CSAT Solved Papers/ 2021/Q27

2021 CSAT — Q27

Quant Logical & quantitative reasoning 2.5 marks Medium

Following is a matrix of certain entries. The entries follow a certain trend row-wise. Choose the missing entry (?)(?) accordingly.

7B7B10A10A3C3C
3C3C9B9B6A6A
10A10A13C13C??
  1. A 9B
  2. B 3A
  3. C 3B Answer
  4. D 3C

Worked rationale

Treat the number and the letter as two independent patterns.

Numbers (row-wise rule): the third entry is the absolute difference of the first two.

  • Row 1: ∣7−10∣=3|7-10| = 3 ✓ (third number is 33).
  • Row 2: ∣3−9∣=6|3-9| = 6 ✓.
  • Row 3: ∣10−13∣=3|10-13| = 3, so the missing number is 33.

Letters (column cycle): read each column down.

  • Col 1: B,C,AB,C,A. Col 2: A,B,CA,B,C. Col 3: C,A,?C,A,? — the cycle C→A→BC\to A\to B gives BB.

So the missing entry is 3B3B.

Answer: (c) 3B.

Why the other options miss

  • A
    wrong number rule: gets the letter (BB) but uses a sum or other rule for the number instead of the absolute difference ∣10−13∣=3|10-13|=3.
  • B
    wrong letter: correct number, but repeats the column-3 letter AA rather than advancing the cycle.
  • D
    recycles a letter: correct number, but reuses CC (the column-3 top entry) instead of the next letter BB.

Specialist insight

Mixed letter–number matrices reward separating the two channels immediately. The numbers obey ∣a−b∣|a-b| row-wise; the letters cycle A→B→C→AA\to B\to C\to A down each column. Verify the numeric rule on the two complete rows (3,63,6) before applying it, and read the letter cycle column-wise (the rows are not where the letter pattern lives). Doing both channels independently kills the temptation to pattern-match the whole cell at once.

The trap, in one line

Number =∣10−13∣=3=|10-13|=3; column-3 letters C,A,BC,A,\mathbf{B} ⇒3B⇒\Rightarrow 3B \Rightarrow (c).

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