Bunuel wrote:
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
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
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
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