Last visit was: 21 Nov 2024, 23:55 It is currently 21 Nov 2024, 23:55

Close

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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
avatar
Intern
Intern
Joined: 21 Apr 2019
Posts: 17
Own Kudos [?]: 30 [14]
Given Kudos: 0
Send PM
Most Helpful Community Reply
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12196 [7]
Given Kudos: 136
Send PM
General Discussion
User avatar
Director
Director
Joined: 22 Jun 2019
Posts: 521
Own Kudos [?]: 711 [0]
Given Kudos: 161
Send PM
avatar
Active Member
Active Member
Joined: 27 Aug 2019
Posts: 59
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: How many different 3-digit even numbers can be formed [#permalink]
Can you please explain why you wrote "HOWEVER, the hundreds digit cannot be zero" in the second stage?
avatar
Intern
Intern
Joined: 14 Sep 2019
Posts: 49
Own Kudos [?]: 22 [0]
Given Kudos: 0
Send PM
Re: How many different 3-digit even numbers can be formed [#permalink]
1
sal60 wrote:
Can you please explain why you wrote "HOWEVER, the hundreds digit cannot be zero" in the second stage?


That will make it a two-digit number.

For example, 098 is 98.
avatar
Intern
Intern
Joined: 19 Oct 2019
Posts: 4
Own Kudos [?]: 3 [0]
Given Kudos: 0
Re: How many different 3-digit even numbers can be formed [#permalink]
Hi Brent,

Could you please explain why
"Stage 1: Select a units digit
Since the units digit must be EVEN (but can't be 0), the units digit can be (2,4,6 or 8)"?

Why can't we have odd numbers in the second case for the units? Why do they have to be even? Thanks
Intern
Intern
Joined: 15 Apr 2021
Posts: 12
Own Kudos [?]: 19 [2]
Given Kudos: 31
Send PM
Re: How many different 3-digit even numbers can be formed [#permalink]
2
Another way to solve it this:
Count the number of ways a zero can be the hundred's digit. Subtract this number from the total number of ways.

First, total number of ways:
Put an even digit in the unit's place: this can be done in 5 ways (0, 2, 4, 6, 8).
Put any remaining digit in the ten's place: this can be done in 9 ways.
Put any remaining digit in the hundred's place: this can be done in 8 ways.

Total: 5x9x8 = 360

Second, count the number of ways a zero can be the hundred's digit:

Put an even digit in the unit's place: this can be done in 4 ways (2, 4, 6, 8). Remember, we will put 0 in the hundred's place.
Put any remaining digit in the ten's place: this can be done in 8 ways.
Put any a zero in the hundred's place: this can be done in 1 ways.

Total: 32

The answer is 360-32 = 328
Intern
Intern
Joined: 12 Mar 2024
Posts: 46
Own Kudos [?]: 17 [0]
Given Kudos: 44
Send PM
Re: How many different 3-digit even numbers can be formed [#permalink]
I am getting 315; in the units digit we have just 5 options (2,4,6,8 and 0) ; for the tens digit we have 9 options (a digit has been selected for the units place) and for the hundreds digit we have 7 options (1 for units; 1 for tens place and we cant select 0 so we have 10-1-1-1=7 options) so we have 7 x 9 x 5 which is 315; let me know if this is correct.....
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36341 [0]
Given Kudos: 25927
Send PM
Re: How many different 3-digit even numbers can be formed [#permalink]
Expert Reply
total even digits ; with 0 at units place ; 9*8*1 ; 72
total even digits with 0 at tens place; 8*1*4 ; 32
and total even digits without 0 ; 8*7*4; 224
total ; 224+32+72 ; 328
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36341 [0]
Given Kudos: 25927
Send PM
How many different 3-digit even numbers can be formed [#permalink]
Expert Reply
Total number of 3-digit even number include 0 at the hundreds digit = 5*9*8 = 360
Total number of 3-digit even number with 0 at the hundreds digit = 1*4*8 = 32
--> Answer = 360 - 32 = 328
Intern
Intern
Joined: 12 Mar 2024
Posts: 46
Own Kudos [?]: 17 [0]
Given Kudos: 44
Send PM
Re: How many different 3-digit even numbers can be formed [#permalink]
Thanks very much for the both the solutions :), if could you please tell me what was wrong in my calculation where the answer was coming 315..
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36341 [0]
Given Kudos: 25927
Send PM
Re: How many different 3-digit even numbers can be formed [#permalink]
Expert Reply
Put an even digit in the unit's place: this can be done in 5 ways (0, 2, 4, 6, 8).
Put any remaining digit in the ten's place: this can be done in 9 ways.
Put any remaining digit in the hundred's place: this can be done in 8 ways.

From the above

Please also refer to Brent explanation fora thorough understanding

https://gre.myprepclub.com/forum/how-ma ... tml#p35540

Please let me know if yu need further assistance
Prep Club for GRE Bot
Re: How many different 3-digit even numbers can be formed [#permalink]
Moderators:
GRE Instructor
84 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne