## Set $$X$$ consists of exactly four distinct integers that are greater than $$1.$$ For each integer in the set, all of

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### Set $$X$$ consists of exactly four distinct integers that are greater than $$1.$$ For each integer in the set, all of

by Vincen » Fri Jan 28, 2022 5:04 am

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Set $$X$$ consists of exactly four distinct integers that are greater than $$1.$$ For each integer in the set, all of that integer’s unique prime factors are also in the set. For example, if $$20$$ is in set $$X,$$ then $$2$$ and $$5$$ must also be in set $$X.$$ How many of the distinct integers in set $$X$$ are prime?

(1) The product of the integers in set $$X$$ is divisible by $$36.$$

(2) The product of the integers in set $$X$$ is divisible by $$60.$$