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

BTGmoderatorDC wrote: ↑

Wed May 25, 2022 3:26 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


OA C

Source: GMAT Prep

Take the task of creating the 4-digit numbers and break it into stages.

Stage 1: Select an even digit for the thousands digit.
Since 0 cannot be the first digit of a 4-digit number, this digit can be 2, 4, 6 or 8
So, we can complete stage 1 in 4 ways

Stage 2: Select an even digit for the hundreds digit.
This digit can be 0, 2, 4, 6, or 8
We can complete stage 2 in 5 ways

Stage 3: Select an even digit for the tens digit.
We can complete stage 3 in 5 ways

Stage 4: Select an even digit for the units digit.
We can complete stage 3 in 5 ways

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus a 4-digit) in (4)(5)(5)(5) ways (= 500 ways)

Answer: C