GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Jan 2019, 13:07

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winners of the GMAT game show

January 22, 2019

January 22, 2019

10:00 PM PST

11:00 PM PST

In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.
• ### Key Strategies to Master GMAT SC

January 26, 2019

January 26, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

# How many odd three-digit integers greater than 800 are there

Author Message
TAGS:

### Hide Tags

Suspended Member
Joined: 23 Jul 2009
Posts: 57
How many odd three-digit integers greater than 800 are there  [#permalink]

### Show Tags

21 Aug 2009, 04:07
3
3
00:00

Difficulty:

55% (hard)

Question Stats:

65% (02:13) correct 35% (02:37) wrong based on 143 sessions

### HideShow timer Statistics

How many odd three-digit integers greater than 800 are there such that all their digits are different?

A. 40
B. 60
C. 72
D. 81
E. 104

If the number begins with 8, there are possibilities (5 possibilities for the last digit and 8 possibilities for the middle digit). If the number begins with 9, there are possibilities (4 possibilities for the last digit and 8 possibilities for the middle digit). In all, there are numbers that satisfy the constraints.

GMAC25 : i think there are 9 possiblities for middle digit, 0-9 and excluding 8, now how can we say that there are 5 possibilties for last digit when middle digit is 1 then possible last digit values are 3,5,7,9.

i am not able to understand this.
Director
Joined: 01 Apr 2008
Posts: 768
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: GMAT CLUB tests - p&c problem  [#permalink]

### Show Tags

21 Aug 2009, 04:27
3
2
Last digit is always ODD:
case1: first digit is 8, then last digit has 5 options(1,3,5,7,9) and middle digit has 8 options as we have already chosen two digits for the first and the last positions.
total numbers = 1*8*5 = 40

case2: first digit is 9, then last digit has 4 options(1,3,5,7) and middle digit has 8 options again.
total numbers = 1*8*4 = 32
Ans:72

NOTE: last digit should always be one of 1,3,5,7,9
##### General Discussion
Suspended Member
Joined: 23 Jul 2009
Posts: 57
Re: GMAT CLUB tests - p&c problem  [#permalink]

### Show Tags

21 Aug 2009, 04:14
1

I am weak in P&C
Suspended Member
Joined: 23 Jul 2009
Posts: 57
Re: GMAT CLUB tests - p&c problem  [#permalink]

### Show Tags

21 Aug 2009, 11:53
1
thanks a lot .... this solution cleared my doubt.
Founder
Joined: 04 Dec 2002
Posts: 17137
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
Re: GMAT CLUB tests - p&c problem  [#permalink]

### Show Tags

21 Aug 2009, 11:59
1
Also here: m25-76554.html

See this post for a listing of all discussions: gmat-club-tests-master-threads-all-tests-78599.html
_________________

Founder of GMAT Club

Just starting out with GMAT? Start here...
OG2019 Directory is here!
Want to know application stats & Profiles from last year? Check the Decision Tracker

Co-author of the GMAT Club tests

Senior Manager
Joined: 18 Aug 2009
Posts: 348
Schools: UT at Austin, Indiana State University, UC at Berkeley
WE 1: 5.5
WE 2: 5.5
WE 3: 6.0
Re: GMAT CLUB tests - p&c problem  [#permalink]

### Show Tags

07 Sep 2010, 17:02
Thank you for explanation. It is very helpful!
_________________

Never give up,,,

Math Expert
Joined: 02 Sep 2009
Posts: 52390
Re: GMAT CLUB tests - p&c problem  [#permalink]

### Show Tags

11 Sep 2010, 21:51
1
1
How many odd three-digit integers greater than 800 are there such that all their digits are different?
A. 40
B. 60
C. 72
D. 81
E. 104

In the range 800 - 900:
1 choice for the first digit: 8;
5 choices for the third digit: 1, 3, 5, 7, 9;
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.

1*5*8 = 40.

In the range 900 - 999:
1 choice for the first digit: 9;
4 choices for the third digit: 1, 3, 5, 7 (9 is out as it's first digit);
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.

1*4*8 = 32.

Total: 40+32 = 72.

Also discussed at: odd-3-digit-integers-94655.html and no-properties-71853.html?hilit=range%20choice%20first%20digit

Hope it helps.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 9464
Re: How many odd three-digit integers greater than 800 are there  [#permalink]

### Show Tags

22 May 2017, 20:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: How many odd three-digit integers greater than 800 are there &nbs [#permalink] 22 May 2017, 20:54
Display posts from previous: Sort by