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Average of Combined Sets

CMAT 2023 · Quantitative Techniques & Data Interpretation · Medium · Averages

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Average of a, b and c is 11; average of c, d and e is 17; average of e and f is 22 and average of e and c is 17. What is the average of a, b, c, d, e and f?

  1. A.

    152315\frac{2}{3}

  2. B.

    181218\frac{1}{2}

  3. C.

    161216\frac{1}{2}

  4. D.

    162316\frac{2}{3}

Answer

A

Explanation

Given:

  1. a+b+c=33a + b + c = 33
  2. c+d+e=51c + d + e = 51
  3. e+f=44e + f = 44
  4. e+c=34e + c = 34

Sum of all six variables (a+b+c+d+e+f)=(a+b+c)+(c+d+e)+(e+f)−(e+c)(a + b + c + d + e + f) = (a + b + c) + (c + d + e) + (e + f) - (e + c) =33+51+44−34=94= 33 + 51 + 44 - 34 = 94

Average =946=473=1523= \frac{94}{6} = \frac{47}{3} = 15\frac{2}{3}.

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