Data Sufficiency

What is the remainder when the sum of the positive integers x and y is divided by 6?
(1) When x is divided by 6, the remainder is 3.
(2) When y is divided by 6, the remainder is 1.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Should be C

We need to find what's the remainder of (x+y)/6

Stmt 1 tells about remainder of x/6. nothing about y so NOT SUFF

Stmt 2 tells about remainder of y/6. nothing about x so NOT SUFF

together (x+y)/6 = x/6 + y/6 remainder would be 3+1 = 4

Alternate approach take numbers
x=9, y=7 (x+y)/6 remainder = 4
x=13, y=15 (x+y)/6 remainder = 4

thanks for the explaination