a + b????

mehravikas wrote:S18-17 If a and b are positive integers, what is the value of a + b ?

1. a/b = 5/8
2. The greatest common divisor of a and b is 1.

(1) gives us the ratio of a:b. However, you can't determine exact values just from a ratio.

We could have a=5 and b=8, so a+b=13.
We could have a=10 and b=16, so a+b=26.

There's more than 1 answer, so (1) is insufficient.

(2) says absolutely nothing about the actual values, so is clearly insufficient by itself.

However, when we combine (1) and (2), we can answer the question. If the GCD of a and b is 1, then multiples of 5 and 8 are no longer possible. For example, we can no longer pick 10 and 16, since the GCD of 10 and 16 is 2. We can't pick 15 and 24, because the GCD of 15 and 24 is 3.. and so on, and so on.

So, if we have both (1) and (2), the only possible values for a and b are 5 and 8: sufficient, choose (c).