Arithmetic Mean!

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

#Algebra

Note by Ayush G Rai
5 years ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

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.

Log in to reply

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

Ayush G Rai - 5 years ago

Log in to reply

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

Log in to reply

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

Ayush G Rai - 5 years ago

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

Ayush G Rai - 5 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) (3,7,71)

Log in to reply

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

Ayush G Rai - 5 years ago

Log in to reply

@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

Log in to reply

@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 - 5 years ago

Log in to reply

@Ayush G Rai each pair. Not a pair.

Log in to reply

@Siddhartha Srivastava that makes no difference.

Ayush G Rai - 5 years ago

Log in to reply

@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.

Log in to reply

@Siddhartha Srivastava ok, ask calvin lin about this.

Ayush G Rai - 5 years ago

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

Ayush G Rai - 5 years ago

Log in to reply

@Ayush G Rai Sure. No problem.

Log in to reply

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

Ayush G Rai - 5 years ago
×

Problem Loading...

Note Loading...

Set Loading...