How Cheenta works to ensure student success?

Explore the Back-StoryTry this beautiful Problem based on Divisibility Problem from AMC 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

Divisibility

Counting Principle

AMC 10A 2020 Problem 6

100

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.

Cheenta is a knowledge partner of Aditya Birla Education Academy

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

JOIN TRIALAcademic Programs

Free Resources

Why Cheenta?

Online Live Classroom Programs

Online Self Paced Programs [*New]

Past Papers

More