The range of the heights of a group of high school juniors and seniors

Given : Range = H - L = 20

Question: \(\frac{H + L}{2} =\) ?

Statement 1: The average of the heights of the juniors in the group is 165 centimeters.

We need the exact height of Tallest and shortest candidates both but average doesn't give us anything hence

NOT SUFFICIENT

Statement 2: The average of the heights of the seniors in the group is 179 centimeters

We need the exact height of Tallest and shortest candidates both but average doesn't give us anything hence

NOT SUFFICIENT

Combining the statements

We need the exact height of Tallest and shortest candidates both but average doesn't give us anything hence

NOT SUFFICIENT

Answer: Option E

Marking E is never easy for me..anyone else feels the same? If yes, How do you ensure the correct-ness?

H-L = 20

To find (H+L)/2
=(L+20+L)/2
= (20 + 2L)/2
=L+10

Bunuel can we straight go to E given we are just given averages since we will need the value of lowest value which cant be determined or do we need to put different values and see

We need to find the average of:

The height of the tallest senior
The height of the shortest junior

We know that the range of heights in the group (difference between the tallest and shortest individuals in the group) is 20 centimeters, but we don't have specific information about who the tallest and shortest individuals are yet. The range might be useful in a Max/min situation

Analyze Each Statement:

Statement (1):
The average of the heights of the juniors in the group is 165 centimeters.

This tells us the average height of the juniors, but it gives no direct information about the individual heights of the tallest senior or the shortest junior. The range of 20 centimeters includes both juniors and seniors, so knowing the juniors' average does not directly help us identify the specific individuals we need (the tallest senior and the shortest junior). Therefore, this statement alone is not sufficient.

Statement (2):
The average of the heights of the seniors in the group is 179 centimeters.

Similarly, this statement gives the average height of the seniors, but it doesn't tell us the individual heights of the tallest senior or the shortest junior. The range of 20 centimeters still applies to the whole group, and knowing the seniors' average height alone does not help determine the specific heights of the tallest senior or the shortest junior. Therefore, this statement alone is not sufficient.

Combine Statements (1) and (2):
Even when combining the two statements, we still do not have the specific heights of the tallest senior or the shortest junior. We only know the average heights of the juniors and the seniors, but averages do not provide enough information about the extreme values (tallest or shortest) in each group.

Note: The range given appears to just be a smokescreen distraction

Answer is E.