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

It is currently 14 Oct 2019, 07:02

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

Each student at a certain business school is assigned a 4-digit studen

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58311
Each student at a certain business school is assigned a 4-digit studen  [#permalink]

Show Tags

New post 29 Feb 2016, 10:51
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

85% (01:10) correct 15% (02:11) wrong based on 155 sessions

HideShow timer Statistics

Each student at a certain business school is assigned a 4-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?

A. 9,000
B. 3,600
C. 2,700
D. 2,592
E. 1,944

_________________
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 7954
Re: Each student at a certain business school is assigned a 4-digit studen  [#permalink]

Show Tags

New post 29 Feb 2016, 20:23
Bunuel wrote:
Each student at a certain business school is assigned a 4-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?

A. 9,000
B. 3,600
C. 2,700
D. 2,592
E. 1,944


Hi,
these are simple Combinations problems..
But the most important point here is to reread if the combination is of different digits or the same digit can be repeated..

Here, there is no restriction..
Let the number be ABCD..
1) A can be any of the 10 digits, 0-9, except 0, so 9 ways..
2) B and C can be any of the 10 digits, so 10 ways each..
3) D is a prime number, so 2,3,5,7 fit in--- 4 ways..


Total ways= 9*10*10*4=3600
B

_________________
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 387
Location: India
GMAT 1: 760 Q50 V44
Each student at a certain business school is assigned a 4-digit studen  [#permalink]

Show Tags

New post Updated on: 03 Mar 2016, 03:08
Bunuel wrote:
Each student at a certain business school is assigned a 4-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?

A. 9,000
B. 3,600
C. 2,700
D. 2,592
E. 1,944


The identification number is of the form _ _ _ _

1. First digit cannot be 0
2. Middle digits can be anything
3. Last digit has to be prime - 2, 3, 5, 7

We can have the following number of possibilities for each space
__ __ __ __
9 10 10 4
Total cases = 3600
Option B

Originally posted by TeamGMATIFY on 03 Mar 2016, 02:27.
Last edited by TeamGMATIFY on 03 Mar 2016, 03:08, edited 1 time in total.
Manager
Manager
avatar
Joined: 25 Dec 2012
Posts: 116
Re: Each student at a certain business school is assigned a 4-digit studen  [#permalink]

Show Tags

New post 03 Mar 2016, 02:56
Bunuel wrote:
Each student at a certain business school is assigned a 4-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?

A. 9,000
B. 3,600
C. 2,700
D. 2,592
E. 1,944


__ __ __ __
9 10 10 4

9*10*10*4 = 3600.

Just for understanding, If the same question mentioned as no repetition allowed, then it would be

Always start with the most restrictive clause, which number should end with a prime - 4 options are available.
__ __ __ __
4

The next restrictive clause is the number should not start with a zero. Already one number has been placed in the unit position and now we cant include zero to. So we have remaining 8 numbers to put in first place.

__ __ __ __
8 4

Remaining two positions has not restrictions. Hence we have 8 numbers (including zero) for one position and 7 numbers for the other.

__ __ __ __
8 8 7 4

= 8*8*7*4
Senior Manager
Senior Manager
avatar
Joined: 15 Sep 2011
Posts: 310
Location: United States
WE: Corporate Finance (Manufacturing)
GMAT ToolKit User
Re: Each student at a certain business school is assigned a 4-digit studen  [#permalink]

Show Tags

New post 03 Mar 2016, 18:46
Using the slot method, there are four choices so four slots.

The first restriction is that the number must not begin with zero, thus 9 choices.
The follow two slots, or digits, do not have restrictions, thus 10 choices each.
The last slot must be a prime number, thus four choices (2,3,5, and 7).

Therefore,
\(9 * 10 * 10 * 4 = 3600\)
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
Location: United States (CA)
Re: Each student at a certain business school is assigned a 4-digit studen  [#permalink]

Show Tags

New post 19 Mar 2018, 16:22
Bunuel wrote:
Each student at a certain business school is assigned a 4-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?

A. 9,000
B. 3,600
C. 2,700
D. 2,592
E. 1,944


There are 9 possible options for the first digit, 10 for the second digit, 10 for the third digit, and 4 for the last digit, since the prime digits are 2, 3, 5, and 7.

Thus, the number of codes that can be created is 9 x 10 x 10 x 4 = 3600.

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
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.

GMAT Club Bot
Re: Each student at a certain business school is assigned a 4-digit studen   [#permalink] 19 Mar 2018, 16:22
Display posts from previous: Sort by

Each student at a certain business school is assigned a 4-digit studen

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne