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
2 years, 6 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.

Brilliant Member - 2 years, 5 months ago

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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 \( (3,7,71) \)

Siddhartha Srivastava - 2 years, 5 months ago

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

Ayush G Rai - 2 years, 5 months ago

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@Ayush G Rai 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

Siddhartha Srivastava - 2 years, 5 months ago

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@Siddhartha Srivastava 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.

Ayush G Rai - 2 years, 5 months ago

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@Ayush G Rai each pair. Not a pair.

Siddhartha Srivastava - 2 years, 5 months ago

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@Siddhartha Srivastava that makes no difference.

Ayush G Rai - 2 years, 5 months ago

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@Ayush G Rai 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.

Siddhartha Srivastava - 2 years, 5 months ago

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@Siddhartha Srivastava I still don't agree with you.

Ayush G Rai - 2 years, 5 months ago

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@Ayush G Rai Sure. No problem.

Siddhartha Srivastava - 2 years, 5 months ago

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@Siddhartha Srivastava Did you ask the staff about this question??

Ayush G Rai - 2 years, 5 months ago

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@Siddhartha Srivastava ok, ask calvin lin about this.

Ayush G Rai - 2 years, 5 months ago

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

Ayush G Rai - 2 years, 5 months ago

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

Brilliant Member - 2 years, 5 months ago

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

Ayush G Rai - 2 years, 5 months ago

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@Brilliant Member Yes! It was really tough for me.

Ayush G Rai - 2 years, 5 months ago

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