It is currently 19 Oct 2017, 04:21

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A company plans to assign identification numbers to its empl

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Director
Director
avatar
S
Joined: 12 Nov 2016
Posts: 784

Kudos [?]: 35 [0], given: 164

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

Show Tags

New post 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 [?]: 35 [0], given: 164

BSchool Forum Moderator
avatar
G
Joined: 17 Jun 2016
Posts: 399

Kudos [?]: 184 [0], given: 198

Location: India
GMAT 1: 720 Q49 V39
GPA: 3.65
WE: Engineering (Energy and Utilities)
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: A company plans to assign identification numbers to its empl [#permalink]

Show Tags

New post 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!!
_________________

Compilation of Blogs by Mike Mcgarry - Magoosh

Kudos [?]: 184 [0], given: 198

Director
Director
User avatar
G
Joined: 13 Mar 2017
Posts: 521

Kudos [?]: 120 [0], given: 62

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

New post 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 [?]: 120 [0], given: 62

Expert Post
Top Contributor
Director
Director
User avatar
B
Joined: 17 Dec 2012
Posts: 608

Kudos [?]: 517 [0], given: 16

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

Show Tags

New post 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

Pay After Use
Standardized Approaches

Kudos [?]: 517 [0], given: 16

Intern
Intern
avatar
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

New post 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.

Answer: B.
-- >
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

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128822 [0], given: 12183

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

Show Tags

New post 26 Jun 2017, 01:32
sarthak99 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

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.


Check the highlighted part.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128822 [0], given: 12183

Intern
Intern
User avatar
B
Joined: 30 Jun 2017
Posts: 18

Kudos [?]: 7 [0], given: 80

Location: India
Concentration: Technology, General Management
WE: Consulting (Computer Software)
GMAT ToolKit User CAT Tests
A company plans to assign identification numbers to its empl [#permalink]

Show Tags

New post 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.

Answer: B.

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?

Kudos [?]: 7 [0], given: 80

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128822 [1], given: 12183

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

Show Tags

New post 07 Sep 2017, 06:48
1
This post received
KUDOS
Expert's post
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.

Answer: B.

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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128822 [1], given: 12183

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1634

Kudos [?]: 837 [0], given: 2

Location: United States (CA)
Re: A company plans to assign identification numbers to its empl [#permalink]

Show Tags

New post 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.

Answer: B
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 837 [0], given: 2

Re: A company plans to assign identification numbers to its empl   [#permalink] 11 Sep 2017, 11:41

Go to page   Previous    1   2   [ 29 posts ] 

Display posts from previous: Sort by

A company plans to assign identification numbers to its empl

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.