Question 3

The arithmetic mean of a number of pairwise distinct prime numbers is 27. Determine the biggest prime among them.


Correct Answer: 47

Solution

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Looking for pairs of distinct primes averaging to 27 (so summing to 54), the valid pairs are $$(47,7)$$, $$(11,43)$$, $$(41,13)$$ and $$(19,37)$$. Among all primes appearing across these valid pairs, the largest is 47.

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