Data Sufficiency

if x and y are positive integers, what is the remainder when x is divided by y?
(1) When x is divided by 2y, the remainder is 4
(2) When x+y is divided by y, the remainder is 4

OA B

I'm not agree with OA, I would go for D, instead.

(1)Let's say remainder is R and result is Z, then x=2y*Z + R => x=y*(2Z) + R, so remainder for x/y would be R (Sufficient)
(2)Let's say remainder is R and result is Z, then x+y=y*Z + R => x=y*(Z-1) + R, so remainder for x/y would be R (Sufficient)

Can someone explain, if there is any problem in my explanation or suggest how OA could be correct?

This is a VALUE DS question, so we have sufficiency when we have a unique value for the prompt.

What is the remainder when x is divided by y?

Statement 1:

When x is divided by 2y, remainder is 4.

eg. 1. If x = 42 and y = 19, remainder when x is divided by 2y = 4 and when x is divided by y is also 4
2. If x = 34 and y = 3, remainder when x is divided by 2y = 4 and when x is divided by y = 1

INSUFFICIENT

Statement 2:

When x+y is divided by y, the remainder is 4

(x+y) / y = (x/y) + (y/y)

Remainder of (y/y) is 0. So this remainder must be entirely sourced out of (x/y).

SUFFICIENT

Pick B.


Your approach for statement 1 is slightly incorrect.

x = A*(2y) + 4

You can never manipulate the quotient in this equation because it affects the remainder.