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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.

@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.

@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
–
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.

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## Comments

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TopNewestThis 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.

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

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

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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 $(3,7,71)$

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

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

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It clearly states a pair of elements which means two elements.

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eachpair. Notapair.Log in to reply

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here or this. Notice how none of them refer to only two elements when talking about pairwise distinct elements.

You can check the top commentLog in to reply

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