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Difficulty: 2/102022 NMTC 2022 (QII-46)

How many prime numbers are less than 50?

Guide / Hint

Hint 1: List all prime numbers in the range .

Hint 2: Double-check numbers near 50 (like 47 is prime, 49 is composite ).

Hint 3: Count the elements in your list to find the total.

Solution

Step 1 (Enumerate Primes): We systematically list all the prime numbers strictly smaller than 50:

Step 2 (Count the list): Let's count the number of primes in our list:

  1. 2

  2. 3

  3. 5

  4. 7

  5. 11

  6. 13

  7. 17

  8. 19

  9. 23

  10. 29

  11. 31

  12. 37

  13. 41

  14. 43

  15. 47

Step 3 (Conclusion): There are exactly 15 prime numbers less than 50. The answer is 15.

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    2022 NMTC 2022 QII-46 - Olympiad Math Olympiad Question | Leminno