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
