2020 AMC 12A Problem 4

How many

4

-digit positive integers (that is, integers between

1000

and

9999,

inclusive) having only even digits are divisible by

5?

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Solution

To be divisible by

5

the last digit is

0

5,

and to be even it must be

0.

So the units digit is fixed. The leading digit is a nonzero even digit:

2, 4, 6, 8

give

4

choices. Each of the two middle digits is any even digit

0, 2, 4, 6, 8,

giving

5

choices each. The total is

4 \cdot 5 \cdot 5 \cdot 1 = 100.

Thus, B is the correct answer.

Tagged: multiplication principle · divisibility · digits