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

 It is currently 20 Jan 2019, 01:08

### 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
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.

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

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 28 Mar 2012
Posts: 311
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Re: How many odd three-digit integers greater than 800 are there  [#permalink]

### Show Tags

20 Jun 2012, 00:40
Hi,

My solution is as follows:
You have to find the odd (3digit) numbers greater than 800, all distict digits. Available digits would be (0 to 9)
Odd numbers starting with 8 = 1*8*5 = 40 (Hundredth digit is 8 - so, only 1 choice. Unit digit can be (1, 3, 5, 7, 9). Now tens digit will not be 8 & a digit chosen at units place - 8 possibilities)
Odd numbers starting with 9 = 1*8*4 = 40 (Hundredth digit is 9 - so, only 1 choice. Unit digit can be (1, 3, 5, 7). Now tens digit will not be 9 & a digit chosen at units place - 8 possibilities)
Total numbers = 32

Regards,
Senior Manager
Joined: 06 Aug 2011
Posts: 336
Re: How many odd three-digit integers greater than 800 are there  [#permalink]

### Show Tags

20 Jun 2012, 11:11
1 8 4 = 32
- - -

1 means that we can only 9 at that place, 4 is for odd numbers, 1,3,5,7 we cant take 9 bacause we have already taken 9 , and 8 is for putting (10-2=8 numbers which we already taken so question asked differnt number so we can 8 digits over there)

1 8 5=40
- - -
so 1 for 8, 5 for using 1,3,5,7,9 five odd digits and again (10-2=8) ..

40+32=72...
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Manager
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 206
Re: How many odd three-digit integers greater than 800 are there  [#permalink]

### Show Tags

23 Jun 2012, 10:12
2*9*8=144/2 = 72

1st digit: 2 (can be either 8 or 9)
2nd digit: 9 (can be any number out of 10 but must be different from the 1st digit, hence 9 options)
3rd digit: 8 (8 options after filling first two spots)
/2 (because we need only odd numbers)
_________________

press +1 Kudos to appreciate posts

Director
Joined: 22 Mar 2011
Posts: 600
WE: Science (Education)

### Show Tags

Updated on: 01 Aug 2012, 06:39
Here is my solution, using reasoning based on symmetry:

The total number of three digit numbers, greater than 800 with all three digits distinct, is 2 * 9 * 8 = 144.
We have two choices for the first digit (8 or 9), 9 choices for the second digit (it must be different from the first digit) and 8 choices for the third digit, as it should be different from the two previous digits).

Now, here is where, I think, symmetry can help:

Among those starting with 8, there are less even numbers, as the last digit cannot be 8 (so, only 4 choices), while odd choices for the last digit are 5.
For the numbers starting with 9, the situation is reversed, as there are only 4 choices for the third digit for odd numbers and 5 choices for the even numbers.
If we put all the numbers together, at the end, we have a balanced outcome, there must be the same number of each type.
It means that among the above 144 numbers, there are as many even as odd numbers, so 72 of each type.

Did you meet questions where some type of reasoning based on symmetry can be used?
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Originally posted by EvaJager on 01 Aug 2012, 03:07.
Last edited by EvaJager on 01 Aug 2012, 06:39, edited 1 time in total.
Manager
Joined: 15 Jan 2011
Posts: 101
Re: How many odd three-digit integers greater than 800 are there  [#permalink]

### Show Tags

01 Aug 2012, 06:18
first we consider 1*8*5=40, but doesn't this mean, that among 8 numbers there are 5 odd ones? The restriction in the question is
Quote:
such that all their digits are different

the same is for 1*8*4=32

i solved this problem this way: 1*8*5+1*8*4-2=70, since there is no such an answer among choices went with 72, but could you please help me to understand where i was wrong?
Director
Joined: 22 Mar 2011
Posts: 600
WE: Science (Education)
Re: How many odd three-digit integers greater than 800 are there  [#permalink]

### Show Tags

01 Aug 2012, 06:34
Galiya wrote:
first we consider 1*8*5=40, but doesn't this mean, that among 8 numbers there are 5 odd ones? The restriction in the question is
Quote:
such that all their digits are different

the same is for 1*8*4=32

i solved this problem this way: 1*8*5+1*8*4-2=70, since there is no such an answer among choices went with 72, but could you please help me to understand where i was wrong?

The second digit can be odd or even, the sole restriction is just to have all three digits distinct. You are not supposed to subtract the 2.
You have the 8 because the first and the last digits are eliminated, so you can choose from 10 - 2 = 8 possibilities for the second digit.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Manager
Joined: 15 Jan 2011
Posts: 101
Re: How many odd three-digit integers greater than 800 are there  [#permalink]

### Show Tags

01 Aug 2012, 06:59
EvaJager
afraid we are talking about different things:
8 includes 5 odd numbers (4 in the second case).
for instance,lets assume the unit digit is 3, we can't consider 3 in tenths - so have to eliminate 1 choice from 8
Math Expert
Joined: 02 Sep 2009
Posts: 52294
Re: How many odd three-digit integers greater than 800 are there  [#permalink]

### Show Tags

08 Jul 2013, 00:10
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

To find DS questions by Kudos, sort by Kudos here: gmat-data-sufficiency-ds-141/
To find PS questions by Kudos, sort by Kudos here: gmat-problem-solving-ps-140/

_________________
Manager
Joined: 10 Jun 2015
Posts: 118
Re: How many odd three-digit integers greater than 800 are there  [#permalink]

### Show Tags

13 Aug 2015, 07:36
dimitri92 wrote:
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

From 801 to 899, there are 9x8=72 numbers have all their digits different
From 900 to 999, there are 9x8=72 numbers have all their digits different
so, we have 144 number in all and half of them odd.
Non-Human User
Joined: 09 Sep 2013
Posts: 9451
Re: How many odd three-digit integers greater than 800 are there  [#permalink]

### Show Tags

28 Aug 2018, 14:13
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] 28 Aug 2018, 14:13

Go to page   Previous    1   2   [ 30 posts ]

Display posts from previous: Sort by