CSAT Solved Papers/ 2022/Q50

2022 CSAT — Q50

Quant Data sufficiency 2.5 marks Hard

Six lectures $A, B, C, D, E$ and $F$ , each of one hour duration, are scheduled between $8{:}00$ a.m. and $2{:}00$ p.m. Consider the Question and two Statements given below:

Question: Which lecture is in the third period?

Statement-1: Lecture $F$ is preceded by $A$ and followed by $C$ .

Statement-2: There is no lecture after lecture $B$ .

Which one of the following is correct in respect of the Question and the Statements?

A Statement-1 alone is sufficient to answer the Question
B Statement-2 alone is sufficient to answer the Question
C Both Statement-1 and Statement-2 are sufficient to answer the Question
D Both Statement-1 and Statement-2 are not sufficient to answer the Question Answer

Worked rationale

Six one-hour periods fill $8{:}00$ – $14{:}00$ , so the periods are $1$ through $6$ .

Statement-1 alone ( $A, F, C$ consecutive in that order): the block $A\text{-}F\text{-}C$ can sit at periods $1$ – $3$ , $2$ – $4$ , $3$ – $5$ or $4$ – $6$ , so period $3$ could be $C$ , $F$ , $A$ or a free lecture. Insufficient.

Statement-2 alone ( $B$ is last, period $6$ ): says nothing about period $3$ . Insufficient.

Both together: $B$ occupies period $6$ , so the $A\text{-}F\text{-}C$ block lies within periods $1$ – $5$ . The block can still be placed at periods $1$ – $3$ , $2$ – $4$ , or $3$ – $5$ :

block at	period 3 is
$1$ – $3$	$C$
$2$ – $4$	$F$
$3$ – $5$	$A$

Three different answers survive (lectures $D, E$ are unconstrained), so period $3$ is still not determined.

Answer: (d) Both Statement-1 and Statement-2 are not sufficient.

Visual solution

The same solve, worked by hand — read it, then trace it.

Hand-drawn worked solution for UPSC 2022 CSAT Q50 — Data sufficiency — Tap the drawing to open it full size for the fine detail.

Why the other options miss

A

claims more than one statement gives: assumes the $A\text{-}F\text{-}C$ block must start at period $1$ , forcing period $3 = C$ .
B

over-trusts one statement: thinks fixing the last lecture pins the third.
C

stops after one arrangement: pins $B$ at $6$ but enumerates only one block position, missing that $A\text{-}F\text{-}C$ still floats across periods $1$ – $5$ .

Specialist insight

Counting degrees of freedom is the move: a $3$ -block plus a pinned last slot still leaves the block three landing positions inside periods $1$ – $5$ , and $D, E$ float freely. The examiner’s trap is the tidy reading “block at the front $\Rightarrow$ $C$ in period $3$ ” — but nothing forces the block to the front, so the answer is undecidable even jointly.

The trap, in one line

With $B$ at period $6$ , the $A\text{-}F\text{-}C$ block still fits periods $1$ – $3$ , $2$ – $4$ or $3$ – $5$ $\Rightarrow$ period $3$ unfixed $=$ (d).

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