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# How many eight letter words exist that are composed of Xs an

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Manager
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How many eight letter words exist that are composed of Xs an [#permalink]

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19 May 2011, 07:15
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20% (02:23) correct 80% (01:49) wrong based on 15 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
[Reveal] Spoiler: OA

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Manager
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29 Jun 2011, 00:28
I am getting a huge number can someone pls explain the solution to the problem
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01 Jul 2011, 12:34
toughmat wrote:
I am getting a huge number can someone pls explain the solution to the problem

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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01 Jul 2011, 22:51
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hussi9 wrote:
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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Re: How many eight letter words exist that are composed of Xs an [#permalink]

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29 May 2014, 11:16
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29 May 2014, 11:16
sudhir18n wrote:
hussi9 wrote:
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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29 May 2014, 11:27
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Expert's post
jlgdr wrote:
sudhir18n wrote:
hussi9 wrote:
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

Not a GMAT question. Ignore it.
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Re: eight letter words   [#permalink] 29 May 2014, 11:27
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