CSAT Solved Papers/ 2025/Q60

2025 CSAT — Q60

Quant Logical & quantitative reasoning 2.5 marks Easy

What is $X$ in the sequence $1, 3, 6, 11, 18, X, 42$ ?

A 26
B 27
C 29 Answer
D 30

Worked rationale

Take first differences:

3-1=2,\quad 6-3=3,\quad 11-6=5,\quad 18-11=7,\quad X-18=?,\quad 42-X=?

The differences so far are $2, 3, 5, 7$ — the primes in order. The next two primes are $11$ and $13$ :

X = 18 + 11 = 29,\qquad 42 - 29 = 13 \checkmark.

The closing check $42 - 29 = 13$ (the next prime) confirms the pattern.

Answer: (c) 29.

Why the other options miss

A

reached for the wrong rule: adds a difference of $8$ (continues $2,3,5,7$ as if $+1$ each), not recognising the gaps as primes.
B

an arithmetic slip: takes the next difference as $9$ ( $18+9$ ), a near-prime slip.
D

off by one: uses difference $12$ , overshooting the prime $11$ .

Specialist insight

The series is innocuous once you read the first differences as the prime sequence $2,3,5,7,11,13$ . The discipline that scores: don’t just match $X$ to one difference — use the final given term ( $42$ ) as a constraint, since $42 - X$ must equal the next prime $13$ . That two-sided check ( $18+11=29$ and $29+13=42$ ) rules out the off-by-one decoys instantly and confirms the pattern with certainty.

The trap, in one line

First differences are the primes $2,3,5,7,11,13$ : $X = 18+11 = 29$ , and $42-29 = 13$ confirms it.

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