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MathNet 2004 — Part 02 Question 35

Math Olympiad Vault · MathNet 2004 — Part 02

Question 35

Four natural numbers are given such that, however three distinct ones are taken and added, a number greater than or equal to $24$ is obtained. How many of the following statements are definitely true?

I - each of the four numbers is greater than or equal to $8$;

II - two of the given numbers have a sum greater than or equal to $16$;

III - two of the given numbers yielded greater than or equal to $64$;

IV - the product of any two of the numbers is always greater than or equal to $32$.
  1. None
  2. one
  3. two
  4. three
  5. four.