisible by 2. Following example will make it clear.
If x = 3, then (x - 1)(x + 1) = 2 * 4 = 8, divisible by 2; SUFFICIENT.

The correct answer is B.