Aptitude - Average - Discussion

Thanks @Praveen.

Here,

If we take 20 numbers in this way.

-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9,10.

Sum = 0,
Avg = Sum/no however Avg= 0/20,
Answer should be option C.

Thanks @Harika.

@Akshay.

It is also a possible case but in the question it is mentioned as "atmost positive numbers".

Suppose if we consider.

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19.

As 19 positive numbers and the 20th number as -189.

Then we will get maximum positive numbers.

When the sum of +ve no.'s = sum of -ve no.'s.

Then Average is Zero.
Sum of Maximum possible.

+ve/-ve numbers = -ve/+ve number.
Hence avg is zero.
And the answer is 19.

If the question includes "at least ".

Then the answer is 1.

If you consider 20 numbers for example like.
-10,-9,.....,-1,+1,+2,.....+10.

Then the no of numbers greater than 0 is 10.

First when average can be Zero:
0(Sum of observation)/20 Number of Observations =0 is answer (Average).

Than means we must get 0 sum on the top of /20 that will make average Zero.

Even single nagative number can make 0 on top of /20. If sum of 19 numbers is +1 one nagative number -1 can make it zero you can assume sum of 19 numbers as positive and put same nagative number to make it Zero.


Now coming to answer, they are asking how many number can be above 0 i.e. in positive (numbers below zero are nagative). 19 Max number can be positive to make one nagative number 0 so that we get average zero.

Hope it's clear now.

The average of two numbers A and B is 20, that of B and C is 19 and of C and A it is 21. What is the value of A?

@Tarun.

Good explanation. Thank You.