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

The original question: [min(J) + max(S)] / 2 = ?

1) We know that Average(J) = 165.

If J = {165, 165} and S = {173, 185}, then the combined range is 185 - 165 = 20 and the averege of interest is (165 + 185) / 2 = 175.

However, if J = {159, 171} and S = {179, 179}, then the combined range is 179 - 159 = 20 and the averege of interest is (159 + 179) / 2 = 169.

Thus, we can't get a unique value to answer the original question. \(\implies\) Insufficient

2) We know that Average(S) = 179.

We can use the same cases we used in statement 1) to prove that statement 2) alone is also insufficient. Thus, we can't get a unique value to answer the original question. \(\implies\) Insufficient

1&2) Since we can use the same cases to prove that each of statements 1) and 2) alone is insufficient, 1&2) must also be insufficient. Thus, we can't get a unique value to answer the original question. \(\implies\) Insufficient

Answer: E

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?

Height Range,R = 2; \(\frac{T_s + S_j}{2}\) = ?
\(R = T_s\) OR \(T_j - S_s\) OR \(S_j\) (2*2 = 4 possibilities)

(1) The average of the heights of the juniors in the group is 165 centimeters.
\(T_j - S_j = 175 - 155 = 180 - 160 \) Or all are same height
Nothing more given.
INSUFFICIENT.

(2) The average of the heights of the seniors in the group is 179 centimeters.
\(T_s - S_s = 189 - 169 = 185 - 165\) Or all are same height
Nothing more given.
INSUFFICIENT.

Together 1 and 2
As 179 - 165 = 14 and since there is a range of 20 neither all seniors not all juniors are of same height.
Combined we have \(T_s - S_j = 184 - 164 = 180 - 160\)
We still don't now actual details and so many values are possible.

Answer E.
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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

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