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.
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Svatejas Shivakumar
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1 year ago

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@Svatejas Shivakumar
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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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Siddhartha Srivastava
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1 year ago

@Ayush Rai
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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
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Siddhartha Srivastava
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1 year ago

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@Siddhartha Srivastava
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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.
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Ayush Rai
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1 year ago

@Ayush Rai
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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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Siddhartha Srivastava
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1 year ago

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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. – Svatejas Shivakumar · 1 year ago

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Otherwise, there can be other solutions like \( (3,7,71) \) – Siddhartha Srivastava · 1 year ago

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– Ayush Rai · 1 year ago

It clearly states pair wise that means only two prime numbers.Log in to reply

https://proofwiki.org/wiki/Definition:Distinct/Plural/Pairwise_Distinct – Siddhartha Srivastava · 1 year ago

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It clearly states a pair of elements which means two elements. – Ayush Rai · 1 year ago

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eachpair. Notapair. – Siddhartha Srivastava · 1 year agoLog in to reply

– Ayush Rai · 1 year ago

that makes no difference.Log in to reply

here or this. Notice how none of them refer to only two elements when talking about pairwise distinct elements. – Siddhartha Srivastava · 1 year ago

You can check the top commentLog in to reply

– Ayush Rai · 1 year ago

I still don't agree with you.Log in to reply

– Siddhartha Srivastava · 1 year ago

Sure. No problem.Log in to reply

– Ayush Rai · 1 year ago

Did you ask the staff about this question??Log in to reply

– Ayush Rai · 1 year ago

ok, ask calvin lin about this.Log in to reply

– Ayush Rai · 1 year ago

you are absolutely correct.Did you appear for the NMTC 2nd level test?Log in to reply

– Svatejas Shivakumar · 1 year ago

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

– Ayush Rai · 1 year ago

Can solve the other set of problems?their also from NMTC.Log in to reply

– Ayush Rai · 1 year ago

Yes! It was really tough for me.Log in to reply