CSAT Solved Papers/ 2021/Q74

2021 CSAT — Q74

Quant Arithmetic & numeracy 2.5 marks Easy

A pie diagram shows the percentage distribution of proteins, water and other dry elements in the human body. Given that proteins correspond to 16%16\% and water corresponds to 70%70\%. If both proteins and the other dry elements correspond to p%p\%, then what is the central angle of the sector representing pp on the pie diagram?

  1. A 54°
  2. B 96°
  3. C 108° Answer
  4. D 120°

Worked rationale

The three parts sum to 100%100\%: proteins 16%16\%, water 70%70\%, so other dry elements =100−16−70=14%= 100 - 16 - 70 = 14\%.

“Both proteins and other dry elements” =16+14=30%= 16 + 14 = 30\%, so p=30p = 30. The central angle of a sector is its percentage of 360∘360^\circ:

angle=30%×360∘=0.30×360=108∘.\text{angle} = 30\% \times 360^\circ = 0.30 \times 360 = 108^\circ.

Answer: (c) 108°.

Why the other options miss

  • A
    an arithmetic slip: takes p=15%p = 15\% (halves it, or uses only the 14%14\% then mishandles) before converting.
  • B
    bundled the wrong slices: uses proteins alone, or water’s complement, instead of proteins ++ other dry.
  • D
    rounded the percentage: treats pp as 13\tfrac13 of 100100 (120∘=13×360120^\circ = \tfrac13\times 360) instead of 30%30\%.

Specialist insight

Two clean steps: get the missing slice by complement (100−16−70=14100 - 16 - 70 = 14), then convert the asked percentage to an angle via ×3.6\times 3.6 (since 1%=3.6∘1\% = 3.6^\circ). Here p=16+14=30%p = 16 + 14 = 30\% and 30×3.6=108∘30 \times 3.6 = 108^\circ. The trap is misreading what "pp" bundles — it’s proteins plus other dry elements (everything that is not water), which is also just 100−70=30%100 - 70 = 30\%, a useful cross-check.

The trap, in one line

Other dry =14%=14\%, so p=16+14=30%p = 16+14 = 30\%, angle =30×3.6=108∘⇒= 30\times 3.6 = 108^\circ \Rightarrow (c).

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