# 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?

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:

134 comments Page 1 of 14.
Teja Reddy said:
2 years 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.

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

Their sum will be 0, the answer may be 10.

(50)

Guna said:
2 years 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.

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.

(24)

Vrush said:
3 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.

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.

(10)

Geetanjali said:
3 years ago

I don't understand this, Anyone, please explain shortly.

(9)

Nanthakumar said:
8 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

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

(9)

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.

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.

(6)

Jagadeesh said:
7 months ago

In question, if they are consecutive. Definitely the answer will be 10, but they didn't mention what type of numbers are there, it's asking the possibility of max. Positive numbers satisfy the given condition, so in 20 numbers average is 0. So 20 positive numbers can't take place there is a possibility of 19 numbers positive and the remaining number is numerically equal to the sum of those 19 positive numbers but the sign is negative.

(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?)

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)

Saif said:
4 months ago

At max,

1 + 2 + 3....….... + 19 + (-190) = 0(sum)

So, the average is 0/20= 0.

Therefore at most 19 numbers can be greater than zero & 1 number will be less than it.

1 + 2 + 3....….... + 19 + (-190) = 0(sum)

So, the average is 0/20= 0.

Therefore at most 19 numbers can be greater than zero & 1 number will be less than it.

(5)

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.

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.

(4)

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