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The average of five numbers x1 , x2 , x3 , x4 , and x5 is S and the a
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14 Oct 2024, 00:12
14 Oct 2024, 00:12
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The average of five numbers \(x_1, x_2, x_3, x_4,\) and \(x_5\) is S and the average of three other numbers \(y_1, y_2, y_3\) is R. What is the average of the numbers \(x_1, x_2, x_3,x_4, x_5, y_1, y_2\) and \(y_3\)?
A. \(\frac{5S+3R}{8}\)
B. \(\frac{S}{8}\)
C. \(\frac{R}{8}\)
D. \(\frac{S+R}{8}\)
E. \(\frac{3S+5R}{8}\)
A. \(\frac{5S+3R}{8}\)
B. \(\frac{S}{8}\)
C. \(\frac{R}{8}\)
D. \(\frac{S+R}{8}\)
E. \(\frac{3S+5R}{8}\)
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The average of five numbers x1 , x2 , x3 , x4 , and x5 is S and the a
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16 Dec 2024, 16:06
16 Dec 2024, 16:06
Expert Reply
As the average of 5 numbers $\(x_1, x_2, x_3, x_4 \& x_5\)$ is $\(S\)$, we get their sum as $\(\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3+\mathrm{x}_4+\mathrm{x}_5=5 \mathrm{~S)\)$
Similarly as the average of 3 numbers $\(y_1, y_2\) & \(y_3\)$ is $\(R\)$, we get their sum as
$$
\(y_1+y_2+y_3=3 R\)
$$
Finally the combined average of $\(x_1, x_2, x_3, x_4, x_5\) & \(\quad y_1, y_2, y_3\)$ is $\(\frac{\left(x_1+x_2+x_3+x_4+x_5\right)+\left(y_1+y_2+y_3\right)}{5+3}=\frac{5 S+3 R}{8}\)$
Hence the answer is (A).
Similarly as the average of 3 numbers $\(y_1, y_2\) & \(y_3\)$ is $\(R\)$, we get their sum as
$$
\(y_1+y_2+y_3=3 R\)
$$
Finally the combined average of $\(x_1, x_2, x_3, x_4, x_5\) & \(\quad y_1, y_2, y_3\)$ is $\(\frac{\left(x_1+x_2+x_3+x_4+x_5\right)+\left(y_1+y_2+y_3\right)}{5+3}=\frac{5 S+3 R}{8}\)$
Hence the answer is (A).
gmatclubot
The average of five numbers x1 , x2 , x3 , x4 , and x5 is S and the a [#permalink]
16 Dec 2024, 16:06
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