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

 It is currently 21 Jul 2018, 10:47

### 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 numbers from 1 to 1000, both inclusive, have digits repeated

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 14 Feb 2018
Posts: 380
How many numbers from 1 to 1000, both inclusive, have digits repeated  [#permalink]

### Show Tags

Updated on: 14 Apr 2018, 10:31
4
00:00

Difficulty:

35% (medium)

Question Stats:

67% (02:09) correct 33% (01:15) wrong based on 52 sessions

### HideShow timer Statistics

How many numbers from 1 to 1000, both inclusive, have digits repeated ?

A. 9
B. 81
C. 262
D. 648
E. 738

Originally posted by SonalSinha803 on 14 Apr 2018, 09:23.
Last edited by Bunuel on 14 Apr 2018, 10:31, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Math Expert
Joined: 02 Aug 2009
Posts: 6269
Re: How many numbers from 1 to 1000, both inclusive, have digits repeated  [#permalink]

### Show Tags

14 Apr 2018, 09:46
2
2
SonalSinha803 wrote:
How many numbers from 1 to 1000, both inclusive, have digits repeated ?

A. 9
B. 81
C.262
D.648
E.738

Will post the OA and OE after a few discussions.

Sent from my Lenovo K53a48 using GMAT Club Forum mobile app

Hi..

3-digits without repetition = 9*9*8=648
2-digits without repetition = 9*9=81
1-digit without repetition= 9

Total = 648+81+9=738..

So numbers with repetition = 1000-738=262
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

VP
Joined: 07 Dec 2014
Posts: 1037
How many numbers from 1 to 1000, both inclusive, have digits repeated  [#permalink]

### Show Tags

14 Apr 2018, 12:48
1
SonalSinha803 wrote:
How many numbers from 1 to 1000, both inclusive, have digits repeated ?

A. 9
B. 81
C. 262
D. 648
E. 738

1-99➡9 numbers
1000➡1 number
100-999➡252 numbers:
xxx=9*1*1=9
xxy=9*1*9=81
xyx=9*9*1=81
yxx=9*9*1=81
252+9+1=262 numbers
C
Intern
Joined: 28 Mar 2018
Posts: 3
Re: How many numbers from 1 to 1000, both inclusive, have digits repeated  [#permalink]

### Show Tags

14 Apr 2018, 13:04
I don't get this. Can someone explain more? Somebody please. Thanks

Sent from my iPhone using GMAT Club Forum mobile app
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2948
Location: India
GPA: 3.12
How many numbers from 1 to 1000, both inclusive, have digits repeated  [#permalink]

### Show Tags

15 Apr 2018, 00:15
1
eddwwaarrd wrote:
I don't get this. Can someone explain more? Somebody please. Thanks

Sent from my iPhone using GMAT Club Forum mobile app

Hi eddwwaarrd

I have merely elaborated on solutions given by chetan2u and gracie

Between 1 and 1000(both inclusive),
there are 1 digit numbers, 2 digit numbers, and 3 digit numbers.

There are no 1 digit number that has repeated digits [9 possibilities]

For two digit numbers, 0 can't be the first digit
The first digit can be 1-9 [9 possibilities]
The second digit can be 0,1-9(except the first digit) [9 possibilities]
Total possible 2 digit numbers are 9*9 = 81

For three digit numbers, again 0 can't be the first digit
The first digit can be 1-9 [9 possibilities]
The second digit can be 0,1-9(except the first digit) [9 possibilities]
The third digit can be any of the 8 digits that are not the first and second digits [8 possibilities]
Total possible 3 digit numbers are 9*9*8 = 81*8 = 648

Total numbers(without repeated digits) between 0 and 1000 are $$9+81+648 = 738$$

Therefore, the numbers which have repeated digits are 1000 - 738 = 262(Option C)

_________________

You've got what it takes, but it will take everything you've got

Manager
Joined: 03 Mar 2017
Posts: 58
How many numbers from 1 to 1000, both inclusive, have digits repeated  [#permalink]

### Show Tags

15 Apr 2018, 00:39
Hi eddwwaarrd

Please look at the solution below.

There are in total 1000 Numbers.

Now to find all the numbers that have repeated digits,we can subtract all the numbers that do not have repeated digits from the total 1000.

1-9 --> 9 numbers which are distinct
10-99--> Take this as a form of AB, where at A place you have 9 options(1-9 excluding 0) and at B place you have 9 options(0 can come up)
So total 9*9=81
100-999--> In the same manner ,Take this as a form of ABC, where at A place you have 9 options(1-9 excluding 0) and at B place you have 9 options(0 can come up) and at C place you have 8 options
So total 9*9*8=648

1000 cannot be considered since it has 0 as the digit repeating.

Total cases:- 9+81+648=738
Note 738 are those numbers that do not have repeating digits

Therefore, numbers having repeated digits are 1000-738=262
IMO C.
Hope it helps.
Director
Joined: 02 Oct 2017
Posts: 603
Re: How many numbers from 1 to 1000, both inclusive, have digits repeated  [#permalink]

### Show Tags

28 Apr 2018, 20:06
Total-1000 numbers

Calculate numbers in which no digit is repeated

1 digit number-0 to 9= 9 cases
2 digit cases -9*9=81 cases

As 0 can't come in tens digit and digit in tens digit can't come at units place

3 digit cases-9*9*8=648

1000-(9+81+648)=262

Posted from my mobile device
Re: How many numbers from 1 to 1000, both inclusive, have digits repeated &nbs [#permalink] 28 Apr 2018, 20:06
Display posts from previous: Sort by

# Events & Promotions

 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®.