Three primes - p,q, and r- satisfy p+q=r and 1<p<q. What is the value of p?

Let a, b, c, and d be integers with a<2b, b<3c and c<4d. If d <100, what is the largest possible value for a?

Here's a hint for the first problem. If p+q = r, then at least one of them must be even - can you see why that is? Now, thinking about prime numbers - how many of them are even? Which one(s)? Can you take it from there?

As to the second problem - start with the fact that d<100, select the largest possible value of d and work backwards in turn to figure out the largest possible values of c, b, and finally a.