Don't understand this problem: There are only 2 pairs of positive integers $(x,y)$ for which... ..both $\frac{21}{x}$ and $\frac{70}{y}$ are in lowest terms and for which $\frac{21}{x} + \frac{70}{y}$ is an integer. One such pair is $(1,1)$. What is the other such pair? 
This is a Mathematics League problem. The answer sheet says, "...GCD of x and 21 is 1. Therefore x divides y." This is concluded from the fact that the fractions are in lowest terms. But I don't really get how that works because I can think of a bunch of ways for the fractions to be in lowest term and NOT divide each other. Such as $\frac{70}{11}$ and $\frac{21}{4}$. 
Thanks

Hint:  add the numerators then look at the factors of the sum. 
