1994 AMC 8 Problem 6

Below is the professionally curated solution for Problem 6 of the 1994 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1994 AMC 8 solutions, or check the answer key.

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Concepts:units digit divisibility

Difficulty rating: 730

The unit's digit (one's digit) of the product of any six consecutive positive whole numbers is

$0$

$2$

$4$

$6$

$8$

Solution:

Any six consecutive whole numbers include at least one multiple of $5$ and at least one even number, so their product is a multiple of $5 \times 2 = 10.$

A multiple of $10$ always ends in $0$ .

Thus, the correct answer is A .

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