It is currently 11 Dec 2017, 19:48

### 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 June
Open Detailed Calendar

# A company plans to assign identification numbers to its empl

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 19 Mar 2008
Posts: 351

Kudos [?]: 68 [3], given: 0

A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

23 Aug 2008, 08:21
3
KUDOS
15
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

61% (00:49) correct 39% (00:36) wrong based on 1015 sessions

### HideShow timer Statistics

A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Feb 2013, 03:20, edited 1 time in total.
Edited the question and added the OA.

Kudos [?]: 68 [3], given: 0

SVP
Joined: 07 Nov 2007
Posts: 1790

Kudos [?]: 1101 [2], given: 5

Location: New York

### Show Tags

23 Aug 2008, 08:34
2
KUDOS
2
This post was
BOOKMARKED
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

3024
4536
5040
9000
10000

= No. of ways select first digit (other than 0) * No of wasy select second digit (exclude first digit selected) * no of ways select 3rd digit (exclude first 2) * no of ways to select 4 th digit (excllude first 3 digits)
= 9*9*8*6= 4536
_________________

Smiling wins more friends than frowning

Kudos [?]: 1101 [2], given: 5

Manager
Joined: 14 Feb 2011
Posts: 183

Kudos [?]: 157 [1], given: 3

Re: A company plans to assign identification numbers to its employees. Eac [#permalink]

### Show Tags

09 Mar 2011, 22:20
1
KUDOS
geisends wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

A)3,024
B)4,536
C)5,040
D)9,000
E)10,000

First digit (1000th place) can be any of 0 to 9 except 0, so it can be chosen in nine ways

Second digit (100th place) can be any of 0 to 9 except the one already chosen for 1000th place, so it can be chosen in nine ways

Third digit (10th place) can be any of 0 to 9 except the ones already chosen for 1000th place and 100th place, so it can be chosen in eight ways

Fourth digit (units place) can be any of 0 to 9 except the ones already chosen for 1000th place, 100th place and 10th place, so it can be chosen in seven ways

Total number of ways = 9*9*8*7 = 81*56. Only option with 6 in units place is B, so answer is B.

Kudos [?]: 157 [1], given: 3

Director
Joined: 29 Nov 2012
Posts: 863

Kudos [?]: 1484 [1], given: 543

Re: A company plans to assign identification numbers to its [#permalink]

### Show Tags

25 Feb 2013, 20:23
1
KUDOS
It should be 9*9*8*7 right?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Kudos [?]: 1484 [1], given: 543

Manager
Joined: 24 Sep 2012
Posts: 90

Kudos [?]: 172 [0], given: 3

Location: United States
GMAT 1: 730 Q50 V39
GPA: 3.2
WE: Education (Education)
Re: A company plans to assign identification numbers to its [#permalink]

### Show Tags

25 Feb 2013, 22:00
Yes. The total number of ways=9*9*8*7

fozzzy wrote:
It should be 9*9*8*7 right?

Kudos [?]: 172 [0], given: 3

Math Expert
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135285 [3], given: 12679

Re: A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

26 Feb 2013, 03:27
3
KUDOS
Expert's post
4
This post was
BOOKMARKED
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000

The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit of 6.

Hope it's clear.
_________________

Kudos [?]: 135285 [3], given: 12679

Director
Joined: 28 Jul 2011
Posts: 516

Kudos [?]: 312 [1], given: 16

Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)
Re: A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

23 Mar 2013, 08:28
1
KUDOS
Bunuel wrote:
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000

The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit if 6.

Hope it's clear.

Hi Bunnel,

I took 9*10*10*10=9000 i thought he didn't mention any thing such as repetition not allowed or not allowed may i know if i misread the question?

May i know where i went wrong?
_________________

Kudos [?]: 312 [1], given: 16

Math Expert
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135285 [2], given: 12679

Re: A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

23 Mar 2013, 08:52
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
mydreammba wrote:
Bunuel wrote:
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000

The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit if 6.

Hope it's clear.

Hi Bunnel,

I took 9*10*10*10=9000 i thought he didn't mention any thing such as repetition not allowed or not allowed may i know if i misread the question?

May i know where i went wrong?

"Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0"
_________________

Kudos [?]: 135285 [2], given: 12679

Intern
Joined: 08 Dec 2012
Posts: 45

Kudos [?]: 34 [0], given: 12

Re: A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

31 Aug 2013, 05:50
Bunuel wrote:
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000

The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit if 6.

Hope it's clear.

why can't it be 9 * 10 * 10* 10 ?

Kudos [?]: 34 [0], given: 12

Math Expert
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135285 [1], given: 12679

Re: A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

31 Aug 2013, 05:59
1
KUDOS
Expert's post
SUNGMAT710 wrote:
Bunuel wrote:
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000

The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit if 6.

Hope it's clear.

why can't it be 9 * 10 * 10* 10 ?

Check the post just above yours: "Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0"
_________________

Kudos [?]: 135285 [1], given: 12679

Current Student
Joined: 06 Sep 2013
Posts: 1966

Kudos [?]: 757 [1], given: 355

Concentration: Finance
Re: A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

31 Mar 2014, 08:32
1
KUDOS
Four DIFFERENT digits. 9*9*8*7.

Only answer with units digit 6 is B.

Hope this helps
Cheers
J

Kudos [?]: 757 [1], given: 355

Math Expert
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135285 [1], given: 12679

A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

28 Oct 2014, 07:36
1
KUDOS
Expert's post

Kudos [?]: 135285 [1], given: 12679

Intern
Joined: 18 Sep 2014
Posts: 1

Kudos [?]: [0], given: 0

Re: A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

26 Nov 2014, 08:53
When you start from the right hand side (from the 4th digit) you should get the same result but "magically" it doesn't. Can someone explain?
What I mean is this: lets say the number is xyzt. t can take 10 digits, z can take 9 digits, y can take 8 digits and x can take 7-1=6 digits (deducting 1 for the "0" that it cannot take). The total number for probabilities is 10*9*8*6, which is different from 9*9*8*7. Can someone explain why we cannot do this version?

Kudos [?]: [0], given: 0

Manager
Joined: 01 Mar 2014
Posts: 138

Kudos [?]: 10 [0], given: 616

Schools: Tepper '18
Re: A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

08 Apr 2016, 10:59
Bunuel wrote:
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000

The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit of 6.

Hope it's clear.

I got the same answer almost but I multiplied it by 4! in the end assuming we could rearrange the digits and get a different number. Can you please explain why this is not correct?? Thank you.

Kudos [?]: 10 [0], given: 616

Math Expert
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135285 [0], given: 12679

Re: A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

09 Apr 2016, 01:47
MeghaP wrote:
Bunuel wrote:
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000

The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit of 6.

Hope it's clear.

I got the same answer almost but I multiplied it by 4! in the end assuming we could rearrange the digits and get a different number. Can you please explain why this is not correct?? Thank you.

The method used already takes care of all different arrangements. Try to test with smaller numbers to check.
_________________

Kudos [?]: 135285 [0], given: 12679

Director
Joined: 12 Nov 2016
Posts: 793

Kudos [?]: 39 [0], given: 166

Re: A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

21 Apr 2017, 23:42
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000

The first thing to note is that the possibility of choices is 0-9- which actually is ten numbers if you count [0,1,2,3,4,5,6,7,8,9] yet the first number of the digit cannot have 0 so there is a pool of 9 choices to choose from for the first number

9 x 9 x 8 x 7 =
4536

Thus B

Kudos [?]: 39 [0], given: 166

BSchool Forum Moderator
Joined: 17 Jun 2016
Posts: 480

Kudos [?]: 227 [0], given: 200

Location: India
GMAT 1: 720 Q49 V39
GMAT 2: 710 Q50 V37
GPA: 3.65
WE: Engineering (Energy and Utilities)
Re: A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

11 May 2017, 21:40
1st digit can be anything from 1 to 9, So 9 possible digits
2nd can be anything from 0 to 9 but not the one used as 1st digit, so again 10- 1 = 9 possible values
3rd can be anything from 0 to 9 except the two digits used as 1st & 2nd digit, so 10-2 = 8 possible values
4th can be anything from 0 to 9 except the 3 digits used as 1st, 2nd and 3rd digit, so 10-3 = 7

Hence total possibilities = 9x9x8x7 = 4536

Hit kudos if you like the solution!!
_________________

Kudos [?]: 227 [0], given: 200

Director
Joined: 13 Mar 2017
Posts: 556

Kudos [?]: 139 [0], given: 64

Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

11 May 2017, 22:48
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000

Since we have to form 4 digit number with 1st digit non-zero and all different digits.
It can be formed in following way
1st digit -> 9 ways (1 to 9)
2nd digit -> 9 ways (0 to 9 excluding 1st digit)
3rd digit -> 8 ways ( 0 to 9 excluding 1st and 2nd digit)
4th digit -> 7 ways ( 0 to 9 excluding 1st , 2nd and 3rd digit)
So total no. of ways = 9*9*8*7 = 4536 ways

[Reveal] Spoiler:
So different identification numbers possible : 4536

_________________

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

Kudos [?]: 139 [0], given: 64

Director
Joined: 17 Dec 2012
Posts: 623

Kudos [?]: 547 [0], given: 16

Location: India
Re: A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

20 May 2017, 20:25
Expert's post
Top Contributor
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000

1. Ordering is important and there is no repetition, so this is an nPr problem
2. Is there a constraint?. The first digit cannot be zero
3. Number of ways the first digit can be selected is 9
4. Number of ways the second third and last digits can be ordered is 9P3
5. Total number of permutations is 9*9*8*7=4536
_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com/regularcourse.php

Standardized Approaches

Kudos [?]: 547 [0], given: 16

Intern
Joined: 26 Jun 2017
Posts: 1

Kudos [?]: 0 [0], given: 0

Re: A company plans to assign identification numbers to its empl [#permalink]

### Show Tags

26 Jun 2017, 01:28
bethebest wrote:
Bunuel wrote:
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000

The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit of 6.

-- >
Where in the question has it been mentioned that succeeding digits cannot inherit the preceding value(there is no mentions about repetitions). By that logic, values like 9999 or 9988 or 7777 cannot be used as identification numbers.

Kudos [?]: 0 [0], given: 0

Re: A company plans to assign identification numbers to its empl   [#permalink] 26 Jun 2017, 01:28

Go to page    1   2    Next  [ 24 posts ]

Display posts from previous: Sort by