# 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 13 of 14.

@Tarun your answer s perfect but i have one doubt that if 10 nos are positive n 10 nos are negative means also the average will be zero? i mean for example (11,12,14,15,16,4,6,8,7,9,-11,-12,-14,-15,-16,-4,-6,-8,-7,-9)it mean also the average will be zero, so y the answer may be 10 for this problem?

Hi, even i didn't understood the question asked and solution provided. Even if one number is greater than zero than average has to change then howcome stil zero and especially answer provided 19.

Pls explain

in this question,
how many numbers may be graterthan zero.
if any number is graterthan 1.the avg is not zero.so, no number graterthan zero.
ans:A
(1)

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.

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.

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....

@ 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)

@ Jeeva.

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