Arithmetic Mean!

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

Note by Ayush Rai
2 years 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.

- 2 years 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 $$(3,7,71)$$

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

- 2 years 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

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.

- 2 years ago

each pair. Not a pair.

that makes no difference.

- 2 years 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.

I still don't agree with you.

- 2 years ago

Sure. No problem.

- 2 years ago

- 2 years ago

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

- 2 years ago

nope. I came to know about this exam this year only. Have you written it?

- 2 years ago

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

- 2 years ago

Yes! It was really tough for me.

- 2 years ago