How it Works › Forums › Introductory Problems (AMC 8 Problems 10-20) › Unique Properties of Integers Introductory Problems Set 2 › Reply To: Unique Properties of Integers Introductory Problems Set 2

Anthony

1) 2

I made two lists, each with one requirement, then I looked for common terms.

2) 0

If a mod 4 = 0, then a mod 8 will equal 0 or 4, not 2.

3) 2

You can group it into 48 groups of -1. -48 mod 10 = 2.

4) 11 for two composites, 7 for two primes.

If it is the sum of two composites, then it will have to be an even plus an odd (primes cannot be even). If it is the sum of two primes, same thing, and the only even prime is 2. That means that only groups of primes like {2,5,7} or {29,31} should be counted. You can make a list using these two tips.