**Quote:**

If x is positive is x divisible by 2 ?

(1) x^3+x is divisible by 4

(2) 5x+4 is divisible by 6

x>0. is x a multiple of 2 (i.e. is x an even number)?

I got B for answer.

I am working based on the assumption that x is an integer, so that the question will be within the scope of GMAT..

Rules applied:

even + even = even

odd + even = odd

odd + odd = even

even * even = even

even * odd = even

Statement 1x^3+x=4k ---> k being an integer

x(x^2+1)=4k

if x is even, (x^2+1) will be odd, multiplying both results in 4k (even).

if x is odd, (x^2+1) will be even, which also results in 4k (even)

--> insufficient

Statement 25x+4=6w ---> w being an integer

if x is even --> 5x will be even --> even + even = even --> results in even outcome i.e. 6w (true)

if x is odd --> 5x will be odd --> odd + even = odd --> results in odd outcome i.e. cannot be 6w

So x must be even.

--> sufficient

Answer: B

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