2020 AMC 10A Problem 6

Below is the video solution and professionally curated solution for Problem 6 of the 2020 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 10A solutions, or check the answer key.

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Concepts:multiplication principle digits divisibility

Difficulty rating: 980

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

$80$

$100$

$125$

$200$

$500$

Video solution:

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Written solution:

The last digit must be $0$ , because the number is divisible by $5$ and all digits are even. The thousands digit can be $2,4,6,$ or $8$ , and each of the hundreds and tens digits has $5$ choices. Thus there are $4\cdot5\cdot5=100$ such integers. Thus, B is the correct answer.

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