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.

Teja Reddy said:   1 year ago
@All.

Why can't we take the same 10 positives and 10 negative numbers?

Their sum will be 0, the answer may be 10.
(41)

Guna said:   1 year ago
Average means Sum of numbers divided by total;

Ex: average of first 5 numbers is;
(1+2+3+4+5)/5.
Similarly for the average of 20 numbers "any 20 numbers" is;
Let's say (1+1+1+1+1...+1-19(20th number)= 0
Because 19*1 = 19 and adding it to -19 so the average is 0/20=0.
So there 19 numbers that are greater than 0.
(19)

Vrush said:   2 years ago
You are right. @Swathy.

But they are asking for at most means maximum how many numbers. You have taken 10 but till 19 numbers you can take then the sum will get cancelled by the 20th negative number. And the average becomes zero.
(9)

Geetanjali said:   2 years ago
I don't understand this, Anyone, please explain shortly.
(6)

Ankit Dere said:   6 years ago
It is asked in the question.

Avg of 20 numbers is Zero,
Given avg=0.
Numbers=20.

Explanation:
Avg=sum÷number i.e.
0=sum÷20
Now, cross multiply.
Sum=20x0=0.
This means the sum of 20 numbers is equal to 0.
{1+2+...+20}= is 0.

{1+2+...+19}= Will not be 0.

But the sum of rest 19 number will not be 0 it will be greater than 0(as the 2nd part of the question says how many may be greater than 0?)
(5)

MRP said:   3 years ago
Given avg of 20 number is 0.i.e 20 * 0 = 0.

And also they given almost i. e less than 20.so 19 because to get the sum as zero if we take 19 +ve numbers and 20th is -ve number which is equivalent to the sum of 19no.s(152+ve means -152ve). Then we get sum as 0.

Mainly in atmost they didn't mention almost 12 like that so it's better to take up to 19.
(4)

N A said:   4 years ago
Here, it is asked that at the most, how many may be greater than zero.
So let see.

(1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1-19)/20 = 0.
Now see it's 19 number which is greater 0.
(3)

Bires said:   2 years ago
{(1+2+3+....+19)-(x)}/20 =0.

Adding the series 1 - 19,

Sum=n/2 (a+L) {n-no. Of term, a-1st term, L-last term},
S=20/2 (1+19).
= 200.

So, (200 - x)/20 = 0.
x = -200.

Therefore, 19 nos. Of term can be possible to be greater than 0.
The 20th is negative which is less than zero.
(3)

Pradnyesh said:   3 years ago
@Tarun.

Good explanation.
(2)

Nanthakumar said:   2 months ago
First 1-19 numbers = each number is -1.
Therefore Adding these numbers the answer is = -19.
Then the 20th number is +19.
Therefore -19+19 = 0
The average of 20 numbers is 0/20=0
(2)


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