The chetan explanation is wrong.

This is a single answer choice to pick among and NOT multiple answer choices.
The answer is D
Refer to the explanation provided by Brent above

Regards

Let's first examine the 4 lightest fish.
Their average weight is 20.5 pounds
This means the TOTAL weight of the FOUR LIGHTEST fish = (4)(20.5) = 82 pounds.
So, it's possible that the 4 weights are 20.5, 20.5, 20.5 and 20.5

Notice that, AMONG THE FOUR LIGHTEST fish, 20.5 is the LIGHTEST possible weight for the heaviest fish.
If decrease one of the four weights, then we must increase another weight so that the TOTAL weight remains at 82 pounds.
For example, if we decrease one weight from 20.5 to 19.5, then we must increase another weight from 20.5 to 21.5 (to maintain the total weight of 82 pounds)
So, it's also possible that the 4 weights are: 19.5, 20.5, 20.5, 21.5

At this point, we can see that the median weight can be 21.5
We just need for the lightest fish AMONG THE FOUR HEAVIEST fish to weigh 21.5 pounds.

We're told that the four heaviest fishes have a total weight of 117 pounds
So, the 4 weights COULD be 21.5, 22.5, 30, 43

This means all seven weights are: 19.5, 20.5, 20.5, 21.5, 22.5, 30, 43

Answer: D

Cheers,
Brent

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Hello! Why don't we keep the sequence as 20,5 20,5 20,5 20,5 ? I mean why we increase one of them?

Hi...

Although it is explained quite nicely by Brent, let me pitch in my bit.

Median is the center value and we are given four lightest and then the four heaviest, so the common fish in the TWO groups is the median as 4th fish out of 7 is the median.
So CAN we be sure of a specific value .... NO

But we can surely think of a range..
Let the fishes in ascending order be A, B, C, D, E, F, G and we are looking for D.

1) If we take the lightest four-D, E, F, G-, the lightest out of this four, D is the median.
the largest value of D will be when all these fishes weigh the same.
So the largest value of median is \(\frac{117}{4}=28.75\)

2) If we take the heaviest four-A, B, C, D-, the heaviest out of this four, D is the median.
the smallest value of D will be when all these fishes weigh the same.
So the smallest value of median is 20.5 itself

The range is \(20.5\leq{median}\leq{28.75}\)..
Thus C, D and E , all three choices fit in..

C. 20.5 ------- 20.5, 20.5, 20.5, 20.5, 28, 30, 38.5
D. 21.5 ------- 20, 20, 20.5, 21.5, 28, 30, 37.5
E. 22 ------- 19.5, 20, 20.5, 22, 28, 30, 37

Note - If the question was asked in a multiple choice question and could have more than 1 answer, all three choices C, D and E fit in. However if we had to pick only one, the choices must be different or there may be some restrictions on the weight in initial statements.