2022 CSAT — Q4

Quant Logical & quantitative reasoning 2.5 marks Easy

What is the value of $X$ in the sequence $20,\ 10,\ 10,\ 15,\ 30,\ 75,\ X$ ?

A 105
B 120
C 150
D 225 Answer

Worked rationale

Look at the ratio of each term to the previous one — the multipliers rise in steps of $0.5$ :

$20 \to 10$ : $\times 0.5$
$10 \to 10$ : $\times 1.0$
$10 \to 15$ : $\times 1.5$
$15 \to 30$ : $\times 2.0$
$30 \to 75$ : $\times 2.5$

The multiplier increases by $0.5$ each time, so the next is $\times 3.0$ :

X = 75 \times 3 = 225.

Answer: (d) 225.

Why the other options miss

A

wrong formula: forces a difference pattern ( $75 + 30 = 105$ ) instead of the multiplicative one the data actually follow.
B

an arithmetic slip: takes the next multiplier as $\times 1.6$ or adds a wrong constant.
C

wrong formula: repeats the previous multiplier ( $\times 2.5$ would give $187.5$ ; doubling gives $150$ ), failing to advance the step.

Specialist insight

When successive differences look erratic ( $-10, 0, +5, +15, +45$ ) but the numbers grow, immediately test the ratio chain. Here the ratios $0.5, 1.0, 1.5, 2.0, 2.5$ form a clean arithmetic progression — the cleanest possible signature. Always read a series both additively and multiplicatively before committing.

The trap, in one line

Ratios rise $0.5, 1, 1.5, 2, 2.5,\dots$ so next is $\times 3$ : $75 \times 3 = 225 \Rightarrow$ (d).

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