An algebra problem by Rahil Sehgal

Algebra Level pending

Let 𝑆 be a set of real numbers with mean 𝑀. If the means of the sets 𝑆 ∪ {15} and 𝑆 ∪ {15,1} are 𝑀 + 2 and 𝑀 + 1, respectively, then how many elements does 𝑆 have?

2 4 3 5 6

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