i got D
is x=5k, where k integer
(1) x/2=5a where a- integer
x=2*5a
(2*5a)/5=2a-integer so sufficient
(2)3x+5-multiple of 5
as 5 is multiple of 5 it gives remaider 0
3 is not multiple of 5 so x must be multiple of 5 to be (3x+5)/5 - integer

From statement 1,

x/2=5*n

x=5*(2n)

sufficient.

3x+5=5*n

3x=5n-5-->x=5*(n-1)/3

Since x is an integer,x will be multiple of 5.

sufficient.

Answer is D

IMO D
1) implies that whenever x/2 is divided by 5 we get an int value---> x is a multiple of 10 and all multiple of 10 are multiple of 5
suff
2)3x+5 is multiple of 5 implies that (3x+5)/5=integer----> 3x/5 is an int which is possible if and only if x is div by 5
suff

How I thought about it, no real math just logic.

(1) tell us that x is a multiple of 5 because if 5 is a factor of x/2, then x must be a factor of x. Any number that has 5 as a factor after being divided by 2, the original number must have a factor of 5 also. Thus, x is a multiple of 5.

(2) If 3x+5 is a multiple of 5, then 3x must be a multiple of 5 also. If 3x is a multiple of 5, then x must be a multiple of five because 3 is not.

Thus, D.

Thanks,

Jared