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Oliver1

08-22-2013, 06:19 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

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, 06:27 PM

Thank you Jane!

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