If x is an integer, is(x^2+)(x+5) an even number?
1) x is an odd number
2) Each prime factor of x^2 is greater than 7.
OAD
1) x is an odd number
2) Each prime factor of x^2 is greater than 7.
OAD
Statement 1: x is oddIf 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.
If x=1, then (x²+1)(x+5) = (1² + 1)(1 + 5) = 2*6 = 12.
If x=3, then (x²+1)(x+5) = (3² + 1)(3 + 5) = 10*8 = 80.
If x=5, then (x²+1)(x+5) = (5² + 1)(5 + 5) = 26*10 = 260.
The cases above illustrate that -- if x is odd -- then (x²+1)(x+5) = even.
SUFFICIENT.
Statement 2: Each prime factor of x² is greater than 7.
Since each prime factor of x² is greater than 7, each prime factor of X ITSELF must be greater than 7.
Options for x:
11, 13, 17, 19, 23...
Notice that only ODD VALUES FOR X will satisfy statement 2.
As we saw in statement 1, if x is odd, then (x²+1)(x+5) = even.
SUFFICIENT.
The correct answer is D.
