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    Siustrulka's Avatar
    Siustrulka Posts: 33, Reputation: 1
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    #1

    Feb 25, 2008, 08:29 AM
    primes and integers
    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?
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Feb 25, 2008, 10:50 AM
    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.
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