CSAT Solved Papers/ 2021/Q38

2021 CSAT — Q38

Quant Data sufficiency 2.5 marks Medium

Consider two Statements and a Question:

Statement-1: Priya is 44 ranks below Seema and is 3131st from the bottom.

Statement-2: Ena is 22 ranks above Seema and is 3737th from the bottom.

Question: What is Seema’s rank from the top in the class of 4040 students?

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

  1. A Statement-1 alone is not sufficient to answer the Question
  2. B Statement-2 alone is not sufficient to answer the Question
  3. C Either Statement-1 alone or Statement-2 alone is sufficient to answer the Question Answer
  4. D Both Statement-1 and Statement-2 are required to answer the Question

Worked rationale

Use rank-from-top =41−(rank-from-bottom)= 41 - (\text{rank-from-bottom}) in a class of 4040.

Statement-1 alone: Priya is 3131st from the bottom ⇒\Rightarrow 41−31=1041-31 = 10th from the top. Priya is 44 ranks below Seema, so Seema is 44 ranks higher: 10−4=610 - 4 = 6th from the top. Determines Seema =6=6th. Sufficient.

Statement-2 alone: Ena is 3737th from the bottom ⇒\Rightarrow 41−37=441-37 = 4th from the top. Ena is 22 ranks above Seema, so Seema is 22 ranks lower: 4+2=64 + 2 = 6th from the top. Determines Seema =6=6th. Sufficient.

Each statement alone pins Seema at the 66th rank from the top.

Answer: (c) Either Statement-1 alone or Statement-2 alone is sufficient.

Visual solution

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

Hand-drawn worked solution for UPSC 2021 CSAT Q38 — Data sufficiency
Tap the drawing to open it full size for the fine detail.

Why the other options miss

  • A
    thought it wasn’t enough when it was: denies S1’s sufficiency, perhaps mishandling the bottom-to-top conversion 41−3141-31.
  • B
    thought it wasn’t enough when it was: denies S2’s sufficiency, often by reversing “above/below.”
  • D
    thought neither alone was enough when each was: assumes neither alone fixes Seema, missing that each statement independently locks her position.

Specialist insight

The lever is the conversion rank-from-top ++ rank-from-bottom =n+1=41= n+1 = 41. Each statement gives one person’s absolute position plus Seema’s offset, which is enough on its own — so the correct DS verdict is “either alone.” The recurring slip is the direction of “above/below”: below in rank means a larger number from the top, so Priya at 1010th ⇒\Rightarrow Seema at 66th. Convert to a single reference (rank from top) before applying offsets.

The trap, in one line

Both routes give Seema =6=6th from top (41−31−441-31-4 and 41−37+241-37+2), so either alone suffices ⇒\Rightarrow (c).

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