Correct Option
The given sequence is c_accaa_aa_bc_b. To identify the missing letters, a recurring pattern within the sequence must be determined.
Upon analysis, the sequence can be segmented into repeating blocks of five letters, each adhering to the structure XXYXX, where X and Y are specific letters that cycle through the blocks:
- The first segment,
c_acc, when filled with 'c', becomesccacc. Here, X='c' and Y='a'. - The second segment,
aa_aa, when filled with 'b', becomesaabaa. Here, X='a' and Y='b'. - The third segment,
_bc_b, when filled with 'b' and 'b', becomesbbcbb. Here, X='b' and Y='c'.
This pattern consistently applies across the entire sequence. Therefore, the letters that correctly fill the gaps are 'c', 'b', 'b', 'b', which corresponds to the option 'cbbb'. The complete sequence is ccaccaabaabbcbb.
Incorrect Options
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Option 1 (abba): If 'abba' is used to fill the gaps, the sequence becomes
ccaccaaabaabbab. This arrangement disrupts the identified XXYXX pattern, particularly in the third segment, which would becomeabbabinstead of the expectedbbcbb. -
Option 3 (bbbb): Substituting 'bbbb' into the gaps results in
cbaccaababbbcbb. This does not conform to the established XXYXX pattern. For instance, the first segmentcbaccdeviates from the required structure where the first and second letters should be identical. -
Option 4 (cccc): Using 'cccc' for the gaps yields
ccaccaacaaccbcc. This option also fails to maintain the consistent XXYXX pattern throughout the sequence. For example, the second segmentaacaadoes not fit the pattern where the first and second letters should be identical (i.e., 'aa').