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

 It is currently 16 Jun 2019, 21:52

### 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

# In how many ways can the letters of the word JUPITER be arranged in a

Author Message
TAGS:

### Hide Tags

Manager
Status: GMAT in 4 weeks
Joined: 28 Mar 2010
Posts: 157
GPA: 3.89
In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

20 May 2011, 06:55
1
27
00:00

Difficulty:

45% (medium)

Question Stats:

69% (02:12) correct 31% (02:24) wrong based on 214 sessions

### HideShow timer Statistics

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
------------------------------------------------------

_________________
If you liked my post, please consider a Kudos for me. Thanks!
Senior Manager
Joined: 18 Jun 2016
Posts: 261
Location: India
GMAT 1: 720 Q50 V38
GMAT 2: 750 Q49 V42
GPA: 4
WE: General Management (Other)
Re: In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

30 Apr 2017, 11:27
2
3
hussi9 wrote:
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
------------------------------------------------------

Though I got it wrong, Here is the best Method to solve this question.

JUPITER -> 7 Alphabets -> 3 Vowels and 4 Consonants.

# Arrangements of 3 Vowels = 3! = 6.
# of Valid arrangements out of these = 1 For all the other arrangements, vowels will not be arranged alphabetically.

Number of Legitimate Arrangements = Total Arrangements - Illegitimate arrangements.

$$= 7! - \frac{5}{6}*7!$$
$$= 7!*(1 - \frac{5}{6})$$
$$=7! * \frac{1}{6}$$
= 840
_________________
I'd appreciate learning about the grammatical errors in my posts

Please hit Kudos If my Solution helps

My Debrief for 750 - https://gmatclub.com/forum/from-720-to-750-one-of-the-most-difficult-pleatues-to-overcome-246420.html

My CR notes - https://gmatclub.com/forum/patterns-in-cr-questions-243450.html
##### General Discussion
Director
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 953
Re: In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

20 May 2011, 08:12
1
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
Retired Moderator
Joined: 16 Nov 2010
Posts: 1367
Location: United States (IN)
Concentration: Strategy, Technology
Re: In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

20 May 2011, 08:51
@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
Director
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 953
Re: In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

20 May 2011, 11:10
2
1
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
Manager
Joined: 19 Nov 2010
Posts: 80
Re: In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

20 May 2011, 13:51
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: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 706
Re: In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

20 May 2011, 19:20
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: 157
GPA: 3.89
Re: In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

20 May 2011, 23:27
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!
Manager
Joined: 07 Jul 2016
Posts: 78
GPA: 4
Re: In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

05 Aug 2016, 23:44
1
hussi9 wrote:
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

Commenting as I struggled getting my head around the concept. Kudos given above.

There are $$7_P7 = 7!$$ ways to arrange the 7 letters.

For each of these combinations, there is a single valid arrangement of the vowels: $$\frac{1}{3_P3}$$

$$7! \times \frac{1}{3!} = \frac{7!}{3!} = \frac{7 \times 6 \times 5 \times 4 \times 3!}{3!} = 840 = D$$
_________________
Please press +1 Kudos if this post helps.
Director
Joined: 13 Mar 2017
Posts: 730
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

05 Jul 2017, 05:43
1
1
hussi9 wrote:
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
------------------------------------------------------

Without limitation the words of JUPITER can be arranged in 7! ways..
Now there are 3 vowels I, E, U

So these vowels can be arranged among themselves in 3! ways.
We need to find the arrangement in vowels are in alphabetical order i.e. EIU which is only one out of 3! ways.

Hence, total number of required arrangement = 7!/3! = 7*6*5*4 = 42 * 20 = 840

_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Manager
Joined: 18 Apr 2018
Posts: 94
In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

09 Dec 2018, 01:58
I have really tried to understand the concepts applied here from all the explanations but I still don't.Can someone be kind enough to help with a link that explains these concepts clearly...:-(

Thanks.

Posted from my mobile device
Intern
Affiliations: National Institute of Technology, Durgapur
Joined: 22 Feb 2017
Posts: 30
Location: India
GMAT 1: 720 Q49 V38
GPA: 3.6
WE: Engineering (Manufacturing)
In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

23 Jan 2019, 00:07
1
1
Kem12 wrote:
I have really tried to understand the concepts applied here from all the explanations but I still don't.Can someone be kind enough to help with a link that explains these concepts clearly...:-(

Thanks.

Posted from my mobile device

If you are struggling with the above methods like me, I'm going to explain to you my way of solving ; However I don't know whether it would be sufficient to clear your doubts or not ?!

There are a TOTAL '7-seats' for the alphabets of the letter 'JUPITER' out of which '3' are vowels & '4' are consonants ;

The question asks us to find the total no. of ways in which vowels will be in a particular order (,i.e, alphabetical order & if it was a no. code maybe the question would have told ascending/descending order) ;

Coming back to the question, we know there are '7-seats' => We have to choose '3-seats' for our vowels ( E, I, & U ) => we can do that in 7C3 ways ;
Or, simply [7!/(3!x4!)] ways [This is what I meant => C C V V V C C, C V C V C V C, C C C V V V C, etc.]
Now, the order of vowels is 'E I U' => Total no. of arrangements = (7C3 x 1)
[And NOT (7C3 x 3!) Since, doing so we would include the arrangements 'UIE, UEI, IUE, IEU, EUI' along with 'EIU' which we don't want as per the question]

Now, we are left with '4-seats' for consonants (J, P,T, & R) => We can choose '4-seats' for '4' consonants in 4C4 (or 1) way ;
[But here we are allowed for arrangements, i.e, JEUITPR, JEUITRP, EUIJPRT, EUITPR, etc] ;
Hence, we can do it in 4C4x4! ways ;

THEREFORE, TOTAL NO. of WAYS IN WHICH VOWELS STAYS IN ALPHABETICAL ORDER IN 'JUPITER' = 7C3x1x4C4x4! = 840 ways = option D.
Hope it helps...
Manager
Joined: 18 Apr 2018
Posts: 94
Re: In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

23 Jan 2019, 04:13
Lithium wrote:
Kem12 wrote:
I have really tried to understand the concepts applied here from all the explanations but I still don't.Can someone be kind enough to help with a link that explains these concepts clearly...:-(

Thanks.

Posted from my mobile device

If you are struggling with the above methods like me, I'm going to explain to you my way of solving ; However I don't know whether it would be sufficient to clear your doubts or not ?!

There are a TOTAL '7-seats' for the alphabets of the letter 'JUPITER' out of which '3' are vowels & '4' are consonants ;

The question asks us to find the total no. of ways in which vowels will be in a particular order (,i.e, alphabetical order & if it was a no. code maybe the question would have told ascending/descending order) ;

Coming back to the question, we know there are '7-seats' => We have to choose '3-seats' for our vowels ( E, I, & U ) => we can do that in 7C3 ways ;
Or, simply [7!/(3!x4!)] ways [This is what I meant => C C V V V C C, C V C V C V C, C C C V V V C, etc.]
Now, the order of vowels is 'E I U' => Total no. of arrangements = (7C3 x 1)
[And NOT (7C3 x 3!) Since, doing so we would include the arrangements 'UIE, UEI, IUE, IEU, EUI' along with 'EIU' which we don't want as per the question]

Now, we are left with '4-seats' for consonants (J, P,T, & R) => We can choose '4-seats' for '4' consonants in 4C4 (or 1) way ;
[But here we are allowed for arrangements, i.e, JEUITPR, JEUITRP, EUIJPRT, EUITPR, etc] ;
Hence, we can do it in 4C4x4! ways ;

THEREFORE, TOTAL NO. of WAYS IN WHICH VOWELS STAYS IN ALPHABETICAL ORDER IN 'JUPITER' = 7C3x1x4C4x4! = 840 ways = option D.

Hope it helps...

Thank you so much
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9320
Location: Pune, India
Re: In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

23 Jan 2019, 04:36
hussi9 wrote:
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
------------------------------------------------------

Alternatively, think of it this way:

The vowels must be arranged like this:

E I U
Now there are 4 spots (shown by x) for J:
x E x I x U x
Say we choose E J I U

Next we place P. There are 5 spots for P:
x E x J x I x U x

and so on for T and R too.

So in all we get 4*5*6*7 = 840 different ways (you don't need to calculate this. Since there is a 2 and 5, it will end in 0)

_________________
Karishma
Veritas Prep GMAT Instructor

CEO
Joined: 18 Aug 2017
Posts: 3834
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

23 Jan 2019, 04:50
hussi9 wrote:
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
------------------------------------------------------

JUPITER
total 7 ! is the ways it can be arranged
but question has asked vowels appear in alphabetical order
so
EIUJPTR would be the sequence
we can put EIU ; 3!

7!/3! = 840

IMO D
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Intern
Joined: 04 Oct 2016
Posts: 17
Re: In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

24 Jan 2019, 20:15
hussi9 wrote:
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
------------------------------------------------------

Alternatively, think of it this way:

The vowels must be arranged like this:

E I U
Now there are 4 spots (shown by x) for J:
x E x I x U x
Say we choose E J I U

Next we place P. There are 5 spots for P:
x E x J x I x U x

and so on for T and R too.

So in all we get 4*5*6*7 = 840 different ways (you don't need to calculate this. Since there is a 2 and 5, it will end in 0)

Kindly, help me understand why P has 5 spots and so on.
J has 4 spots and then should't be 3 spots for P and so on...
VP
Joined: 09 Mar 2018
Posts: 1004
Location: India
In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

Updated on: 24 Jan 2019, 20:57
hussi9 wrote:
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
------------------------------------------------------

I solved this question,in the inline way
i fixed the position of E
E _ _ _ _ _ _, Now here if I U takes the 1st 2 spots Then the remaining spots will be filled in 4*3*2*1 = 24 ways and I U can move 4 more times making the total ways as 24*5 = 120 ways

In the next case I will fix E I this time and move the rest of the alphabets i.e. E I _ U _ _ _ and so on, this will give you 96 ways.

Next Case, I fixed E I U, this will give you 24 ways.

Total = 120 + 96 + 24= 240, now EIU can also be UIE, this makes 240*2 ways = 840 ways

OA D
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Originally posted by KanishkM on 24 Jan 2019, 20:39.
Last edited by KanishkM on 24 Jan 2019, 20:57, edited 1 time in total.
Intern
Joined: 26 Apr 2017
Posts: 46
Re: In how many ways can the letters of the word JUPITER be arranged in a  [#permalink]

### Show Tags

24 Jan 2019, 20:44
amit2k9 wrote:
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

amit2k9 wrote:
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

Sent from my Moto G (5) Plus using GMAT Club Forum mobile app
Re: In how many ways can the letters of the word JUPITER be arranged in a   [#permalink] 24 Jan 2019, 20:44
Display posts from previous: Sort by