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# A certain sequence of x letters complies with the following

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Senior Manager
Joined: 21 Oct 2013
Posts: 419
A certain sequence of x letters complies with the following  [#permalink]

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21 Aug 2014, 08:31
1
9
00:00

Difficulty:

55% (hard)

Question Stats:

68% (02:41) correct 32% (02:15) wrong based on 112 sessions

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A certain sequence of x letters complies with the following rules: The letter 'I' may be followed only by a 'J'; The letter 'J' may be followed only by a 'K'; The letter 'K' may be followed only by an 'L'; The letter 'L' may be followed only by an 'M'; The letter 'M' may be followed only by an 'N'; The letter 'N' may be followed only by a 'K'. If the first letter of that sequence is 'I', and the last letter of the sequence is 'M', then x could be

A) 10
B) 19
C) 29
D) 39
E) 40
Manager
Joined: 29 Apr 2014
Posts: 67
Location: India
Concentration: Other, Finance
GMAT 1: 770 Q51 V42
WE: Analyst (Retail Banking)
A certain sequence of x letters complies with the following  [#permalink]

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21 Aug 2014, 11:18
3
2
goodyear2013 wrote:
A certain sequence of x letters complies with the following rules: The letter 'I' may be followed only by a 'J'; The letter 'J' may be followed only by a 'K'; The letter 'K' may be followed only by an 'L'; The letter 'L' may be followed only by an 'M'; The letter 'M' may be followed only by an 'N'; The letter 'N' may be followed only by a 'K'. If the first letter of that sequence is 'I', and the last letter of the sequence is 'M', then x could be

A) 10
B) 19
C) 29
D) 39
E) 40

If the first letter is 'I', then according to the rules, the sequence should be
I J K L M N K L M...M

From the above sequence we can see than the for 'M' to be the last character, the minimum possible length is 5 --> Not an option

Then we can see that M will be the last character only if the sequence 'N K L M' is repeated. So, the sequence can be written as
I J K L M (N K L M)n times

Therefore, the number of characters should be of the form '5 + 4n' and only 29 satisfies this criteria. Hence the answer is 'C'.

Hope that makes it clear.
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Joined: 02 Sep 2009
Posts: 52231
Re: A certain sequence of x letters complies with the following  [#permalink]

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21 Aug 2014, 13:49
1
goodyear2013 wrote:
A certain sequence of x letters complies with the following rules: The letter 'I' may be followed only by a 'J'; The letter 'J' may be followed only by a 'K'; The letter 'K' may be followed only by an 'L'; The letter 'L' may be followed only by an 'M'; The letter 'M' may be followed only by an 'N'; The letter 'N' may be followed only by a 'K'. If the first letter of that sequence is 'I', and the last letter of the sequence is 'M', then x could be

A) 10
B) 19
C) 29
D) 39
E) 40

Similar question to practice: 12-easy-pieces-or-not-126366.html#p1033936
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Posts: 559
Schools: Cambridge'16
Re: A certain sequence of x letters complies with the following  [#permalink]

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29 Oct 2014, 05:24
The infinite sequence is

I,J,K,L,M, N,K,L,M, N,K,L,M.....

the number of terms is multiple of 4 plus 5. Only 29=4*6+5

C
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Posts: 9419
Re: A certain sequence of x letters complies with the following  [#permalink]

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22 Sep 2018, 05:57
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A certain sequence of x letters complies with the following &nbs [#permalink] 22 Sep 2018, 05:57
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