Bunuel
There are different packages in a shipping depot, and each package weight is recorded in grams.
We need to find: The number of packages weighing MORE THAN 420 grams.
Statement 1:
The average (arithmetic mean) weight per package is equal to the weight of the lightest package.
Average = ( heaviest weight + lightest weight ) /2
If that average value = lightest weight, then heaviest weight should be equal to lightest weight.
Which means, all the weights in the shipping depot are of equal weights (SAME).
As, we don’t know the exact weight of the depot. It can be either 420 grams, OR less than 420 grams OR more than 420 grams.
Hence,
Insufficient Statement 2:
The median weight of all packages in the depot is 410 grams.
The median weight is the middle value of the packages arranged in ascending order.
Since, there are many combinations for this case.
All values equal to 410 grams.
Some less than 410 grams and some greater than 410 grams.
Even in that, there are chances where the values are higher than 420 grams, and some less than 420 grams.
Hence,
Insufficient Combining both Statements 1 and 2, we get
There are packages where all values are equal, and the median is 410.
Thus, there is ONLY ONE CASE, where all the packages have equal values and the value is equal to 410.
So, the number of packages greater than 420 grams =
0 We have got a concrete unique solution. Hence,
Sufficient Option C