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

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', becomes ccacc. Here, X='c' and Y='a'.
• The second segment, aa_aa, when filled with 'b', becomes aabaa. Here, X='a' and Y='b'.
• The third segment, _bc_b, when filled with 'b' and 'b', becomes bbcbb. 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

• 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 become abbab instead of the expected bbcbb.

• Option 3 (bbbb): Substituting 'bbbb' into the gaps results in cbaccaababbbcbb. This does not conform to the established XXYXX pattern. For instance, the first segment cbacc deviates 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 segment aacaa does not fit the pattern where the first and second letters should be identical (i.e., 'aa').