CSAT Solved Papers/ 2025/Q36

2025 CSAT — Q36

Quant Logical & quantitative reasoning 2.5 marks Medium

What is $X$ in the sequence $24,\ X,\ 12,\ 18,\ 36,\ 90$ ?

A 18
B 12 Answer
C 9
D 6

Worked rationale

Read the multipliers between known consecutive terms from the right:

12 \to 18 \ (\times 1.5), \quad 18 \to 36 \ (\times 2), \quad 36 \to 90 \ (\times 2.5).

The ratio rises by $0.5$ each step. Extending the same rule backward to the left:

24 \to X \ (\times 0.5), \quad X \to 12 \ (\times 1).

So $X = 24 \times 0.5 = 12$ , and the check $X \times 1 = 12 \times 1 = 12$ ✓ matches the third term. The full multiplier chain is $\times 0.5,\ \times 1,\ \times 1.5,\ \times 2,\ \times 2.5$ .

Answer: (b) 12.

Why the other options miss

A

reached for the wrong rule: assumes an additive pattern (differences) rather than a multiplicative one, interpolating $X$ between $24$ and $12$ as a midpoint-ish $18$ .
C

an arithmetic slip: applies the wrong multiplier ( $24 \times 0.375$ or a mis-stepped ratio), landing on $9$ .
D

reached for the wrong rule: reads the multiplier as $\times 0.25$ ( $24 \to 6$ ), over-shrinking the first step.

Specialist insight

The fastest series-decoding move is to read the operation between adjacent terms rather than the terms themselves: here the clean arithmetic progression of multipliers ( $1.5, 2, 2.5$ , step $0.5$ ) is far more visible than any pattern in $12, 18, 36, 90$ . Extend that progression leftward ( $1.0, 0.5$ ) to recover the hidden term. A CSAT series rewards the student who classifies the rule (additive? multiplicative? second-difference?) in one pass and then runs it both directions — guessing a “nice” interpolated value (a) is the planted trap.

The trap, in one line

The pattern is multiplicative with ratios stepping by $0.5$ ( $\times0.5, \times1, \times1.5, \dots$ ), so $X = 24 \times 0.5 = 12$ — not an additive midpoint.

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