Last visit was: 29 Apr 2026, 21:23 It is currently 29 Apr 2026, 21:23
Home
Messages
Tests
Schools
Events
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 Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
hussi9
User avatar
Joined: 28 Mar 2010
Last visit: 05 Mar 2020
Posts: 125
Own Kudos:
525
Given Kudos: 25
Status:GMAT in 4 weeks
GPA: 3.89
Posts: 125
Kudos: 525
How many eight letter words exist that are composed of Xs an 19 May 2011, 07:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

27% (02:09) correct 73% (02:00) wrong based on 11 sessions

History

Date
Time
Result
Not Attempted Yet
How many eight letter words exist that are composed of Xs and Ys, and which contain neither three consecutive Xs nor three consecutive Ys?

(A) 74
(B) 66
(C) 76
(D) 68
(E) none of these

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
ShowHide Answer
Official Answer
D
User avatar
toughmat
User avatar
Joined: 19 Apr 2011
Last visit: 13 Nov 2011
Posts: 58
Own Kudos:
11
Given Kudos: 2
Posts: 58
Kudos: 11
How many eight letter words exist that are composed of Xs an 29 Jun 2011, 00:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I am getting a huge number can someone pls explain the solution to the problem
User avatar
manishgeorge
User avatar
Joined: 07 Jun 2011
Last visit: 27 Dec 2012
Posts: 24
Own Kudos:
19
Given Kudos: 31
Posts: 24
Kudos: 19
How many eight letter words exist that are composed of Xs an 01 Jul 2011, 12:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
toughmat
I am getting a huge number can someone pls explain the solution to the problem
Show more

I am not 100% sure about my answer, how ever following is what i am thinking

possible letters are x and y, so for each letter in the 8 letter work there are 2 possibilities. so in essence there are 2^8 = 128 possibilities

3 consecutive xs means of the 8 letters 3 have only one possibility so there are 2^5 different ways = 32

same applies for 3 consecutive Ys = 32


so our answer is 128 -32 -32 = 64
User avatar
sudhir18n
User avatar
Current Student
Joined: 26 May 2005
Last visit: 13 Feb 2013
Posts: 351
Own Kudos:
616
 [1]
Given Kudos: 13
Posts: 351
Kudos: 616
 [1]
How many eight letter words exist that are composed of Xs an 01 Jul 2011, 22:51
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
hussi9
How many eight letter words exist that are composed of Xs and Ys, and which contain neither three consecutive Xs nor three consecutive Ys?

(1) 74 (2) 66 (3) 76 (4) 68 (5) none of these
Show more

Whats the source? i see a CAT in this:P
its D .68

I see this more of a pattern question + probability. Using pattern is very useful here as we have a constraint .

let f(n) = no of words with Xs and Ys
f(1) = 2 (XY, YX)
f(2)= 4 (XY XX, YX, YY)

Now the problem is F(3) .. we cant have 3 consecutive X or Y
so we can write F(3) = F(2)+(1).. this will give us a pattern
F(n) = f(n-1)+f(n-2)
f(3) = 2+4 = 6
f(4) = 6+4 = 10
f(5) = 10+6 = 16
f(6) = 16+10 = 26
f(7) = 26+ 16 = 42
f(8) - 42 + 26 = 68
User avatar
jlgdr
User avatar
Joined: 06 Sep 2013
Last visit: 24 Jul 2015
Posts: 1,302
Own Kudos:
2,980
Given Kudos: 355
Concentration: Finance
Schools: Wharton '17 (A) HBS '17 (WA$)
Schools: Wharton '17 (A) HBS '17 (WA$)
Posts: 1,302
Kudos: 2,980
How many eight letter words exist that are composed of Xs an 29 May 2014, 11:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sudhir18n
hussi9
How many eight letter words exist that are composed of Xs and Ys, and which contain neither three consecutive Xs nor three consecutive Ys?

(1) 74 (2) 66 (3) 76 (4) 68 (5) none of these

Whats the source? i see a CAT in this:P
its D .68

I see this more of a pattern question + probability. Using pattern is very useful here as we have a constraint .

let f(n) = no of words with Xs and Ys
f(1) = 2 (XY, YX)
f(2)= 4 (XY XX, YX, YY)

Now the problem is F(3) .. we cant have 3 consecutive X or Y
so we can write F(3) = F(2)+(1).. this will give us a pattern
F(n) = f(n-1)+f(n-2)
f(3) = 2+4 = 6
f(4) = 6+4 = 10
f(5) = 10+6 = 16
f(6) = 16+10 = 26
f(7) = 26+ 16 = 42
f(8) - 42 + 26 = 68
Show more

Bunuel, could you shed some light over here?

Cheers!
J
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 29 Apr 2026
Posts: 109,975
Own Kudos:
812,004
 [1]
Given Kudos: 105,949
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,975
Kudos: 812,004
 [1]
How many eight letter words exist that are composed of Xs an 29 May 2014, 11:27
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
jlgdr
sudhir18n
hussi9
How many eight letter words exist that are composed of Xs and Ys, and which contain neither three consecutive Xs nor three consecutive Ys?

(1) 74 (2) 66 (3) 76 (4) 68 (5) none of these

Whats the source? i see a CAT in this:P
its D .68

I see this more of a pattern question + probability. Using pattern is very useful here as we have a constraint .

let f(n) = no of words with Xs and Ys
f(1) = 2 (XY, YX)
f(2)= 4 (XY XX, YX, YY)

Now the problem is F(3) .. we cant have 3 consecutive X or Y
so we can write F(3) = F(2)+(1).. this will give us a pattern
F(n) = f(n-1)+f(n-2)
f(3) = 2+4 = 6
f(4) = 6+4 = 10
f(5) = 10+6 = 16
f(6) = 16+10 = 26
f(7) = 26+ 16 = 42
f(8) - 42 + 26 = 68

Bunuel, could you shed some light over here?

Cheers!
J
Show more

Not a GMAT question. Ignore it.

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderator:
Bunuel
Math Expert
109975 posts