Problem Solving

Although I answered it correctly while taking the test, but somehow not convinced with the answer. Appreciate if anyone could post an explanation or link of previous thread with expln

Thanks

Given
1)total sample size is 15
2) Average = 150 K
3) Median = 130 K

Statement 1) At least 1 value is >165 K

To see if at least one value has to be more than 165 maximize the values of all other no. in the set with the given restrictions

Since Median will be the 8th value in the set of 15 and it is 130 K. All values from 1 to 7 have to be = or < than the median. So assume they are all 130.

Assume all values above the median are 164.

Since Avg is 150 total of all values has to be 150 * 15 = 225 K

Now check with the values you have taken i.e (130*8) + (164*7)

total is less than 225K so to get the avg to 150 at least one value has to be more than 165

You can work out the ans to the other 2 statements in the same way