Change in Average Scores

CAT 2017 Slot 1 · QA · Medium · Averages

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A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is:

  1. A.

    9.5

  2. B.

    10

  3. C.

    4.5

  4. D.

    6

Answer

A

Explanation

Total change in class score = 50×2=10050 \times 2 = 100. Total change in girls' score = 30×(−3)=−9030 \times (-3) = -90. Total change in boys' score = 100−(−90)=190100 - (-90) = 190. Increase in average score of boys = 19020=9.5\frac{190}{20} = 9.5.

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