4-digit positive integers

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ska7945: Master | Next Rank: 500 Posts; Posts: 200; Joined: Thu Aug 07, 2008 5:14 pm; Thanked: 1 times

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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

oa c

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Source: Beat The GMAT — Problem Solving | Fri Aug 22, 2008 11:16 pm

sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pm; Location: INDIA; Thanked: 84 times; Followed by:3 members

Re: 4-digit positive integers

by sudhir3127 » Fri Aug 22, 2008 11:22 pm

ska7945 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

oa c

C 500

to be an even number we have to take into consideration only 0,2,4,6,8

first digit can be formed in 4 ways( cant take 0 )
next 3 digits out of 5 in 5^3 ways

thus its
4*5^3 = 500

hope it helps..

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carefreeamit: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Fri Aug 22, 2008 9:51 pm; Thanked: 3 times

by carefreeamit » Fri Aug 22, 2008 11:22 pm

4 digit number means it should be >= 1000 and <= 9999.
The first place can be taken by 2,4,6,8 i.e. in 4 ways.
The second, third & fourth place can be taken by 0,2,4,6,8 i.e. 5 ways each.
So the number of positive integers will be = 4*5*5*5 = 500

Ans C.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: 4-digit positive integers

by Scott@TargetTestPrep » Fri Apr 16, 2021 7:33 am

ska7945 wrote: ↑
Fri Aug 22, 2008 11:16 pm
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

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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