kaudes11114 wrote:If x is an integer, is (x² + 1)(x + 5) an even number?
(1) x is an odd number.
(2) Each prime factor of x² is greater than 7.

My solution is similar to Rahul's, except I handle statement 2 a little differently

Aside: Don't forget these useful rules:
(ODD)(ODD) = ODD
(EVEN)(ODD) = EVEN
(EVEN)(EVEN) = EVEN

ODD + ODD = EVEN
EVEN + ODD = ODD
EVEN + EVEN = EVEN

Okay, onto the question...

Target question: Is (x² + 1)(x + 5) an even number?

Statement 1: x is an odd number.
If x is ODD, then x² is ODD, which means (x² + 1) is EVEN
If x is ODD, then (x + 5) is EVEN
So, (x² + 1)(x + 5) = (EVEN)(EVEN) = EVEN
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Each prime factor of x² is greater than 7.
This is a clever way of telling us that the number 2 is NOT a prime factor of x².
In other words, x² is ODD
If x² is ODD, then x is ODD
At this point, we should recognize that statements 1 and 2 are both telling us that x is odd
So, if statement 1 is SUFFICIENT, then statement 2 must be SUFFICIENT.

Answer = D

Cheers,
Brent