Question

Using each of the four digits 2, 4, 6, and 8 exactly once, how many four-digit multiples of 4 can be made?

A. 6
B. 8
C. 12
D. 24

Answer 1

The number of four-digit multiples of 4 that can be made using the digits 2, 4, 6, and 8 exactly once is 12. This is because there are 6 pairs of digits that can form the last two digits of a multiple of 4, and for each pair, there are 2 possibilities for arranging the remaining digits.

Step-by-step explanation:

To determine how many four-digit multiples of 4 can be made using the digits 2, 4, 6, and 8 exactly once, we must remember the rule for divisibility by 4: A number is divisible by 4 if its last two digits form a number that is a multiple of 4. Let's systematically consider the possible combinations for the last two digits from the given numbers (2, 4, 6, 8) that satisfy this condition: 24, 32, 64, 84, 48, 68. For each of these pairs, there are two choices for the first digit and one choice remaining for the second digit, which gives us 2 possibilities for each pair.

Now, count the number of pairs: we have 6 pairs. Since there are 2 possibilities for each pair, the total number of four-digit multiples of 4 we can form is 6 × 2, which is 12. Thus, the correct answer is C. 12.