(From the GRE Practice Exam)* Let p and q be distinct primes. Suppose that H is a proper subset of the integers that is a group under addition that contains exactly three elements of the set {p, p + q, pq, pq, qp}. Determine which of the following are the three elements in H.

1-20-17 Tuesday, September 6, 20111:06 AM Important Points • The Scientific Method ○ Observation, Representation, Interpretation ○ Representationis a model • Classification of Matter ○ Anything that occupies spaceand has mass. ○ Governed by two things: compositionand energy. ○ Mixtures: A combinationof two or more substancesin which the substancesretain their identities. Homogenous mixtures: compositionof the mixture is the samethroughout. Heterogenousmixtures: compositionis not uniform throughout Physical means can be used to seperatemixtures into its pure components ○ Substances:Compounds and elements. Elements cannot be seperatedinto simplersubstancesby chemical mean