2025 CSAT — Q8

Quant Logical & quantitative reasoning 2.5 marks Medium

What comes at $X$ and $Y$ respectively in the following sequence?

January, January, December, October, $X$ , March, October, $Y$ , September

A July, May
B July, April Answer
C June, May
D June, April

Worked rationale

Number the months $1$ – $12$ (Jan $=1$ , …, Dec $=12$ ) and read the sequence as a running back-step that grows by one each time, cycling mod $12$ .

Position	1	2	3	4	5	6	7	8	9
Month	Jan	Jan	Dec	Oct	$X$	Mar	Oct	$Y$	Sep
Value	1	1	12	10	?	3	10	?	9
Step	—	$-0$	$-1$	$-2$	$-3$	$-4$	$-5$	$-6$	$-7$

Apply the steps (subtract, wrapping mod $12$ so $0 \to 12$ ):

1 \xrightarrow{-0} 1 \xrightarrow{-1} 12 \xrightarrow{-2} 10 \xrightarrow{-3} 7 \xrightarrow{-4} 3 \xrightarrow{-5} 10 \xrightarrow{-6} 4 \xrightarrow{-7} 9.

$X$ (position $5$ ) $= 10 - 3 = 7 =$ July.
$Y$ (position $8$ ) $= 10 - 6 = 4 =$ April.

Every given term is reproduced (Mar $=3$ ✓, Oct $=10$ ✓ at position $7$ via $3-5 = -2 \equiv 10$ , Sep $=9$ ✓), so the rule is confirmed.

Answer: (b) July, April.

Why the other options miss

A

an arithmetic slip: gets $X=$ July correctly but mis-steps the $Y$ back-step ( $-6$ ), landing on May ( $5$ ) instead of April ( $4$ ).
C

off by one: uses back-steps $-4,-7$ (or starts the step count at $-1$ ), shifting both answers one month early to June/May.
D

off by one: correct $Y =$ April but an off-by-one on $X$ ‘s step gives June instead of July.

Specialist insight

The trap is assuming a constant step (e.g. always $-2$ ) — that reproduces the first few terms then fails. The governing rule is a cumulative back-step $-0,-1,-2,-3,\dots$ with mod- $12$ wrap, which is verified only by checking that the known later terms (March, October, September) also fall out. Always validate a guessed rule against every fixed term before committing; here the wrap $3 \to 10$ (October at position $7$ ) is the checkpoint that distinguishes the right pattern from a near-miss.

The trap, in one line

The back-step is cumulative ( $-0,-1,-2,\dots$ mod $12$ ), not constant: $X = 10-3 = 7$ (July), $Y = 10-6 = 4$ (April).

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