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What is the average (arithmetic mean) of w, x, y, z, and 10?

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What is the average (arithmetic mean) of w, x, y, z, and 10?

by VJesus12 » Thu Jun 14, 2018 1:07 am

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What is the average (arithmetic mean) of w, x, y, z, and 10?

(1) The average (arithmetic mean) of w and y is 7.5; the average (arithmetic mean) of x and z is 2.5
(2) -(-z - y -x - w) = 20

The OA is the option D.

Could anyone explain how to prove that each statement is sufficient to me? Thanks in advance.
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by Vincen » Thu Jun 14, 2018 2:46 am

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Hello Vjesus12.

Here, we have to find the value of $$\frac{w+x+y+z+10}{5}=\frac{w+x+y+z}{5}+2\ .$$

First statement
(1) The average (arithmetic mean) of w and y is 7.5; the average (arithmetic mean) of x and z is 2.5
Now, we know that $$\frac{w+y}{2}=7.5\ \ \ \ \ \ \ ;\ \ \ \ \ \ \frac{x+z}{2}=2.5\ \ $$ $$w+y=15\ \ \ \ \ \ \ ;\ \ \ \ \ \ x+z=5\ \ $$ Then $$\frac{w+x+y+z}{5}+2=\frac{\left(w+y\right)+\left(x+z\right)}{5}+2=\frac{15+5}{2}+2=12.$$ Therefore, this statement is sufficient.

Second statement
(2) -(-z - y -x - w) = 20
Now, we know that $$-\left(-z-y-x-w\right)=20\ \ \Rightarrow\ \ \ z+y+x+w=20.$$ Then we get $$\frac{w+x+y+z}{5}+2=\frac{20}{5}+2=6.$$ Therefore, this statement is sufficient.

In conclusion, the correct answer is the option D.

I hope it helps.
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