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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.

Try 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.

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