# Aptitude - Average - Discussion

Discussion Forum : Average - General Questions (Q.No. 4)
4.
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
0
1
10
19
Explanation:

Average of 20 numbers = 0.

Sum of 20 numbers (0 x 20) = 0.

It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).

Discussion:
132 comments Page 1 of 14.

Hi Hema,

Here average of 20 numbers= 0.

So we have avg = sum/20.

That implies sum = 0.

Now for the sum of 20 numbers to be equal to zero, there may be all 19 numbers of them >0 and only one number which is -ve of all the 19 numbers sum.

Hope you understood now.

All the best.

Sum of 10 +ve no's + 10 -ve no's = 0

So, sum is zero.

@ Jeeva.

In question it s asked numbers greater than 0, how negative nos be greater than 0. Negative no is less than 0.

@ hema ...
see here the sum is zero ...
sum of 20 numbers has to be 0
ex: 1+2+3+4+5+6...+20 = 0
let 1+2+3+4+5...19=a and the 20th number should be '-a' in order to get the sum as zero .
(a(1st 19numbers)-a(last 20th munber)=0 , hence a-a=0)
hence all 1st 19 numbers are positive means greater than zero and the last 20th is negative .
hence answer is 19 positive i.e greater than zero numbers.
(1)

You said that it is average of 20 numbers, avg is sum of num's/number of nums.....but how does the answer suits by doing a multiplication...if all the num's r zeros the ans shud be (0+0+0..............+0)/20....

The question ask "at the most".

So you have to give maximum numbers that can be positive,.

And that is 19.

For example:
take any 19 positive numbers (11, 10, 9, 8, 5, 12, 18, 16, 1, 3, 5, 6, 3, 7, 8, 22, 3, 4, 1).

Avg = (152+x) /20.

Now put x = -152.

So, Avg= (152-152) /20=0.

Hey Jeevanandham ans will never 20,.

Because if all 20 numbers are positive then their avg will never be zero,.

And Vamsikrishna according to question they ask about numbers greater than zero.

So you cant put zero,.

Because zero equals to zero, not greater than zero.