GMAT Practice Question: How many 4 -digit positive integers are there in which all 4 digits are even?
Question
How many 4 -digit positive integers are there in which all 4 digits are even?
- 625
- 600
- 500
- 400
- 256
Topics: combinations
Solution
Step 1
We first define each digit of the 4-digit number with a variable.
a = \text{thousands digit} b = \text{hundreds digit} c = \text{tens digit} d = \text{units digit}
Step 2
We then count the possible values for the thousands digit, which cannot be zero for a 4-digit number.
a \in \{2,4,6,8\}\text{ (4 options)}
Step 3
We next count the possible values for the hundreds, tens, and units digits, which can include zero.
b,c,d \in \{0,2,4,6,8\}\text{ (5 options each)}
Step 4
We multiply the counts for each digit since each choice is independent.
4 \times 5 \times 5 \times 5 = 500
Answer
500
