CSAT Solved Papers/ 2021/Q39

2021 CSAT — Q39

Quant Data sufficiency 2.5 marks Hard

Consider two Statements and a Question:

Statement-1: Each of $A$ and $D$ is heavier than each of $B$ , $E$ and $F$ , but none of them is the heaviest.

Statement-2: $A$ is heavier than $D$ , but is lighter than $C$ .

Question: Who is the heaviest among $A$ , $B$ , $C$ , $D$ and $E$ ?

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

A Statement-1 alone is sufficient to answer the Question Answer
B Statement-2 alone is sufficient to answer the Question
C Both Statement-1 and Statement-2 are required to answer the Question
D Neither Statement-1 alone nor Statement-2 alone is sufficient to answer the Question

Worked rationale

There are six people $A,B,C,D,E,F$ ; the question asks for the heaviest among the five $A,B,C,D,E$ .

Statement-1 alone: $A$ and $D$ are each heavier than $B,E,F$ , and neither $A$ nor $D$ is the heaviest. So the heaviest overall is none of $A,D$ (excluded by the clause) and none of $B,E,F$ (each lighter than $A,D$ ). The only remaining person is $C$ , so $C$ is the heaviest — and $C$ is among the five asked about. Determines the answer ( $C$ ). Sufficient.

Statement-2 alone: $C > A > D$ , but nothing relates $C$ to $B$ or $E$ . It is possible $C$ is heaviest, but also $B$ or $E$ could exceed $C$ . Not sufficient.

Answer: (a) Statement-1 alone is sufficient.

Visual solution

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

Hand-drawn worked solution for UPSC 2021 CSAT Q39 — Data sufficiency — Tap the drawing to open it full size for the fine detail.

Why the other options miss

B

thought it was enough when it wasn’t: reads $C>A>D$ as making $C$ heaviest, ignoring that $B,E$ are unranked against $C$ .
C

thought both were needed when S1 alone suffices: thinks S1 needs S2’s ” $C$ heaviest” to finish, missing that S1 already forces $C$ by elimination.
D

missed a case: overlooks the eliminating clause “none of them is the heaviest,” which closes S1’s deduction.

Specialist insight

Statement-1 hides a complete deduction inside a clause: $A,D$ beat $B,E,F$ and are not the heaviest, so by elimination the heaviest must be $C$ — no second statement needed. The killer is reading the whole sentence: the phrase “but none of them is the heaviest” is not decoration, it removes $A,D$ from contention and leaves exactly one candidate. Statement-2 looks decisive ( $C>A>D$ ) but leaves $B,E$ wild, so it cannot crown $C$ . Always test a statement for counterexamples among the unmentioned people.

The trap, in one line

S1: $A,D$ beat $B,E,F$ and aren't heaviest $\Rightarrow$ only $C$ left $=$ heaviest; S2 leaves $B,E$ unranked $\Rightarrow$ (a).

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