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

 It is currently 20 Apr 2019, 19:36

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

How many integers between 3000 and 4000 that have distinct

Author Message
TAGS:

Hide Tags

Intern
Joined: 03 Aug 2013
Posts: 15
How many integers between 3000 and 4000 that have distinct  [#permalink]

Show Tags

05 Sep 2013, 22:58
3
4
00:00

Difficulty:

75% (hard)

Question Stats:

55% (02:21) correct 45% (02:36) wrong based on 163 sessions

HideShow timer Statistics

How many integers between 3000 and 4000 that have distinct digits and increase from left to right ?

(A) 20
(B) 48
(C) 60
(D) 120
(E) 600

My answer doesn't match with the OA so BUNUEL, NARENN, VERTITASKARISHMA, ZARRALOU, I am calling for your help
Intern
Joined: 13 Jan 2013
Posts: 4
Re: How many integers between 3000 and 4000 that have distinct  [#permalink]

Show Tags

06 Sep 2013, 15:52
8
You have 0 1 2 3 4 5 6 7 8 9; So eliminate 0 1 2 3; Remain S = {4, 5, 6, 7, 8, 9} (6 digits)
Because you need 3 distinct digits which increase from left to right, take 3 digits from S.
With 3 digits which increase from left to right : only one way to arrange; Ex: 468 (not 486)
It means: 6C3 = 6!/[3!x(6 - 3)!] = 6!/[3!x3!] = 4 x 5 x 6 / 3! = 4 x 5 = 20.
General Discussion
Intern
Joined: 31 Jan 2013
Posts: 17
Schools: ISB '15
WE: Consulting (Energy and Utilities)
Re: How many integers between 3000 & 4000 having distinct digits  [#permalink]

Show Tags

05 Sep 2013, 23:54
2
Since the numbers must be distinct and increasing from left to right,

The only arrangements we could come-up with are:

345_ --> 4
346_ --> 3
347_ --> 2
348_ --> 1
356_ --> 3
357_ --> 2
358_ --> 1
367_ --> 2
368_ --> 1
378_ --> 1

Number of integers =
20

/SW
Senior Manager
Joined: 18 Jun 2016
Posts: 262
Location: India
GMAT 1: 720 Q50 V38
GMAT 2: 750 Q49 V42
GPA: 4
WE: General Management (Other)
Re: How many integers between 3000 and 4000 that have distinct  [#permalink]

Show Tags

09 Sep 2016, 03:49
dngboy89nh wrote:
You have 0 1 2 3 4 5 6 7 8 9; So eliminate 0 1 2 3; Remain S = {4, 5, 6, 7, 8, 9} (6 digits)
Because you need 3 distinct digits which increase from left to right, take 3 digits from S.
With 3 digits which increase from left to right : only one way to arrange; Ex: 468 (not 486)
It means: 6C3 = 6!/[3!x(6 - 3)!] = 6!/[3!x3!] = 4 x 5 x 6 / 3! = 4 x 5 = 20.

For those who could not understand why we using Combination Formula here:

We have to pick 3 different digits from the Set S = {4, 5, 6, 7, 8, 9}

We are using Combination because we are only selecting the digits as there is only 1 way to arrange them i.e. increasing order.
_________________
I'd appreciate learning about the grammatical errors in my posts

Please hit Kudos If my Solution helps

My Debrief for 750 - https://gmatclub.com/forum/from-720-to-750-one-of-the-most-difficult-pleatues-to-overcome-246420.html

My CR notes - https://gmatclub.com/forum/patterns-in-cr-questions-243450.html
Non-Human User
Joined: 09 Sep 2013
Posts: 10564
Re: How many integers between 3000 and 4000 that have distinct  [#permalink]

Show Tags

10 Sep 2017, 23:59
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 integers between 3000 and 4000 that have distinct   [#permalink] 10 Sep 2017, 23:59
Display posts from previous: Sort by

How many integers between 3000 and 4000 that have distinct

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.