Last visit was: 23 Apr 2026, 22:08 It is currently 23 Apr 2026, 22:08
Home
Messages
Tests
Schools
Events
Close
GMAT 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 GMAT 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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 22 Apr 2026
Posts: 11,229
Own Kudos:
45,005
 [26]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,005
 [26]
How many 3-digit even numbers are possible 29 Feb 2016, 04:47
Kudos
Add Kudos
26
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

30% (02:06) correct 70% (01:36) wrong based on 223 sessions

History

Date
Time
Result
Not Attempted Yet
How many 3-digit even numbers are possible such that if one of the digits is 5, the next/succeeding digit to it should be 7?
A) 5
B) 305
C) 365
D) 405
E) 495
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 22 Apr 2026
Posts: 11,229
Own Kudos:
45,005
 [6]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,005
 [6]
How many 3-digit even numbers are possible 01 Mar 2016, 19:06
6
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
How many 3-digit even numbers are possible such that if one of the digits is 5, the next digit to it should be 7?
A) 5
B) 305
C) 365
D) 405
E) 495

OA after 3 days
Show more

Hi,
this Q can be answered correctly if we do not fall in trap of 'if'..
"if one of the digits is 5, the next digit to it should be 7" means that all other solutions are valid and only if 5 is used, we have restrictions..

the answer can be found in two different sets:-

1) when 5 is not used..
a) first digit can be any of 10 digits except 0 and 5-- so 8 ways..
b) the second digit can be any of the ten except 5===so 9 ways..
c) the third digit has to one of 5 even digits as the number is EVEN- so 5 ways.. 0,2,4,6,8

total ways= 8*9*5=360 ways...

2) when 5 is used...
a) only 5 can be used here as it is to be followed by 7 and last digit has to be even..
b) only 7 can be used
c) any of 5 even number..

total ways= 1*1*5=5 ways

TOTAL = 360 +5=365 ways
C
General Discussion
avatar
Why2settleForLess
avatar
Joined: 07 Feb 2016
Last visit: 30 May 2019
Posts: 6
Own Kudos:
10
Given Kudos: 23
Posts: 6
Kudos: 10
How many 3-digit even numbers are possible 29 Feb 2016, 07:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
570, 572, 574, 576, and 578, so total 5. Hence Option A.
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 22 Apr 2026
Posts: 11,229
Own Kudos:
45,005
 [1]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,005
 [1]
How many 3-digit even numbers are possible 29 Feb 2016, 20:26
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Why2settleForLess
570, 572, 574, 576, and 578, so total 5. Hence Option A.
Show more

Hi,
you have fallen into trap of "IF" and a choice matching your solution....
User avatar
vitaliyGMAT
User avatar
Joined: 13 Oct 2016
Last visit: 26 Jul 2017
Posts: 297
Own Kudos:
895
Given Kudos: 40
GPA: 3.98
Posts: 297
Kudos: 895
How many 3-digit even numbers are possible 15 Nov 2016, 03:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi, we also can solve this question using properties of a compliment.

Total # of 3 digit even numbers:
(# of choices for hundreds digit)*(#... for tens digit)*(#... for units digit) = 9*10*5 = 450

Now leet’s look at two cases when we break the restriction:

Case #1. 5 appears at hundreds digit place:
(# of choices for hundreds digit)*(#... for tens digit)*(#... for units digit) = 1*9 (we can’t use 7)*5 = 45

Case #2. 5 appears at tens digit place:
Same logic: 8 (can’t use 0 or 7)*1*5=40

The resultant = Total # of 3 digit even integers - # of integers, when we break the restriction = 450 – 45 – 40 = 365

Answer C.
User avatar
law258
User avatar
Joined: 05 Sep 2016
Last visit: 11 Oct 2020
Posts: 259
Own Kudos:
121
Given Kudos: 283
Status:DONE!
Posts: 259
Kudos: 121
How many 3-digit even numbers are possible 18 Nov 2016, 20:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think the common trap here, based on the answer distribution, is that many are forgetting the question is talking about all 3 digit even numbers (the information provided about 5 and 7 is an exception within 500 and 700 levels).
avatar
ss4689
avatar
Joined: 27 Jun 2016
Last visit: 13 May 2022
Posts: 2
Given Kudos: 8
Posts: 2
Kudos: 0
How many 3-digit even numbers are possible 30 Jan 2018, 21:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Would anyone please explain the trap. I could not see where the except 5&7 comes in?
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 22 Apr 2026
Posts: 11,229
Own Kudos:
45,005
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,005
How many 3-digit even numbers are possible 30 Jan 2018, 21:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ss4689
Would anyone please explain the trap. I could not see where the except 5&7 comes in?
Show more


Hi...

The use of " IF 5 is there, then 7 has to be next to it...
So we can have a number having 7 but not 5..
We can also have numbers without 5 and 7..
But we cannot have a number having 5 but not 7
User avatar
gmatexam439
User avatar
Moderator
Joined: 28 Mar 2017
Last visit: 18 Oct 2024
Posts: 1,054
Own Kudos:
2,195
 [1]
Given Kudos: 200
Location: India
Concentration: Finance, Technology
Schools: McDonough '21 (A$) Jones '21 (A$) Kelley '23 (A)
GMAT 1: 730 Q49 V41
GPA: 4
Products:
My Reviews
Schools: McDonough '21 (A$) Jones '21 (A$) Kelley '23 (A)
GMAT 1: 730 Q49 V41
Posts: 1,054
Kudos: 2,195
 [1]
How many 3-digit even numbers are possible 31 Jan 2018, 02:24
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
chetan2u
How many 3-digit even numbers are possible such that if one of the digits is 5, the next/succeeding digit to it should be 7?
A) 5
B) 305
C) 365
D) 405
E) 495
Show more

Since the number should be even, the last place can be taken by 0,2,4,6 or 8.
Since 5 has to be followed by 7, 5 can't be the tens digit.
Knowing this information we can solve this problem:

Case 1: When 5 is present at the hundreds place:
The number will be 57_. Now _ can be filled in 5 ways - 0,2,4,6 or 8. Thus total ways=5

Case 2: When 5 is not present at the hundreds place:
The number will have 8 digits at the hundreds place (except 0 & 5).
The number will have 9 digits at the tens place (except 5).
The number will have 5 digits at the units place.
So total ways=8*9*5=360

Hence, total ways=360+5=365
User avatar
onlymalapink
User avatar
Joined: 06 Aug 2024
Last visit: 24 Aug 2025
Posts: 81
Own Kudos:
13
Given Kudos: 749
Posts: 81
Kudos: 13
How many 3-digit even numbers are possible 11 Sep 2024, 06:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatexam439
chetan2u
How many 3-digit even numbers are possible such that if one of the digits is 5, the next/succeeding digit to it should be 7?
A) 5
B) 305
C) 365
D) 405
E) 495

Since the number should be even, the last place can be taken by 0,2,4,6 or 8.
Since 5 has to be followed by 7, 5 can't be the tens digit.
Knowing this information we can solve this problem:

Case 1: When 5 is present at the hundreds place:
The number will be 57_. Now _ can be filled in 5 ways - 0,2,4,6 or 8. Thus total ways=5

Case 2: When 5 is not present at the hundreds place:
The number will have 8 digits at the hundreds place (except 0 & 5).
The number will have 9 digits at the tens place (except 5).
The number will have 5 digits at the units place.
So total ways=8*9*5=360

Hence, total ways=360+5=365
Show more
is there a reason we dont count x57 numbers?

Posted from my mobile device
User avatar
onlymalapink
User avatar
Joined: 06 Aug 2024
Last visit: 24 Aug 2025
Posts: 81
Own Kudos:
13
Given Kudos: 749
Posts: 81
Kudos: 13
How many 3-digit even numbers are possible 11 Sep 2024, 06:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ok i get it even numbers. Questions like this xompletely destroy my confidence sigh.

Posted from my mobile device
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,961
Own Kudos:
1,117
Posts: 38,961
Kudos: 1,117
How many 3-digit even numbers are possible 14 Nov 2025, 11:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109788 posts
Krunaal
Tuck School Moderator
853 posts