Question Details

Consider the following sequence that follows some arrangement:
c_accaa_aa_bc_b
The letters that appear in the gaps are

Options

A

abba

B

cbbb

C

bbbb

D

cccc

Show Answer

Correct Answer :

Option B

cbbb

Solution :

The correct option is cbbb.

Let us analyze the given sequence with gaps:
c _ a c c a a _ a a _ b c _ b

To find the pattern, let us substitute the letters from the correct option cbbb into the four gaps in order. The letters to be filled in are:
1st gap: c
2nd gap: b
3rd gap: b
4th gap: b

Substituting these letters into the sequence, we get:
c c a c c a a b a a b b c b b

Now, let us write down the full resulting sequence:
ccaccaabbabbcbb

Let us divide this 15-letter sequence into equal groups to identify a repeating pattern. If we divide the sequence into five groups of three letters each, we get:
cca | cca | abb | abb | cbb

This division does not show a clear repeating structure. Let us instead divide the sequence into three groups of five letters each:
ccacc | aabbb | bbcbb

Let us look at another grouping. What if we group them as follows:
cca | cca | abb | abb | cbb (which is: two repetitions of "cca", followed by two repetitions of "abb", and then "cbb" starting the next pair)? This suggests a shifting pattern of repeating triplets:
- The first triplet is "cca", which repeats twice: cca cca
- The second triplet is "abb", which repeats twice: abb abb
- The third triplet starts with "cbb", which would repeat twice: cbb cbb (the sequence terminates after the first two letters of the second "cbb", i.e., "cb")

Let us double-check the substitution with this pattern:
Group 1 (Length 6): cca cca
Group 2 (Length 6): abb abb
Group 3 (Length 6): cbb cbb (truncated to cbb cb)

Combining these groups gives:
cca + cca + abb + abb + cbb + cb = ccaccaabbabbcbbcb

If we truncate this at 15 letters, we get:
ccaccaabbabbcbb

This matches our substituted sequence perfectly. Thus, the pattern consists of pairs of repeating 3-letter units, progressing as:
1. cca repeated twice (cca cca)
2. abb repeated twice (abb abb)
3. cbb repeated (cbb ...)

Therefore, the letters that fill the gaps to complete this pattern are indeed c, b, b, b.

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