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The range of the heights of a group of high school juniors and seniors is 20 centimeters. What is the average (arithmeti

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by VJesus12 » Tue Sep 15, 2020 2:19 am

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Difficulty—

The range of the heights of a group of high school juniors and seniors is 20 centimeters. What is the average (arithmetic mean) of the height of the tallest senior in the group and the height of the shortest junior in the group?

(1) The average of the heights of the juniors in the group is 165 centimeters.
(2) The average of the heights of the seniors in the group is 179 centimeters.

Answer: E

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Source: — Data Sufficiency |
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Re: The range of the heights of a group of high school juniors and seniors is 20 centimeters. What is the average (arith

by deloitte247 » Sat Sep 19, 2020 6:27 am
Let the height of tallest senior = t
Let the height of shortest junior = s
Range = t - s

Target question => What is the average heights(arithmetic mean) of the height of the tallest senior in the group and the height of the shortest junior in the group
i.e ts/2 = ??

Statement 1 => The average heights of the juniors in the group is 165cm
$$\frac{sum\ of\ all\ heights\ of\ juniors}{total\ numbeer\ of\ juniors}=165\ cm$$
This does not provide the value of either t or s, so target question cannot be answered and statement 1 is NOT SUFFICIENT

Statement 2 => The average of the heights of the seniors in the group is 179cm
$$\frac{sum\ of\ all\ heights\ of\ seniors}{total\ numbeer\ of\ seniors}=179\ cm$$
This does not provide the value of either t or s so the target question cannot be answered. Statement 2 is NOT SUFFICIENT

Combining both statements together =>
Statement 1 and 2 was providing the average heights of juniors and seniors respectively and this is not in any way related to the value of t and s. Hence, both statements combined together are therefore NOT SUFFICIENT

Answer = E
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