sat math division

[Oliver1]

I need help with the following sat math question
The positive integers x and y leave remainders of 4 and 5, respectively, when divided by 7. Which of the following is the remainder when x-y-2 is divided by 7?
(A) 0
(B) 1
(C) 4
(D) 5
(E) 6

Thanks

[jane]

The remainder is the amount left after the division of two integer numbers. If n and d are positive integers there exist unique integers q and r such that ,
The number q is the quotient, r is the remainder and d is the divisor.

x leaves remainder of 4 when divided by 7 can be expressed as:
(1)
y leaves remainder of 5 when divided by 7 can be expressed as:
(2)

Subtracting (1) and (2) we have


Subtracting 2 on both sides in order to have the amount x-y-2



add and subtract 7 since the remainder cannot be negative (-3)




Therefore the correct answer is that the remainder is 4 (C)

[Oliver1]

Thank you Jane!