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hussi9
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How many eight letter words exist that are composed of Xs an 19 May 2011, 07:15
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Difficulty:

75% (hard)

Question Stats:

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

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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

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toughmat
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How many eight letter words exist that are composed of Xs an 29 Jun 2011, 00:28
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I am getting a huge number can someone pls explain the solution to the problem
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How many eight letter words exist that are composed of Xs an 01 Jul 2011, 12:34
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toughmat
I am getting a huge number can someone pls explain the solution to the problem
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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
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How many eight letter words exist that are composed of Xs an 01 Jul 2011, 22:51
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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
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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
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How many eight letter words exist that are composed of Xs an 29 May 2014, 11:16
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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
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Bunuel, could you shed some light over here?

Cheers!
J
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Bunuel
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How many eight letter words exist that are composed of Xs an 29 May 2014, 11:27
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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
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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!
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Bunuel
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109763 posts