CSAT Solved Papers/ 2024/Q28

2024 CSAT — Q28

Quant Arithmetic & numeracy 2.5 marks Medium

In an examination, 80%80\% of students passed in English, 70%70\% of students passed in Hindi and 15%15\% failed in both the subjects. What is the percentage of students who failed in only one subject?

  1. A 15%15\%
  2. B 20%20\% Answer
  3. C 25%25\%
  4. D 35%35\%

Worked rationale

Work in the fail world, since the question asks about failing. Failing percentages:

failed English=100−80=20%,failed Hindi=100−70=30%.\text{failed English} = 100 - 80 = 20\%,\qquad \text{failed Hindi} = 100 - 70 = 30\%.

Failed in both =15%= 15\%. Peel the overlap out of each:

failed only English=20−15=5%,failed only Hindi=30−15=15%.\text{failed only English} = 20 - 15 = 5\%,\qquad \text{failed only Hindi} = 30 - 15 = 15\%.

“Failed in only one subject” =5+15=20%.= 5 + 15 = 20\%.

Answer: (b) 20%20\%.

Visual solution

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

Hand-drawn worked solution for UPSC 2024 CSAT Q28 — Arithmetic & numeracy
Tap the drawing to open it full size for the fine detail.

Why the other options miss

  • A
    solved the wrong region: reports the “failed in both” figure, confusing “both” with “only one”.
  • C
    an arithmetic slip: computes total failures 20+30−15=3520+30-15 = 35 then mis-subtracts, or adds only-English to both (5+15+55+15+5 type slip).
  • D
    answered the neighbouring quantity: gives “failed in at least one subject” (20+30−15=35%20+30-15=35\%) instead of “failed in only one” — a related but different region.

Specialist insight

Translate to the complement first: pass-percentages become fail-percentages (20%20\%, 30%30\%), and the problem is now a clean two-set Venn with a known intersection (15%15\%). “Only one” is the symmetric difference =(failed E)+(failed H)−2(failed both)=20+30−2(15)=20%= (\text{failed E}) + (\text{failed H}) - 2(\text{failed both}) = 20+30-2(15) = 20\% — the −2×-2\times overlap is the line that separates (b) from the “at least one” trap (d), which subtracts the overlap only once. Know which region the question names: only one ≠\ne at least one.

The trap, in one line

"Only one subject" is the symmetric difference (overlap removed twice): 20+30−2(15)=20%20+30-2(15)=20\% — not "at least one" (35%35\%) nor "both" (15%15\%). <!-- NEW TEMPLATE: ar-two-set-overlap-percentage — anchored to 2024 Q28; fold into taxonomy T1. -->

← All 2024 CSAT questions