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 timesTherefore, 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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