CSAT Solved Papers/ 2023/Q75

2023 CSAT — Q75

Quant Logical & quantitative reasoning 2.5 marks Hard

Consider the sequence

A B C _ _ A B C _ D A B B C D _ A B C DA\ B\ C\ \_\ \_\ A\ B\ C\ \_\ D\ A\ B\ B\ C\ D\ \_\ A\ B\ C\ D

that follows a certain pattern. Which one of the following completes the sequence?

  1. A DACB
  2. B CDAB
  3. C DCCA
  4. D DDCA Answer

Worked rationale

Index the 2020 characters and slice into four blocks of length 55 (positions 1155, 661010, 11111515, 16162020):

  • Block 1 (1155): A B C _ _A\ B\ C\ \_\ \_
  • Block 2 (661010): A B C _ DA\ B\ C\ \_\ D
  • Block 3 (11111515): A B B C DA\ B\ B\ C\ D
  • Block 4 (16162020): _ A B C D\_\ A\ B\ C\ D

Each block is the letters A,B,C,DA, B, C, D with one letter doubled, and the doubled letter marches DCBAD \to C \to B \to A across the blocks:

  • Block 1 =ABCDD= ABC\mathbf{DD} (double DD) \Rightarrow blanks @4,5 =D,D= D, D
  • Block 2 =ABCCD= AB\mathbf{CC}D (double CC) \Rightarrow blank @9 =C= C
  • Block 3 =ABBCD= A\mathbf{BB}CD (double BB) — already complete, matches ✓
  • Block 4 =AABCD= \mathbf{AA}BCD (double AA) \Rightarrow blank @16 =A= A

Reading the blanks in order (positions 4,5,9,164, 5, 9, 16): D, D, C, AD,\ D,\ C,\ A.

Answer: (d) DDCA.

Visual solution

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

Hand-drawn worked solution for UPSC 2023 CSAT Q75 — Logical & quantitative reasoning
Tap the drawing to open it full size for the fine detail.

Why the other options miss

  • A
    solved the wrong question: gets the first doubled DD but scrambles the marching order of the remaining doubled letters.
  • B
    counted one too few: starts the doubled-letter march at CC instead of DD, shifting every blank.
  • C
    missed a case: doubles CC twice (blocks 1–2) instead of DD then CC, mis-reading block 1 as ABCCDABCCD.

Specialist insight

20=4×520 = 4 \times 5, so the period is 55, not 44 — each block is ABCDABCD with exactly one doubled letter, and the doubled letter descends D,C,B,AD, C, B, A across the four blocks (the mirror of the 2024 Q24 ascending variant). Verify against the fully-printed block 3 (ABBCDABBCD, double BB) to lock the direction, then the blanks fall out with zero ambiguity. The move that scores: count 2020, slice in 55s, and read the doubled letter off the complete block.

The trap, in one line

Slice into four blocks of 55; each is ABCDABCD with one doubled letter marching DCBAD\to C\to B\to A, so blanks =D,D,C,A== D,D,C,A = (d).

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