GMAT Changed on April 16th - Read about the latest changes here
close

It is currently 26 Apr 2018, 23:57
Search
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
Unanswered

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.

Go to My Workbook Learn more
Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar
CLICK HERE TO HIDE/SHOW EVENTS

In how many different ways can the letters of the word

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
  Sort by Date Sort by Kudos  
Search for:
 
Print view
First unread post
Author Message
TAGS:

Hide Tags
Manager
Manager
avatar
Joined: 30 Mar 2013
Posts: 113
GMAT ToolKit User
In how many different ways can the letters of the word [#permalink]

Show Tags

New post 23 Sep 2014, 04:41
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

75% (00:42) correct 25% (00:58) wrong based on 159 sessions

HideShow timer Statistics

In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions?

A. None of these

B. 64

C. 120

D. 36

E. 360
[Reveal] Spoiler: OA
Manager
Manager
avatar
Joined: 30 Mar 2013
Posts: 113
GMAT ToolKit User
Re: In how many different ways can the letters of the word [#permalink]

Show Tags

New post 23 Sep 2014, 04:45
what i don't understand is why we don't have 4 positions for the vowels? 1 D 3 T 5 L 7. So here we have 3P3 for consonants, and 4P3 for vowels. This is, after all, how we did this question:
in-how-many-different-ways-can-the-letters-of-the-word-corporation-185090.html

thank you!
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44657
Premium Member CAT Tests
Top Member of the Month
Re: In how many different ways can the letters of the word [#permalink]

Show Tags

New post 23 Sep 2014, 04:52
Expert's post
usre123 wrote:
In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions?

A. None of these

B. 64

C. 120

D. 36

E. 360



OEOEOE

3 vowels EOI can be arranged on odd places in 3!=6 ways. Similarly 3 consonants can be arranged on even places in 3!=6 ways.

Total = 6*6 = 36.

Answer: D.

P.S. This question cannot be from any reliable GMAT source. Please do not post questions from that source again. Thank you.
_________________

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

Manager
Manager
avatar
Joined: 30 Mar 2013
Posts: 113
GMAT ToolKit User
Re: In how many different ways can the letters of the word [#permalink]

Show Tags

New post 23 Sep 2014, 04:58
Bunuel wrote:
usre123 wrote:
In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions?

A. None of these

B. 64

C. 120

D. 36

E. 360



OEOEOE

3 vowels EOI can be arranged on odd places in 3!=6 ways. Similarly 3 consonants can be arranged on even places in 3!=6 ways.

Total = 6*6 = 36.

Answer: D.

P.S. This question cannot be from any reliable GMAT source. Please do not post questions from that source again. Thank you.



Ok, I won't, thank you.
But could you pls explain why we don't consider the one odd position after the 6th even one? just like we did in the link I posted in my answer above?
You can delete this questions if you wish. I don't wan to confuse the other people preparing for the exam.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44657
Premium Member CAT Tests
Top Member of the Month
Re: In how many different ways can the letters of the word [#permalink]

Show Tags

New post 23 Sep 2014, 06:26
Expert's post
usre123 wrote:
Bunuel wrote:
usre123 wrote:
In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions?

A. None of these

B. 64

C. 120

D. 36

E. 360



OEOEOE

3 vowels EOI can be arranged on odd places in 3!=6 ways. Similarly 3 consonants can be arranged on even places in 3!=6 ways.

Total = 6*6 = 36.

Answer: D.

P.S. This question cannot be from any reliable GMAT source. Please do not post questions from that source again. Thank you.



Ok, I won't, thank you.
But could you pls explain why we don't consider the one odd position after the 6th even one? just like we did in the link I posted in my answer above?
You can delete this questions if you wish. I don't wan to confuse the other people preparing for the exam.


We have 6 letters, so only 6 places. There is no 7th place.
_________________

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

Manager
Manager
avatar
Joined: 30 Mar 2013
Posts: 113
GMAT ToolKit User
Re: In how many different ways can the letters of the word [#permalink]

Show Tags

New post 23 Sep 2014, 10:35
OEOEOE

3 vowels EOI can be arranged on odd places in 3!=6 ways. Similarly 3 consonants can be arranged on even places in 3!=6 ways.

Total = 6*6 = 36.

Answer: D.

P.S. This question cannot be from any reliable GMAT source. Please do not post questions from that source again. Thank you.[/quote]


Ok, I won't, thank you.
But could you pls explain why we don't consider the one odd position after the 6th even one? just like we did in the link I posted in my answer above?
You can delete this questions if you wish. I don't wan to confuse the other people preparing for the exam.[/quote]

We have 6 letters, so only 6 places. There is no 7th place.[/quote]

yes, but when we did the corporation eg, we put a place before and after the entire word (7 places fro 5 vowels). why cant we do the same here?

I'm really weak at this, is there is a gmat club book I could buy instead of annoying everyone (esp Bunuel) here?
1 KUDOS received
Intern
Intern
avatar
Joined: 21 Aug 2012
Posts: 1
Concentration: Strategy, Finance
In how many different ways can the letters of the word [#permalink]

Show Tags

New post 30 Sep 2014, 15:50
1
This post received
KUDOS
usre123 wrote:

yes, but when we did the corporation eg, we put a place before and after the entire word (7 places fro 5 vowels). why cant we do the same here?

I'm really weak at this, is there is a gmat club book I could buy instead of annoying everyone (esp Bunuel) here?



The question states that the vowel letters must occupy the odd positions. If you place a vowel in the "7th place" that you are thinking of, then the placement of all letters will shift by one and every vowel will now be in an even position.
Intern
Intern
avatar
Joined: 08 May 2017
Posts: 1
Re: In how many different ways can the letters of the word [#permalink]

Show Tags

New post 29 May 2017, 23:34
I am agree with answer but I have doubt. if option 729 is available additionally than is it possible to consider here repeatation?
Means why answer is not
3*3*3*3*3*3=729 . three vowels can be arranged on first place ..3 consonants on second ..again 3 vowels on third place..and so in.

Posted from my mobile device

Posted from my mobile device
Expert Post
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2493
Location: United States (CA)
Re: In how many different ways can the letters of the word [#permalink]

Show Tags

New post 01 Jun 2017, 10:23
Expert's post
usre123 wrote:
In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions?

A. None of these

B. 64

C. 120

D. 36

E. 360


Since detail has 6 letters, there are 3 odd positions, the 1st, 3rd, and 5th spots. Let’s determine how many ways the word can be arranged when the vowels occupy the odd positions.

1st spot: 3 options (any of the 3 vowels)

2nd spot: 3 options (any of the 3 consonants)

3rd spot: 2 options (any of the 2 remaining vowels)

4th spot: 2 options (any of the 2 remaining consonants)

5th spot: 1 option (the last remaining vowel)

6th spot: 1 option (the last remaining consonant)

So, the word can be arranged in 3 x 3 x 2 x 2 x 1 x 1 = 36 ways.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Expert Post
Top Contributor
SVP
SVP
User avatar
P
Joined: 12 Sep 2015
Posts: 2325
Location: Canada
Re: In how many different ways can the letters of the word [#permalink]

Show Tags

New post 07 Dec 2017, 08:32
Expert's post
Top Contributor
usre123 wrote:
In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions?

A. None of these

B. 64

C. 120

D. 36

E. 360


Vowels: E, A, I
Consonants: D, T, L

Spaces: #1, #2, #3, #4, #5, #6,

Take the task of arranging the letters and break it into stages.

Stage 1: Select a vowel to go in space #1
There are 3 vowels to choose from, so we can complete stage 1 in 3 ways

Stage 2: Select a vowel to go in space #3
There are 2 remaining vowels from which to choose, so we can complete this stage in 2 ways.

Stage 3: Select a vowel to go in space #5
There is 1 remaining vowel from which to choose, so we can complete this stage in 1 ways.

Stage 4: Select a consonant to go in space #2
There are 3 consonants to choose from, so we can complete stage 4 in 3 ways .

Stage 5: Select a consonant to go in space #4
There are 2 remaining consonants from which to choose, so we can complete this stage in 2 ways.

Stage 6: Select a consonant to go in space #6
There is 1 remaining consonant from which to choose, so we can complete this stage in 1 ways.

By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus arrange all of the letters) in (3)(2)(1)(3)(2)(1) ways (= 36 ways)

Answer: D

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

RELATED VIDEOS



_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Re: In how many different ways can the letters of the word   [#permalink] 07 Dec 2017, 08:32
Print view
First unread post
Display posts from previous: Sort by

In how many different ways can the letters of the word

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

Moderators: chetan2u, VeritasPrepKarishma, niks18, Bunuel, mikemcgarry, generis

Search for:


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®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions