How Cheenta works to ensure student success?
Explore the Back-Story

AMC 10A 2020 Problem 6 | Divisibility Problem

Join Trial or Access Free Resources

Try this beautiful Problem based on Divisibility Problem from AMC 2020 Problem 6.

Divisibility Problem: AMC 10A 2020 Problem 6

How many 4-digit positive integers (that is, integers between 1000 and 9999 , inclusive) having only even digits are divisible by 5 ?

  • 80
  • 100
  • 125
  • 200
  • 500

Key Concepts


Counting Principle

Suggested Book | Source | Answer

AMC 10A 2020 Problem 6


Try with Hints

What is the divisibility rule for a number divisible by 5?

Now apply this for unit, tens, hundred and thousand digits.

Here the unit digit must be 0. So I just have one choice for units place.

The middle two digits can be 0, 2, 4, 6, or 8.

But the thousands digit can only be 2, 4, 6, or 8 since it cannot be zero.

Now try to count how many choices are there for each position.

Then there was 1 choice for unit digit.

5 choices for middle two digits.

4 choices for thousands digit.

Now calculate the total number of choices you can make.

AMC-AIME Program at Cheenta

Subscribe to Cheenta at Youtube

Leave a Reply

Your email address will not be published. Required fields are marked *

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

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.
Math Olympiad Program