Get inspired by the success stories of our students in IIT JAM 2021. Learn More 

June 2, 2020

ISI MStat 2019 PSA Problem 11 | Multiplication Principle

This is a beautiful problem from ISI MSTAT 2019 PSA problem 11 based on multiplication principles. We provide sequential hints so that you can try.

Multiplication Principle - ISI MStat 2019 PSA - 11


How many positive divisors of \( 2^55^3{11}^4 \) are perfect squares?

  • 60
  • 18
  • 120
  • 4

Key Concepts


Basic counting principles

Divisors of a number

Check the Answer


Answer: is 18

ISI MStat 2019 PSA Problem 11

A First Course in Probability by Sheldon Ross

Try with Hints


See in order to get the positive divisors of \( 2^55^3{11}^4 \) that are perfect squares , we need to take only the even powers of the primes {2,5,11}.

Now the maximum powers of 2 is 5 . So there are 3 choices for even powers {0,2,4} .

The maximum powers of 5 is 3 . So there are 2 choices for even powers {0,2}.

Now the maximum powers of 2 is 5 . So there are 3 choices for even powers {0,2,4} .

The maximum powers of 11 is 4 . So there are 3 choices for even powers {0,2,4}.

Hence by multiplication principle we have in total \( 3 \times 2 \times 3 =18 \) such positive divisors.

ISI MSTAT PSA and PSB Problems
Outstanding Statistics Program with Applications

Outstanding Statistics Program with Applications

Subscribe to Cheenta at Youtube


Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com