Evaluating an overarching average based on intersecting sub-group averages
Question
The average weight of A, B, C is 40 kg, the average weight of B, D, E is 42 kg and the weight of F is equal to that of B. What is the average weight of A, B, C, D, E and F?
Options
40.5 kg
40.8 kg
41 kg
Cannot be determined as data is inadequate
Explanation
Convert the average statements into absolute sum totals: Equation 1: A + B + C = 3 × 40 = 120 kg. Equation 2: B + D + E = 3 × 42 = 126 kg. Equation 3: F = B.
The question asks for the master average: A + B + C + D + E + F/6. Isolate the sum of (D + E) from Equation 2: D + E = 126 - B.
Substitute the known blocks into the master sum equation: Total = (A + B + C) + (D + E) + F Total = 120 + (126 - B) + B Notice that the overlapping variable ⟨MATH⟩B⟨/MATH⟩ perfectly cancels itself out: Total = 120 + 126 = 246 kg.
Calculate the final 6-person average: 246/6 = 41 kg.
Answer: (c).
Question details
Year
2022
Paper
CSAT
Question
Q80
Section
Numerical Ability
Sub-topic
Averages
Type
Factual single
Difficulty
Medium
Source hint
Average weight A, B, C and B, D, E
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