How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

Probability | AMC-10A, 2003 | Problem 8

Try this beautiful problem from Probability based on Positive factors

Probability - AMC-10A, 2003- Problem 8

What is the probability that a randomly drawn positive factor of \(60\) is less than \(7\)?

  • \(\frac{1}{3}\)
  • \(\frac{1}{2}\)
  • \(\frac{3}{4}\)

Key Concepts




Check the Answer

Answer: \(\frac{1}{2}\)

AMC-10A (2003) Problem 8

Pre College Mathematics

Try with Hints

Now at first we find out the positive factors of \(60\) are \(1,2,3,4,5,6,10,12,15,20,30,60\).but the positive factors which are less than \(7\) are \(1,2,3,4,5,6\)

Can you now finish the problem ..........

so we may say that any For a positive number \(n\) which is not a perfect square, exactly half of the positive factors will be less than \(\sqrt{n}\).here \(60\) is not a perfect square and \(\sqrt 60 \approx 7.746\).Therefore half of the positive factors will be less than \(7\)

can you finish the problem........

Therefore the required probability=\(\frac{1}{2}\)

Subscribe to Cheenta at Youtube

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.