When X is divided by 7 the remainder is U, and when Y is divided by 7 the remainder is V. What is the value of U+V ?
(1) X+Y is divisible by 7
(2) X-Y is divisible by 7
X+Y = 7 (k+m)+U+V
which is divisible by 7
means U+V must be divisable 7 and also U<7 and V<7
X-Y = 7(k-m)+(U-V)
This is divisible by 7 when U-V is also divisible by 7
and also U<7 and V<7..
U-V must be zero. i.e U=V
U can be any number between 1 to 7
I think, answer should be C.
If U and V each can be 0, neither of the statements by itself would be sufficient.