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Oliver1
08-22-2013, 07:19 PM
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:D

jane
08-22-2013, 07:26 PM
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 n=qd+r, 0\leq r<d
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:
x=7k+4 (1)
y leaves remainder of 5 when divided by 7 can be expressed as:
y=7m+5 (2)

Subtracting (1) and (2) we have
x-y=7k-7m+4-5

Subtracting 2 on both sides in order to have the amount x-y-2
x-y-2=7k-7m+4-5-2
x-y-2=7(k-m)-3

add and subtract 7 since the remainder cannot be negative (-3)
x-y-2=7(k-m)-3+7-7
x-y-2=7(k-m-1)-3+7
x-y-2=7(k-m-1)+4

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

Oliver1
08-22-2013, 07:27 PM
Thank you Jane!