How many 4-digit positive integers are there in which all 4 digits are even?

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How many 4-digit positive integers are there in which all 4 digits are even?

A. 625
B. 600
C. 500
D. 400
E. 256

Answer: C

Source: GMAT Prep

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Vincen wrote:
Wed Mar 31, 2021 7:43 am
How many 4-digit positive integers are there in which all 4 digits are even?

A. 625
B. 600
C. 500
D. 400
E. 256

Answer: C

Solution:

The even digits are 0, 2, 4, 6, and 8. However, since the first digit (or the thousands place digit) can’t be 0, there are 4 choices for the thousands digit, while the other three places (hundreds, tens, and units) have 5 choices each. Therefore, the total number of 4-digit numbers with all even digits is 4 x 5 x 5 x 5 = 500.

Answer: C

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