SOLUTION: if both r & s are integers > 1 ,also 11(s-1)=13(r-1) then the remainder when r+s is divided by 8 is ? A.2 B.3 C.5 D.7

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: if both r & s are integers > 1 ,also 11(s-1)=13(r-1) then the remainder when r+s is divided by 8 is ? A.2 B.3 C.5 D.7      Log On


   

Question 815177: if both r & s are integers > 1 ,also 11(s-1)=13(r-1) then the remainder when r+s is divided by 8 is ?
A.2
B.3
C.5
D.7
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
+highlight%282%29
s-1+=13%2A%28%28r-1%29%2F11%29%3E=1 is an integer,
and so is %28r-1%29%2F11%3E=1 .
s=13%2A%28%28r-1%29%29%2F11%2B1

r%2Bs=13%2A%28%28r-1%29%2F11%29%2Br%2B1
r%2Bs=13%2A%28%28r-1%29%2F11%29%2B%28r-1%29%2B2

r%2Bs=%2813%2F11%2B1%29%2A%28r-1%29%2B2
r%2Bs=+%2824%2F11%29%2A%28r-1%29%2B2
r%2Bs=24%2A%28%28r-1%29%2F11%29%2B2+
r%2Bs=+8%2A3%2A%28%28r-1%29%2F11%29%2B2
So r%2Bs had a remainder of highlight%282%29 when divided by 8 , or by 3 , or by 24 .