AMC 10A 2020 Problem 6 | Divisibility Problem
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
Divisibility
Counting Principle
Suggested Book | Source | Answer
AMC 10A 2020 Problem 6
100
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.