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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
1 year, 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 - 1 year, 6 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 - 1 year, 6 months ago

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

Ayush Rai - 1 year, 6 months ago

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@Ayush 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 - 1 year, 6 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 Rai - 1 year, 6 months ago

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@Ayush Rai each pair. Not a pair.

Siddhartha Srivastava - 1 year, 6 months ago

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@Siddhartha Srivastava that makes no difference.

Ayush Rai - 1 year, 6 months ago

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@Ayush 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 - 1 year, 6 months ago

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

Ayush Rai - 1 year, 6 months ago

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@Ayush Rai Sure. No problem.

Siddhartha Srivastava - 1 year, 6 months ago

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

Ayush Rai - 1 year, 6 months ago

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@Siddhartha Srivastava ok, ask calvin lin about this.

Ayush Rai - 1 year, 6 months ago

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

Ayush Rai - 1 year, 6 months ago

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

Brilliant Member - 1 year, 6 months ago

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

Ayush Rai - 1 year, 6 months ago

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

Ayush Rai - 1 year, 6 months ago

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