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Of the three numbers, the average of the first and the second is greater than the average of the second and the third by 15. What is the difference between the first and the third of the three numbers?
Answer & Solution
Correct Answer:
Option
E
Let the numbers be x, y and z.
Then,
$$\eqalign{ & \Rightarrow \left( {\frac{{x + y}}{2}} \right) - \left( {\frac{{y + z}}{2}} \right) = 15 \cr & \Rightarrow \left( {x + y} \right) - \left( {y + z} \right) = 30 \cr & \Rightarrow x - z = 30 \cr} $$
Then,
$$\eqalign{ & \Rightarrow \left( {\frac{{x + y}}{2}} \right) - \left( {\frac{{y + z}}{2}} \right) = 15 \cr & \Rightarrow \left( {x + y} \right) - \left( {y + z} \right) = 30 \cr & \Rightarrow x - z = 30 \cr} $$
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