CSAT Solved Papers/ 2022/Q75

2022 CSAT — Q75

Quant Logical & quantitative reasoning 2.5 marks Medium

What is the value of $X$ in the sequence $2,\ 12,\ 36,\ 80,\ 150,\ X$ ?

A 248
B 252 Answer
C 258
D 262

Worked rationale

Test the pattern $n^2(n+1)$ :

1^2\cdot 2 = 2,\quad 2^2\cdot 3 = 12,\quad 3^2\cdot 4 = 36,\quad 4^2\cdot 5 = 80,\quad 5^2\cdot 6 = 150.

All five match, so the next term ( $n = 6$ ) is

6^2 \cdot 7 = 36 \times 7 = 252.

Answer: (b) 252.

Why the other options miss

A

an arithmetic slip: extrapolates a difference pattern ( $+98$ ) instead of the formula.
C

wrong formula: uses $n(n+1)^2$ or $n^3 + n$ and mis-evaluates near the true value.
D

an arithmetic slip: adds a wrong constant to $150$ from a misread second-difference.

Specialist insight

The terms $2, 12, 36, 80, 150$ are $n^2(n+1)$ — recognisable because each is $n^2$ times the next integer ( $1{\cdot}2, 4{\cdot}3, 9{\cdot}4, 16{\cdot}5, 25{\cdot}6$ ). Spotting a clean product form beats chasing differences ( $10, 24, 44, 70$ — whose own differences are $14, 20, 26$ , a cubic signature). When differences are themselves growing linearly twice over, look for a degree- $3$ closed form.

The trap, in one line

Terms are $n^2(n+1)$ ; next is $6^2\cdot 7 = 252 \Rightarrow$ (b).

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