CSAT Solved Papers/ 2022/Q70

2022 CSAT — Q70

Quant Data interpretation 2.5 marks Easy

A pie chart gives the expenditure on five different items A,B,C,DA, B, C, D and EE in a household. If B,C,DB, C, D and EE correspond to 90∘90^{\circ}, 50∘50^{\circ}, 45∘45^{\circ} and 75∘75^{\circ} respectively, then what is the percentage of expenditure on item AA?

  1. A 1129\dfrac{112}{9}
  2. B 1256\dfrac{125}{6}
  3. C 1559\dfrac{155}{9}
  4. D 2509\dfrac{250}{9} Answer

Worked rationale

The five sectors fill 360∘360^{\circ}. The angle of AA is the residual:

A=360−(90+50+45+75)=360−260=100∘.A = 360 - (90 + 50 + 45 + 75) = 360 - 260 = 100^{\circ}.

Convert the angle to a percentage of the whole:

100360×100%=10000360%=2509%.\frac{100}{360}\times 100\% = \frac{10000}{360}\% = \frac{250}{9}\%.

Answer: (d) 2509\dfrac{250}{9}.

Visual solution

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

Hand-drawn worked solution for UPSC 2022 CSAT Q70 — Data interpretation
Tap the drawing to open it full size for the fine detail.

Why the other options miss

  • A
    an arithmetic slip: uses a wrong residual angle (e.g. 45∘45^{\circ} left over) before converting.
  • B
    an arithmetic slip: divides by 300300 or mis-sums the four given angles.
  • C
    an arithmetic slip: takes the residual angle as 62∘62^{\circ} or mishandles the ×100\times 100.

Specialist insight

Two clean steps: residual angle (360−260=100∘360 - 260 = 100^{\circ}) then the angle-to-percent map θ360×100=5θ18\dfrac{\theta}{360} \times 100 = \dfrac{5\theta}{18}. For θ=100\theta = 100 this is 50018=2509\dfrac{500}{18} = \dfrac{250}{9}. Keep the answer as an exact fraction — the distractors are all near-miss fractions from a wrong residual or a wrong divisor.

The trap, in one line

A=360−260=100∘A = 360 - 260 = 100^{\circ}; 100360×100=2509%\dfrac{100}{360}\times 100 = \dfrac{250}{9}\% ⇒\Rightarrow (d).

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