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Runs Scored Pie Chart Analysis

XAT 2012 · Quantitative Ability & Data Interpretation · Medium · Data Interpretation

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Passage / data set

The following pie chart shows the percentage distribution of runs scored by a batsman in a test innings.

  • 1s: 36.6%
  • 2s: 12.42%
  • 3s: 3.92%
  • 4s: 43.14%
  • 6s: 3.92%

Question 1 of 2

If the batsman has scored a total of 306 runs, how many 4s and 6s did he hit?

  1. A.

    31 and 3 respectively

  2. B.

    32 and 2 respectively

  3. C.

    32 and 3 respectively

  4. D.

    33 and 1 respectively

  5. E.

    33 and 2 respectively

Answer

E

Explanation

Runs from 4s = 43.14%×306≈13243.14\% \times 306 \approx 132 runs   ⟹  132/4=33\implies 132 / 4 = 33 four-runs. Runs from 6s = 3.92%×306≈123.92\% \times 306 \approx 12 runs   ⟹  12/6=2\implies 12 / 6 = 2 six-runs.

Question 2 of 2

If 5 of the dot balls had been hit for 4s, and if two of the shots for which the batsman scored 3 runs each had fetched him one run instead, what would have been the central angle of the sector corresponding to the percentage of runs scored in 4s? {Use data from the previous question}

  1. A.

    160

  2. B.

    163

  3. C.

    165

  4. D.

    167

  5. E.

    170

Answer

E

Explanation

New total runs = 306+(5×4)−2×(3−1)=306+20−4=322306 + (5 \times 4) - 2 \times (3 - 1) = 306 + 20 - 4 = 322 runs. New runs in 4s = 132+20=152132 + 20 = 152 runs. Central angle = 152322×360∘≈169.93∘≈170∘\frac{152}{322} \times 360^\circ \approx 169.93^\circ \approx 170^\circ.

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