Is x – y divisible by 5?

I understand how statements I and II lead to 5(x-y) and thus it must be divisible by 5.

However, what if both x and y are the same number. Their difference would be zero and is zero divisible by 5?

(1) x is divisible by 5.
5 is a factor of x but dont know about y. insufficient

(2) y is divisible by 5
5 is a factor of y but we dont know about factors of x. Insufficient

(1)+(2), 5 is a factor of both x and y, means 5 is a factor of x-y also. Sufficient
C is correct

Statement 1:
x=5
y=1

Answer = No.

x=10
y=5

Answer = Yes.

Not Sufficient.

Statement 2:
x=11
y=5

Answer = No.

x=10
y=5

Answer = Yes.

Not Sufficient.

Combined
Both x and y are multiple of 5 so x-y is divisible by 5. Even if they are equal 5-5 then 0 is divisible by 5.

Answer (C)

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The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

The question that x - y is divisible by 5 is equivalent to the statement x and y have a same remainder when they are divided by 5.

Condition 1) tells x has a remainder 0 when it is divided by 5.
Condition 2) tells y has a remainder 0 when it is divided by 5.

When we consider both conditions together, we realize x and y have the same remainder 0 when they are divided by 5.

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.