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.
What is the average (arithmetic mean) of w, x, y, z, and 10?
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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
Second statement
In conclusion, the correct answer is the option D.
I hope it helps.
Here, we have to find the value of $$\frac{w+x+y+z+10}{5}=\frac{w+x+y+z}{5}+2\ .$$
First statement
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.(1) The average (arithmetic mean) of w and y is 7.5; the average (arithmetic mean) of x and z is 2.5
Second statement
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.(2) -(-z - y -x - w) = 20
In conclusion, the correct answer is the option D.
I hope it helps.