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

It is currently 16 Oct 2018, 20:11

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

There are 6 distinct letters of the English alphabet and 4 d

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

Hide Tags

Intern
Intern
avatar
Joined: 06 Feb 2014
Posts: 5
There are 6 distinct letters of the English alphabet and 4 d  [#permalink]

Show Tags

New post Updated on: 07 Feb 2014, 04:33
3
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (02:14) correct 42% (02:18) wrong based on 100 sessions

HideShow timer Statistics

There are 6 distinct letters of the English alphabet and 4 distinct digits. all possible 6 character apha-numero codes are generated using any 4 letters of the alphabet and any 2 available digits. If in any given code, the characters are all distinct, then what is the maximum number of such codes that can be generated?

A. 4320
B. 64800
C. 8800
D. 22000

Originally posted by ratnanideepak on 06 Feb 2014, 03:15.
Last edited by Bunuel on 07 Feb 2014, 04:33, edited 1 time in total.
RENAMED THE TOPIC.
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4494
Re: permutation and combination  [#permalink]

Show Tags

New post 06 Feb 2014, 14:03
ratnanideepak wrote:
there are 6 distinct letters of the English alphabet and 4 distinct digits. all possible 6 character apha-numero codes are generated using any 4 letters of the alphabet and any 2 available digits. If in any given code, the characters are all distinct, then what is the maximum number of such codes that can be generated?

A. 4320
B. 64800
C. 8800
D. 22000

Dear ratnanideepak
I'm happy to respond. :-) There seems to be a couple problems here. First of all, there are only four answer choices, whereas all GMAT Quant questions have five choices. On the real GMAT, and on all better prep sources, numerical answers always appear in numerical order, at least for positive integers.

From the six letters, we need four distinct letters
# of combinations = 6C4 = 15
From the four numerals, we need 2 distinct digits
4C2 = 6
Once we have our unique four letter and our unique 2 digits, we can put them in any order: each new order would be a different code. The number of orders would be
6! = 720

Now, we use the Fundamental Counting Principle. See:
http://magoosh.com/gmat/2012/gmat-quant-how-to-count/
Total number of codes equals = 15*6*720
Without a calculator, first do 15*6 = 90. Then, 90 = 100 - 10, so
720*90 = 720*(100 - 10) = 72000 - 7200 = 64800
Answer = (B)

Does all this make sense?
_________________

Mike McGarry
Magoosh Test Prep


Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Manager
Manager
avatar
Joined: 09 Jun 2015
Posts: 94
Re: There are 6 distinct letters of the English alphabet and 4 d  [#permalink]

Show Tags

New post 13 Mar 2016, 08:14
ratnanideepak wrote:
There are 6 distinct letters of the English alphabet and 4 distinct digits. all possible 6 character apha-numero codes are generated using any 4 letters of the alphabet and any 2 available digits. If in any given code, the characters are all distinct, then what is the maximum number of such codes that can be generated?

A. 4320
B. 64800
C. 8800
D. 22000


4 letter from 6 can be selected in 6C4 ways or 15 ways
2 numbers from 4 can be selected in 4C2 ways or 6 ways.
Now, we have selected 6 characters in 15*6 = 90 ways.
The 6 characters can be arranged in 6! ways or 720 ways.
Therefore, the total number of codes is 90*720 = 64800
Manager
Manager
User avatar
S
Joined: 21 Jul 2017
Posts: 167
Location: India
Concentration: Social Entrepreneurship, Leadership
GMAT 1: 650 Q47 V33
GPA: 4
WE: Project Management (Education)
Premium Member Reviews Badge CAT Tests
Re: There are 6 distinct letters of the English alphabet and 4 d  [#permalink]

Show Tags

New post 29 Sep 2017, 23:22
Total number of digits in the code is 6.
Out of this 6, 4 are alphabets = 6C4 ways=15
The other 2 are numeric digits = 4C2 ways=6

Now these 6 digits can be arranged among themselves in 6! ways.
So, the answer is 15*6*6!=64800
GMAT Club Bot
Re: There are 6 distinct letters of the English alphabet and 4 d &nbs [#permalink] 29 Sep 2017, 23:22
Display posts from previous: Sort by

There are 6 distinct letters of the English alphabet and 4 d

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.