Question

If two different integers divided by same divisor leaves remainder 7 and 9 respectively,and when their sum divided by same divisor it leaves remainder 5, then what is the divisor?

Answer 1

ok
let say that divisor=d
nd the 2 integers are m and n

so
m=da+7 equation 1
n=db+9 equation 2
where a and b are quotients :)

nd then u divide m+n u get-

m+n=dq+5

and adding equation 1 and 2 u get-

m+n=da+db+7+9
m+n=d(a+b)+16

but the remainder is 5

to get remainder = 5
d shuld be 11 :)