# Arithmetic Mean!

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

Note by Ayush G Rai
4 years, 4 months ago

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This problem came in NMTC 2015. The prime numbers must be less than 54. Listing first few possibilities 53 and 1, 52 and 2, 51 and 3, 50 and 4, 49 and 5, 48 and 6, 47 and 7. Only the pair 47 and 7 are both primes and 47 is the biggest.

- 4 years, 4 months ago

you are absolutely correct.Did you appear for the NMTC 2nd level test?

- 4 years, 4 months ago

- 4 years, 4 months ago

Yes! It was really tough for me.

- 4 years, 4 months ago

Can solve the other set of problems?their also from NMTC.

- 4 years, 4 months ago

You seem to be assuming there are only two prime numbers, when the question doesn't explicitly state that.

Otherwise, there can be other solutions like $(3,7,71)$

- 4 years, 4 months ago

It clearly states pair wise that means only two prime numbers.

- 4 years, 4 months ago

Nope. Pair wise distinct does not mean only two. Pair wise distinct means that given a set of elements, no two elements (pair) of the set are the same. It does not restrict the number of elements in the set.

https://proofwiki.org/wiki/Definition:Distinct/Plural/Pairwise_Distinct

- 4 years, 4 months ago

definition:A set of objects is pairwise distinct if each pair of elements of that set is distinct.
It clearly states a pair of elements which means two elements.

- 4 years, 4 months ago

each pair. Not a pair.

- 4 years, 4 months ago

that makes no difference.

- 4 years, 4 months ago

You can check the top comment here or this. Notice how none of them refer to only two elements when talking about pairwise distinct elements.

- 4 years, 4 months ago

- 4 years, 4 months ago

I still don't agree with you.

- 4 years, 4 months ago

Sure. No problem.

- 4 years, 4 months ago