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
Answer: Option
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.

Hema said:   1 decade ago
I don't unterstand this answer. Please any one explain.

Harika said:   1 decade ago
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.

So the answer is 19.

Hope you understood now.

All the best.

Jeevanandham said:   1 decade ago
Please try this:

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

So, sum is zero.

The answer may be 20.

Raghav said:   1 decade ago
@ Jeeva.

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

Praveen said:   1 decade ago
@ 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)

Vamsikrishna said:   1 decade ago
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....

Tarun said:   1 decade ago
Dear read the question carefully.

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.

Tarun said:   1 decade ago
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.

Loverboy said:   1 decade ago
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)

Goutham said:   1 decade ago
@Tarun Your explanation is perfect...


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