GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
How many 4-digit positive integers are there in which all 4 digits are
[#permalink]
26 Jan 2022, 07:29
26 Jan 2022, 07:29
Expert Reply
00:00
Question Stats:
50% (00:34) correct
50% (00:44) wrong based on 4 sessions
Hide Show timer Statistics
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
A. 625
B. 600
C. 500
D. 400
E. 256
How many 4-digit positive integers are there in which all 4 digits are
[#permalink]
26 Jan 2022, 07:57
26 Jan 2022, 07:57
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.
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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: How many 4-digit positive integers are there in which all 4 digits are
[#permalink]
26 Jan 2022, 08:08
26 Jan 2022, 08:08
Carcass 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
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
