CSAT Solved Papers/ 2025/Q30

2025 CSAT — Q30

Quant Logical & quantitative reasoning 2.5 marks Medium

Consider the sequence AB_CC_A_BCCC_BBC_C\text{AB\_CC\_A\_BCCC\_BBC\_C} that follows a certain pattern. Which one of the following completes the sequence?

  1. A B, C, B, C, A
  2. B A, C, B, C, A
  3. C B, C, B, A, C Answer
  4. D C, B, B, A, C

Worked rationale

The pattern is the repeating block ABBCCC (one A, two B’s, three C’s), laid down end to end. The string AB_CC_A_BCCC_BBC_C\text{AB\_CC\_A\_BCCC\_BBC\_C} has exactly 1818 characters — three full blocks of six — so the tiling is forced. Mark off the blocks and read which letter each blank must carry.

Write the string with the five blanks numbered:

A B [1] C C [2]block 1 [3] B C C Cblock 2 [4] B B C [5] Cblock 3\underbrace{\text{A B }[1]\text{ C C }[2]}_{\text{block 1}}\ \underbrace{\text{A }[3]\text{ B C C C}}_{\text{block 2}}\ \underbrace{[4]\text{ B B C }[5]\text{ C}}_{\text{block 3}}
  • Block 1 A B _ C C _\text{A B \_ C C \_} must read A B B C C C \Rightarrow blank 1=B1=\text{B}, blank 2=C2=\text{C}.
  • Block 2 A _ B C C C\text{A \_ B C C C} must read A B B C C C \Rightarrow blank 3=B3=\text{B}.
  • Block 3 _ B B C _ C\text{\_ B B C \_ C} is the third ABBCCC block (it starts at character 13=2×6+113 = 2\times6+1, exactly a block boundary), so it must read A B B C C C \Rightarrow blank 4=A4=\text{A} (the block-opening A), blank 5=C5=\text{C}.

Reading the blanks in order: B, C, B, A, C\text{B, C, B, A, C}.

Answer: (c) B, C, B, A, C.

Visual solution

The same solve, worked by hand — read it, then trace it.

Hand-drawn worked solution for UPSC 2025 CSAT Q30 — Logical & quantitative reasoning
Tap the drawing to open it full size for the fine detail.

Why the other options miss

  • A
    off by one: the engineered near-miss — fills blanks 1133 correctly but swaps the last two (puts C\text{C} at the third block’s opening and A\text{A} at its interior), displacing the block-opening A by one position and corrupting the boundary at character 1313.
  • B
    solved the wrong question: mis-starts block 1 as AA…, breaking the one-A-per-block rule.
  • D
    solved the wrong question: abandons the ABBCCC block entirely, reading a different (inconsistent) grouping.

Specialist insight

Letter-block completion is won by finding the repeating unit first, then treating every blank as “which letter finishes this block.” The unit here is ABBCCC (counts 1,2,31,2,3); once you see it, blanks 1133 are forced immediately. The decisive check is the third block’s opening: character 1313 is a block boundary (2×6+12\times6+1), so it must be the block-opening A — this is exactly what separates the answer (c)\text{(c)} from the near-miss (a)\text{(a)}, which swaps the last two fills. The engineered distractors each break a different structural rule — the one-A-per-block count, the block boundary, or the unit itself — so verifying that your fill reproduces a clean ABBCCC | ABBCCC | ABBCCC tiling is the discipline that scores.

The trap, in one line

The 1818-character string is three ABBCCC blocks; the third block opens at character 1313 (a boundary), forcing an A there — completing the blanks gives B, C, B, A, C.

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