Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 07 Oct 2015, 12:38

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Arrange letters of the word

Author Message
TAGS:
Manager
Status: GMAT in 4 weeks
Joined: 28 Mar 2010
Posts: 185
GPA: 3.89
Followers: 1

Kudos [?]: 83 [0], given: 25

Arrange letters of the word [#permalink]  20 May 2011, 05:55
00:00

Difficulty:

(N/A)

Question Stats:

63% (01:26) correct 37% (00:09) wrong based on 19 sessions
In how many ways can the letters of the word JUPITER be arranged in a row so that the vowels appear in alphabetic order?

(A) 736 (B) 768 (C) 792 (D) 840 (E) 876

------------------------------------------------------
IIM CAT Level Question
------------------------------------------------------
[Reveal] Spoiler: OA

_________________

If you liked my post, please consider a Kudos for me. Thanks!

VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1356
Followers: 14

Kudos [?]: 179 [0], given: 10

Re: Arrange letters of the word [#permalink]  20 May 2011, 07:12
three letters can be arranged in 3! ways.
only one combination EIU is required.

7 letters can be arranged in 7! ways.

thus 7!/ 3! * 1 = 840.

D
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

SVP
Joined: 16 Nov 2010
Posts: 1676
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 31

Kudos [?]: 382 [0], given: 36

Re: Arrange letters of the word [#permalink]  20 May 2011, 07:51
@amit2k9, could you please explain this in more detail ?
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1356
Followers: 14

Kudos [?]: 179 [0], given: 10

Re: Arrange letters of the word [#permalink]  20 May 2011, 10:10
1. Consider EIU as one. then total possible combination of words = 5* 4! = 120

2. Consider EI and IU together total possible combinations = [5 (positions for EI out of 7) * 5! (rest of the letters)] +

[ 5 (positions for IU)* 5! (rest of the letters)]

Now in half of the combinations U will be ahead of EI and E will be ahead of IU.

So 1/2[5 (positions for EI out of 7) * 5! (rest of the letters)] +1/2 [ 5 (positions for IU)* 5! (rest of the letters)]

total will give = 300 + 300 = 600.

3. Consider E-I-U-- with one letter spacing in between = 3(positions of EIU shifting) * 4! (letters to be arranged) = 72

4. Consider E-I--U- and E---I-U with two letter spacing between IU and EI = 2 * 4! = 48

thus totaling 120 + 600 + 72 + 48 = 840.

Alternately , Consider

all possible letter arrangements = 7!

only one combination out of 3! combinations possible for EIU. meaning 3 are taken in a group,but they are not alike.
Means total combinations remain 7! and not 5! ( EIU together + 4 letters).

So, essentially it is 7P3 =
Hence 7!/ 3! = 840
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Manager
Joined: 19 Nov 2010
Posts: 91
Followers: 6

Kudos [?]: 141 [0], given: 9

Re: Arrange letters of the word [#permalink]  20 May 2011, 12:51
Amt2k9,

Conceptwise, I did not get your 7!/3!. If the word was, Let's say JUPUTUR, number of ways the letter can be arranged is 7!/3! ways (total ! / identical !). You used the same concept where the letters are not identical. You mentioned that those are not alike, but still not clear on why we still can do 7!/3!.
Director
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 923
Followers: 13

Kudos [?]: 251 [0], given: 123

Re: Arrange letters of the word [#permalink]  20 May 2011, 18:20
Darn ! I am not Amt2k9. I think it is pretty obvious that in 1/6th of the ways out of 7! the vowels will be ordered. This reasoning is parallel to the situation when we have 3 people lets say A B C sitting in a row and we want to know the ways in which they will be alphabetical order. There is just one way ie. 3!/6=1 or 3!/3!

The division by 3! is NOT owned by the concept of weeding out the duplicates. We will apply it when we need it

bellcurve wrote:
Amt2k9,

Conceptwise, I did not get your 7!/3!. If the word was, Let's say JUPUTUR, number of ways the letter can be arranged is 7!/3! ways (total ! / identical !). You used the same concept where the letters are not identical. You mentioned that those are not alike, but still not clear on why we still can do 7!/3!.
Manager
Status: GMAT in 4 weeks
Joined: 28 Mar 2010
Posts: 185
GPA: 3.89
Followers: 1

Kudos [?]: 83 [0], given: 25

Re: Arrange letters of the word [#permalink]  20 May 2011, 22:27
bellcurve wrote:
Amt2k9,

Conceptwise, I did not get your 7!/3!. If the word was, Let's say JUPUTUR, number of ways the letter can be arranged is 7!/3! ways (total ! / identical !). You used the same concept where the letters are not identical. You mentioned that those are not alike, but still not clear on why we still can do 7!/3!.

Since the order of vowels will always remain the same despite these occupying different positions -> if we assume each vowel as X then our question is same as asking "arrange JPTRXXX" => in all 7!/3! ways
=> Choice (4) is the right answer
_________________

If you liked my post, please consider a Kudos for me. Thanks!

Re: Arrange letters of the word   [#permalink] 20 May 2011, 22:27
Similar topics Replies Last post
Similar
Topics:
What percent of the different arrangements of the letters of the word 0 04 Aug 2015, 10:35
5 How many ways are there to arrange the letters in the word Tennessee? 5 06 Feb 2015, 06:40
7 The number of arrangement of letters of the word BANANA in 1 28 Oct 2013, 04:26
In how many ways can the letters of the word "COMPUTER" be arranged? 1 10 Jan 2012, 06:08
3 How many arrangements of the letters of the word DEFEATED ar 7 18 Sep 2011, 13:05
Display posts from previous: Sort by