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

 It is currently 21 Aug 2019, 02:32

### 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

# A company plans to assign identification numbers to its empl

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 19 Mar 2008
Posts: 314
A company plans to assign identification numbers to its empl  [#permalink]

### Show Tags

Updated on: 26 Feb 2013, 03:20
7
1
29
00:00

Difficulty:

45% (medium)

Question Stats:

61% (01:18) correct 39% (01:04) wrong based on 938 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

Originally posted by judokan on 23 Aug 2008, 08:21.
Last edited by Bunuel on 26 Feb 2013, 03:20, edited 1 time in total.
Edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 57182
A company plans to assign identification numbers to its empl  [#permalink]

### Show Tags

26 Feb 2013, 03:27
7
5
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

Notice that we are told that "Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0".

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.
_________________
VP
Joined: 07 Nov 2007
Posts: 1496
Location: New York
A company plans to assign identification numbers to its empl  [#permalink]

### Show Tags

23 Aug 2008, 08:34
3
2
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*7= 4536
_________________
Smiling wins more friends than frowning
##### General Discussion
Manager
Joined: 14 Feb 2011
Posts: 163
Re: A company plans to assign identification numbers to its employees. Eac  [#permalink]

### Show Tags

09 Mar 2011, 22:20
1
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.
Senior Manager
Joined: 28 Jul 2011
Posts: 323
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
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?
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 57182
A company plans to assign identification numbers to its empl  [#permalink]

### Show Tags

23 Mar 2013, 08:52
2
1
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"
_________________
SVP
Joined: 06 Sep 2013
Posts: 1630
Concentration: Finance
Re: A company plans to assign identification numbers to its empl  [#permalink]

### Show Tags

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

Only answer with units digit 6 is B.

Hope this helps
Cheers
J
Math Expert
Joined: 02 Sep 2009
Posts: 57182
A company plans to assign identification numbers to its empl  [#permalink]

### Show Tags

28 Oct 2014, 07:36
1
Director
Joined: 12 Nov 2016
Posts: 708
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
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
Retired Moderator
Joined: 17 Jun 2016
Posts: 501
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!!
_________________
Director
Joined: 13 Mar 2017
Posts: 731
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

So different identification numbers possible : 4536

_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

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

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Director
Joined: 17 Dec 2012
Posts: 630
Location: India
Re: A company plans to assign identification numbers to its empl  [#permalink]

### Show Tags

20 May 2017, 20:25
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 Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
Intern
Joined: 30 Jun 2017
Posts: 15
Location: India
Concentration: Technology, General Management
WE: Consulting (Computer Software)
A company plans to assign identification numbers to its empl  [#permalink]

### Show Tags

07 Sep 2017, 06:42
Bunuel 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.

Let's say the question would have said that the first number could as well be a zero, then the number of identification numbers would be : 10*9*8*7 ? Am i going right?
Math Expert
Joined: 02 Sep 2009
Posts: 57182
Re: A company plans to assign identification numbers to its empl  [#permalink]

### Show Tags

07 Sep 2017, 06:48
1
SinhaS wrote:
Bunuel 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.

Let's say the question would have said that the first number could as well be a zero, then the number of identification numbers would be : 10*9*8*7 ? Am i going right?

__________________
Yes, that's correct.
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7412
Location: United States (CA)
Re: A company plans to assign identification numbers to its empl  [#permalink]

### Show Tags

11 Sep 2017, 11:41
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

There are 9 choices for the first digit (1 through 9, inclusive). The second digit can be any of the 10 digits (0 through 9, inclusive) EXCEPT it can’t repeat the first digit; thus, there are 9 options for the second digit. The third digit can’t repeat either of the first two digits, so there are 8 options. Similarly, the fourth digit can’t repeat any of the first 3 digits, so there are 7 options. Thus, the total number of options is 9 x 9 x 8 x 7 = 4,536.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 937
Re: A company plans to assign identification numbers to its empl  [#permalink]

### Show Tags

12 Sep 2018, 14:42
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

Immediate application of the Multiplicative Principle:

$$\begin{array}{*{20}{c}} {\underline {{\text{not}}\,\,0} } \\ 9 \end{array}\begin{array}{*{20}{c}} {\underline {{\text{nr}}} } \\ 9 \end{array}\begin{array}{*{20}{c}} {\underline {{\text{nr}}} } \\ 8 \end{array}\begin{array}{*{20}{c}} {\underline {{\text{nr}}} } \\ 7 \end{array}\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{Multipl}}{\text{.}}\,{\text{Principle}}} \,\,\,\,? = {9^2} \cdot 8 \cdot 7\,\,\,\,\,\,\,\,\,\,\left[ {nr = {\text{no}}\,\,{\text{repetition}}} \right]$$

$$\left\langle ? \right\rangle = \left\langle {{9^2}} \right\rangle \cdot \left\langle {8 \cdot 7} \right\rangle = 1 \cdot 6 = 6\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ {\left\langle N \right\rangle = {\text{units}}\,\,{\text{digit}}\,\,{\text{of}}\,\,N} \right]$$

Just one alternative choice with unit´s digit equal to the correct one... we are done!

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Manager
Joined: 24 Dec 2017
Posts: 191
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21
Re: A company plans to assign identification numbers to its empl  [#permalink]

### Show Tags

13 Oct 2018, 10:17
9 x 9 x 8 x 7 = 4536
1 0
2 2 2
3 3 3 3
4 4 4 4
5 5 5 5
6 6 6 6
7 7 7 7
8 8 8 8
9 9 9 9

Thank you
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4495
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A company plans to assign identification numbers to its empl  [#permalink]

### Show Tags

14 Apr 2019, 11:30
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

total digit =10
4 digits first cannot be 0
so 9*9*8*7 ; 4536
IMO B
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Re: A company plans to assign identification numbers to its empl   [#permalink] 14 Apr 2019, 11:30
Display posts from previous: Sort by