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

It is currently 17 Oct 2018, 15:38

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

In how many ways can a 4-letter word be formed from the letters ABCDEF

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

Hide Tags

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2065
In how many ways can a 4-letter word be formed from the letters ABCDEF  [#permalink]

Show Tags

New post Updated on: 13 Aug 2018, 07:45
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

48% (01:52) correct 53% (02:00) wrong based on 125 sessions

HideShow timer Statistics

Learn when to “Add” and “Multiply” in Permutation & Combination questions- Exercise Question #5

In how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2 consonants? The letters cannot be repeated, and, the words can have no dictionary meaning.

Option:
A) 36
B) 144
C) 288
D) 864
E) 1728

Learn to use the Keyword Approach in Solving PnC question from the following article:

Learn when to “Add” and “Multiply” in Permutation & Combination questions


Image

_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com


Originally posted by EgmatQuantExpert on 04 Apr 2018, 06:47.
Last edited by EgmatQuantExpert on 13 Aug 2018, 07:45, edited 7 times in total.
Most Helpful Community Reply
Manager
Manager
avatar
S
Joined: 05 Feb 2016
Posts: 144
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
GMAT ToolKit User CAT Tests
Re: In how many ways can a 4-letter word be formed from the letters ABCDEF  [#permalink]

Show Tags

New post 04 Apr 2018, 07:11
4
1
EgmatQuantExpert wrote:

Question:



In how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2 consonants? The letters cannot be repeated, and, the words can have no dictionary meaning.

Option:
A) 36
B) 144
C) 288
D) 864
E) 1728


AEIO- 2 vowels can be selected in 4C2 ways.
BCDF- 2 consonant can be selected 4C2 ways.
we can arrannge 4 alphabets in 4! ways.

so total ways=4C2 *4C2 *4!=864

option D
General Discussion
e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2065
Re: In how many ways can a 4-letter word be formed from the letters ABCDEF  [#permalink]

Show Tags

New post 08 Apr 2018, 21:50
1

Solution



Given:
    • We are given 8 letters- ABCDEFIO
    • We need to form 4 letter words from ABCDEFIO such that it contains 2 vowels and 2 consonants
    • No letter in the 4-letter word should be repeated

To find:

    • We need to find the number of ways in which 4-letter word can be formed such that it includes 2 vowels and 2 consonants from the 8 letters- ABCDEFIO


Approach and Working:

The 8 letters- ABCDEFIO has 4 consonants and 4 vowels.
Hence, we first we will pick 2 consonants from 4 consonants and 2 vowels from 4 vowels to form the 4-letter word.

Thus,
    • Total ways= ways to pick 2 consonants from 4 consonants * ways to pick 2 vowels from 4 vowels* ways to fill the four places

Ways to picks 2 consonants from 4 consonants:

    • 2 consonants from the 4 consonants can be picked in 4c2=6 ways

Ways to pick 2 vowels from 4 vowels:

    • 2 vowels from the 4 vowels can be picked in 4c2=6 ways.

Ways to fill the 4 places in the 4-letter word:

    • Total ways to fill the 4 places= Ways to fill the 1st place* ways to fill the 2nd place* ways to fill the 3rd place* ways to fill the 4th place.
Since there are only 4 letters, the place can at max be filled with 4 letters.
    • Hence, ways to fill the first place= 4

Now, there will be 3- letters to fill the 2nd place. Hence,
    • Ways to fill the 2nd place= 3

In the similar fashion,
    • Ways to fill the 3rd place= 2
    • Ways to fill the 1st place= 1

Hence, total ways to form the 4 letters word= 6*6*4*3*2*1= 864

Hence, the correct answer is option D.

Answer: D

_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Intern
Intern
avatar
B
Joined: 10 Mar 2016
Posts: 10
Location: India
Schools: ISB '20
GMAT 1: 640 Q49 V28
GPA: 2.51
Reviews Badge CAT Tests
Re: In how many ways can a 4-letter word be formed from the letters ABCDEF  [#permalink]

Show Tags

New post 21 Aug 2018, 14:30
EgmatQuantExpert wrote:

Solution



Given:
    • We are given 8 letters- ABCDEFIO
    • We need to form 4 letter words from ABCDEFIO such that it contains 2 vowels and 2 consonants
    • No letter in the 4-letter word should be repeated

To find:

    • We need to find the number of ways in which 4-letter word can be formed such that it includes 2 vowels and 2 consonants from the 8 letters- ABCDEFIO


Approach and Working:

The 8 letters- ABCDEFIO has 4 consonants and 4 vowels.
Hence, we first we will pick 2 consonants from 4 consonants and 2 vowels from 4 vowels to form the 4-letter word.

Thus,
    • Total ways= ways to pick 2 consonants from 4 consonants * ways to pick 2 vowels from 4 vowels* ways to fill the four places

Ways to picks 2 consonants from 4 consonants:

    • 2 consonants from the 4 consonants can be picked in 4c2=6 ways

Ways to pick 2 vowels from 4 vowels:

    • 2 vowels from the 4 vowels can be picked in 4c2=6 ways.

Ways to fill the 4 places in the 4-letter word:

    • Total ways to fill the 4 places= Ways to fill the 1st place* ways to fill the 2nd place* ways to fill the 3rd place* ways to fill the 4th place.
Since there are only 4 letters, the place can at max be filled with 4 letters.
    • Hence, ways to fill the first place= 4

Now, there will be 3- letters to fill the 2nd place. Hence,
    • Ways to fill the 2nd place= 3

In the similar fashion,
    • Ways to fill the 3rd place= 2
    • Ways to fill the 1st place= 1

Hence, total ways to form the 4 letters word= 6*6*4*3*2*1= 864

Hence, the correct answer is option D.

Answer: D



while solving the question, the statement "the words can have no dictionary meaning" has not been accounted for.
e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2065
In how many ways can a 4-letter word be formed from the letters ABCDEF  [#permalink]

Show Tags

New post 21 Aug 2018, 23:14
monish447 wrote:
while solving the question, the statement "the words can have no dictionary meaning" has not been accounted for.


Hey monish447,
If we consider a word like ABCE or DFEO - both these words satisfy the given condition in the question. However, none of them are meaningful words that you find in the dictionary.

Hope this answers your query. :-)

Image

_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Intern
Intern
avatar
B
Joined: 10 Mar 2016
Posts: 10
Location: India
Schools: ISB '20
GMAT 1: 640 Q49 V28
GPA: 2.51
Reviews Badge CAT Tests
Re: In how many ways can a 4-letter word be formed from the letters ABCDEF  [#permalink]

Show Tags

New post 22 Aug 2018, 02:57
EgmatQuantExpert wrote:
monish447 wrote:
while solving the question, the statement "the words can have no dictionary meaning" has not been accounted for.


Hey monish447,
If we consider a word like ABCE or DFEO - both these words satisfy the given condition in the question. However, none of them are meaningful words that you find in the dictionary.

Hope this answers your query. :-)

Image




True.
But how about the word "FADE"
As per your solution you have taken this as a part of the solution but It must be excluded as per the ques.
e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2065
Re: In how many ways can a 4-letter word be formed from the letters ABCDEF  [#permalink]

Show Tags

New post 22 Aug 2018, 03:28
monish447 wrote:
True.
But how about the word "FADE"
As per your solution you have taken this as a part of the solution but It must be excluded as per the ques.


In this case let me point out to the specific language given in the question.
The question says "the words can have no dictionary meaning" - 'can have' doesn't necessarily mean it is always true.
What you are saying would have been true if the question was given like "the words must have no dictionary meaning" - the word 'must' ensures that every word is not a dictionary word.

Hope this clarifies your doubt. :-)
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

GMAT Club Bot
Re: In how many ways can a 4-letter word be formed from the letters ABCDEF &nbs [#permalink] 22 Aug 2018, 03:28
Display posts from previous: Sort by

In how many ways can a 4-letter word be formed from the letters ABCDEF

  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®.