(1) When \(x\) is divided by \(2y\), the remainder is \(4\).

--> 2y > 4 --> y>2

If y=3, x=10 --> remainder when x is divided by y is 1

If y=4, x=12 --> remainder when x is divided by y is 0

--> Not sufficient.

(2) When \(x + y\) is divided by \(y\), the remainder is \(4\).

--> \((\frac{x+y}{y})_{Remainder}\) = 4

--> \((\frac{x}{y})_{Remainder} + (\frac{y}{y})_{Remainder}\) = 4

--> \((\frac{x}{y})_{Remainder}\) + 0 = 4

--> \((\frac{x}{y})_{Remainder}\) = 4 --> Sufficient

Answer B.

Harshgmat wrote:

If \(x\) and \(y\) are nonzero 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 \(4\).

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