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Average Height of Toddlers

CAT 2017 Slot 2 · Quantitative Ability · Easy · Averages

This is an easy Quantitative Ability question from the CAT 2017 Slot 2 paper. It tests Averages. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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The average height of 22 toddlers increases by 2 inches when two of them leave this group. If the average height of these two toddlers is one-third the average height of the original 22, then the average height, in inches, of the remaining 20 toddlers is

  1. A.

    30

  2. B.

    28

  3. C.

    32

  4. D.

    26

Answer

C

Explanation

Let the original average height of 22 toddlers be AA. Total height of 22 toddlers = 22A22A.

Average height of the 2 toddlers who left = A3\frac{A}{3}. Sum of heights of these 2 toddlers = 2×A3=2A32 \times \frac{A}{3} = \frac{2A}{3}.

Sum of heights of remaining 20 toddlers = 22A−2A3=64A322A - \frac{2A}{3} = \frac{64A}{3}.

New average height of 20 toddlers = A+2A + 2. Total height of remaining 20 toddlers = 20(A+2)=20A+4020(A + 2) = 20A + 40.

Equating both sums: 64A3=20A+40  ⟹  64A=60A+120  ⟹  4A=120  ⟹  A=30\frac{64A}{3} = 20A + 40 \implies 64A = 60A + 120 \implies 4A = 120 \implies A = 30

Average height of the remaining 20 toddlers = A+2=30+2=32A + 2 = 30 + 2 = 32 inches.

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