Question

The sum of two whole numbers is 256. Which of the
following cannot be their ratios ?
(a) 1:7
(b) 5:11
(c) 7:17
(d) 11:21​

Answer 1

Answer:

How would we split 72 into the ratio a:b where a,b are integers and relatively prime (ie do not have a common factor)

The split would be 72*a/(a+b) and 72*b/(a+b). Since a and b are relatively prime, (a+b) must divide 72 for these numbers to be integers.

One answer is 3:2 as you have noted since 3,2 are relatively prime and 3+2=5 does not divide 72.