Aptitude - Average - Discussion

4. 

The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

[A]. 0
[B]. 1
[C]. 10
[D]. 19

Answer: Option D

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).


Hema said: (Aug 30, 2010)  
I don't unterstand this answer. Please any one explain.

Harika said: (Sep 10, 2010)  
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: (Sep 30, 2010)  
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: (Oct 14, 2010)  
@ 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: (Nov 30, 2010)  
@ 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.

Vamsikrishna said: (Dec 7, 2010)  
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: (Dec 13, 2010)  
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: (Dec 13, 2010)  
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: (Dec 16, 2010)  
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

Goutham said: (Dec 16, 2010)  
@Tarun Your explanation is perfect...

Naim said: (Jan 3, 2011)  
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

Swathy said: (Jan 20, 2011)  
@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?

Chandbasha said: (Jan 24, 2011)  
hi harika i understand this about ur explanation. thank you

Sudheer said: (Feb 3, 2011)  
thank u harika . all the best

King Praba said: (Mar 2, 2011)  
Hi,

We know the formula.average=sum of observations/number of observations.

sum=0(given)..no.of observation=20..sub in above formula 0/20=0..sum of 20 numbers is

0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19.........

among above numbers 0<remaining numbers.

so the remaining numbers are 19(ans)

Bhavin said: (May 13, 2011)  
Pravin, Harika.

Thank you very much for your explanations.

Mrs Pallavi said: (May 19, 2011)  
Hey tarun you explained very nicely good keep it up.

Amit said: (May 30, 2011)  
0+0+0+0+0+0+0+0+0+0+0+0+0.....up 2 18th term
than
+100-100...

Wats gonna b answer ...my dear frns answer is 1.

Arafat said: (Jun 19, 2011)  
Write a java program which will print sum of 5 numbers but each number should not be more than 12. Help any1 plz!!!!!!!

Nilesh said: (Jun 25, 2011)  
Dear read Tarun is right,the question carefully.

The question ask "at the most".

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

And that is 19.

Anu said: (Jul 7, 2011)  
Thank you tarun.

I can understand your explanation.

Laxmi said: (Aug 14, 2011)  
Thank you king praba. Your explanation was good.

Ameer said: (Aug 26, 2011)  
We have to atmost possible values to get sum is zero.

Let 19 num are from 1 to19 &their sum is 190 if we have 20th num as -190 we get total sum is zero.so avg is also zero.

We can have positive num whose range is {1<=num<=19}.hope u will understand.

Ameer said: (Aug 26, 2011)  
We can't get sum zero with out a -ve number. The cases are

Pos     Neg
1     19
2     18
and so on..
19     1

Here he given that max +ve values to get sum is zero soa ans is 19.

Sree said: (Sep 18, 2011)  
Am not clear vth above answers. Still I'm in dilemma. ?

Abhay said: (Sep 20, 2011)  
Praveen answer is the best one to understand this problem.

Good praveen.

Harish said: (Oct 20, 2011)  
How can an age can be negative?

Shekhar said: (Oct 23, 2011)  
Absolutly right.

How can age be negative?

Aishwarya said: (Nov 17, 2011)  
@ tarun
your explanations seems the correct one.

Jordan said: (Jan 27, 2012)  
@tarun.

Your answer is the best.

Ashwin said: (Aug 17, 2012)  
What if the numbers are
1,2,3,4,5,6,7,8,9,10,-1,-2,-3,-4,-5,-6,-7,-8,-9,-10
then average =0
so the answer may be 20 right?

Ashline said: (Jan 3, 2013)  
@Jeevanandham.

your logic was nice but the answer will be 10 in your case which is True but they asked for" At the most" So you need to tell maximum possible numbers that can be greater than zero in order to maintain the sum zero :).

Hope that helps :).

Ajay said: (Jan 8, 2013)  
@Swathy.

In question it is asking for at most how many number Greater then zero.

So answer can't be 10.

Chennareddy said: (Feb 3, 2013)  
@AJAY can give 20 numbers, but the last 20th number average is 0, so we don't no 19 number lesser then 0 are greater then 0, so the question is range.

Kathir Vtv said: (Mar 26, 2013)  
20 numbers = 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1-19/20.

= 0/20.

So total numbers are greater then 0 is 19.

Answer is 19.

Karthik said: (May 9, 2013)  
The question says how many "MAY BE" greater than zero. SO all the numbers MAY BE zero so none are greater than zero so the answer is zero.

Ganesh said: (Sep 27, 2013)  
I agree with @Swathy, there might be 10 +ve nos. and 10 -ve nos.

And questions says at most nos. greater than 0 i.e., at most +ve nos. i.e., maximum +ve nos. then it can be 10 too, why 19 then.

Whats at most means actually, according to me its maximum, please tell me.

Madhu Yadav said: (Dec 31, 2013)  
The answer can be any of the positive number which cannot be defined. Because we can make different assumptions based on our view through which we are seeking the problem. Options may not be available regarding the question.

Rajesh said: (Jan 1, 2014)  
This answer is not a understand so clearly the sum and clean explain. How this answer is possible?

Sumeet said: (Feb 24, 2014)  
Lets consider negative 19 numbers whose sum is -20 and consider there is only one positive number '20', then we will get average of 0.

Here, number greater than zero is only one.

So I think que. is technically not correct :p.

Pavani said: (Mar 18, 2014)  
I have read all the explanation above. But got one doubt. Do we take -ve values while doing averages?

How we assume that the 20th number as -19. Please explain.

Vinay said: (Jun 9, 2014)  
@Pavani.

Actually I think we don't take negative values.

But in the question it is given that average is 0 so obviously negative values will come into picture.

Jossams Mabeti said: (Aug 1, 2014)  
I have also read the explanations above but don't understand very well how you get 19.

Stalin said: (Sep 3, 2014)  
Average = sum of quantities/number of quantities.

If average is zero mean how sum of quantities will greater than zero please explain me.

Mahesh Reddy said: (Nov 2, 2014)  
If the numbers are -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 then the average is 0.

In this case 10 numbers is greater than 0.

Sree Harshini said: (Dec 3, 2014)  
In this question how the sum of numbers can be greater than 0 and I did not understand the statement also explain please.

Sudharshan said: (Jan 2, 2015)  
Here in this question they asked about the almost that means max numbers of numbers those are greater than 0.

>>> So 19 is the answer because we are not considering the 0 because he asked >0.

>>> If he ask about min number of numbers we can say 1.

Sharad said: (Jan 6, 2015)  
If -1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1+19 = 0.

Then 0/20 = 0.

Then positive number is only 1. Then answer is B.

Sandeep said: (Jan 22, 2015)  
What if there is 10 positive numbers and 10 negative numbers? Then the answer may be 10.

Rav said: (Feb 4, 2015)  
@Sandeep.

They have asked "AT MOST how many numbers, may be greater than 0". At most, as in maximum how many numbers can be greater than 0.

Nithya said: (Apr 2, 2015)  
@Hema.

Can you explain me your method once again?

Rahul Kumar said: (Aug 16, 2015)  
I think the solution is wrong as its just a assumption that out of 20 only one is 20. But it may also occurs that out of 20 10 may be positive and rest be negative.

Average of 20 numbers = (Sum of 20)/20.

Sum of 20 numbers = (20*21)/2.

So A/Q === (20*21)/(2*20) = 0.

=> 21/2 = 0.

=> 21 = 0.

Not possible :-).

Akash said: (Nov 2, 2015)  
Why don't all you guys understand that, the question is being asked on the basis of "at the most". I too do agree that, there may be chances of more than one number of appropriate positive and negative number i.e. ten positive and ten negative, fifteen positive and five negative etc. But for at the most, the answer will be 19.

Because there will be the one negative number of all 19 positive number, so that the sum become zero. For the very beginning I also used to think like what you guys thinking now. Hope you will understand.

Md. Zahidur Rahman said: (Mar 13, 2016)  
1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1-19.

0>1

Here 1 is 19
Negative number -19

SO answer is 19.

Shudhu said: (May 18, 2016)  
I suggest the answer may be 10.

Eg. If Avg of 20 numbers can be denoted as:

a + b + c + d + e + f + g + h + I + j + k + l + m + n + o + p + q + r + s + t.

Between j and k the zero will be present because we know that middle number will be the average.

So when zero is present after j so from k the number is greater than zero.

So the answer will be assumed as 10.

Ashwani said: (May 26, 2016)  
The question is rhetoric, at the first glance it looks like well calculated but actually it requires analytical skill. Let's see.

Our average should be 0 and the total number is 20. Hence, we should understand that dividing by 20, if we have 20 then it will be 1.

If we have more than 20 then it will be more than 1 and the most crucial is that it will never be 0.
Then what can be more than 1, and it can be less than 20 so that we can avoid 1.

Therefore 19/20 =. ___ <1.

Vipin said: (Jun 17, 2016)  
The question is not very rigorous but the main adversity of this question is that answer is 19 because in the question only asking that the no. an average of only 20 numbers is zero not asking that 1 to 20 numbers is zero so the 20 = 0 and 0<19 value. i.e 1, 2, 3, 4, 5, 6, 6, 7, 8, 9. 19.

Dsp said: (Jun 27, 2016)  
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1+ 1 + 1 + 1 + 1 + 1 - 19 = 0.

+ve numbers are 19, So, D is the answer.

Himanshu Arora said: (Jul 16, 2016)  
What about the answer if the question would be, "The average of 20 numbers is zero. Of them, at least, how many may be greater than zero"?

Satyam said: (Sep 8, 2016)  
Hi,

In this question, they are asking about the number which is at most (it means maximum numbers which are greater than 0).

So, (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1+ 1) + (-19) /20.

I hope you got it.

Prabhat Kr.Singh said: (Sep 18, 2016)  
19 will be appropriate answer.

Because in the question, it is mention that maximum number greater than zero.
If we take all positive number then sum will never be 0.

So, at least one number should be taken negative that should be equal to the sum of the 19 numbers.

So, (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1+ 1) + (-19) /20.

I hope you got it.

Hemavathi said: (Sep 28, 2016)  
To get a value zero we can use,
(Sum of 19 positive numbers) - (-Value of sum)/(Sum of 18 positive numbers) - (Value of sum),
Here, the maximum probability of positive number is 19 (at most),

So the answer is 19.

Shivu said: (Oct 31, 2016)  
@Prabhat.

Your explanation was good, I got it now. Thank you.

Divya said: (Nov 12, 2016)  
Is there any shortcut to find the answer for this question?

Kumar said: (Dec 21, 2016)  
Thanks for all of your explanations.

Amin Ullah said: (Jan 8, 2017)  
While the actual answer is 20.
Suppose all 20 numbers are of value =1 then,
1+1+1....till 20. Thier sum will be 20.
Avg=sum of all number/total number.
Avg= 20/20.
= 0.

So, as for question is concern there is no option with 20. The nearest 19 will do.

Pooja said: (Jan 20, 2017)  
Your explanation is good @Tarun.

Nobi said: (Jan 26, 2017)  
@Amin Ullah.

Since when 20/20 = 0.

Pingal Rami said: (Mar 25, 2017)  
Your explanation is good, Thanks @Prabhat Kr.Singh.

Trishul said: (Apr 4, 2017)  
Very good explanation. Thank you all.

Arpita Saxena said: (Apr 29, 2017)  
But can it also be like;

All numbers are 0.
Therefore sum =0,
And sum/20 = avg.
Therefore 0/20 = 0.

Hence 0 be the answer.

Dinesh said: (May 27, 2017)  
I can't understand this problem. Please anyone help me.

Amar said: (Jun 27, 2017)  
10 + and 10 - nos gives answer 10 but the correct answer is 19 because he asked most of nos.

Srj said: (Jul 5, 2017)  
Thanks @Tarun.

Praneeth said: (Jul 20, 2017)  
Let assume 10 numbers above 0 (2,3,4,5,6,7,8,9,10).

The remaining 10 numbers are - ve (-2,-3,-4,-5,-6,-7,-9,-10).

Why can 10 be the answer?

Seeramsetty Kavya said: (Oct 3, 2017)  
Why can't there be less than 19 positive numbers?

For example : 1+2+3+0+4+5--------19.

Kotana Narendra Kumar said: (Dec 6, 2017)  
In question, they mentioned atmost Which Means a maximum number of possibilities.

So 19 is the right one.

Divya said: (Jan 16, 2018)  
Can't understand friends

Aman said: (Jan 17, 2018)  
Thanks @Harika.

Ravi said: (Jan 19, 2018)  
Listen, guys.

Question is at most numbers are greater than zero. At most mean maximum.

So let's do.

Av of 20 no are zero.
Lets count.

0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19/20=0. Ok.

Count how many no are greater than zero? 19 then answer is 19.

Sugi S said: (Feb 1, 2018)  
Thanks for your answer @Ravi.

Vignesh said: (Feb 8, 2018)  
For example : The Sum of first 19 number is 20 and the last number is -20. Therefore 20 -20 = 0.

Poonam said: (Apr 10, 2018)  
Thanks @Ravi.

Vignesh said: (May 5, 2018)  
1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1-19 = 0.
Therefore 0/20 =0.

Sai said: (May 25, 2018)  
@All.

Why we think only one no is negative, let we think maybe 10 numbers -ve; i.e 10 numbers less than zero and 10 numbers is +ve i.e 10 numbers greater than zero. so the avg of -10 numbers and +10 numbers is equal to zero.

Subash said: (May 30, 2018)  
@Sai.

In the question, they had given AT THE MOST.

So, the maximum value must be the answer.

Saikat said: (Jun 5, 2018)  
Please anyone help I can't understand this.

Habib said: (Jul 3, 2018)  
Thanks @Praveen.

Denis said: (Jul 17, 2018)  
How? Explain me the answer.

Ankit Dere said: (Jul 31, 2018)  
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?)

Prudhvi Raju said: (Aug 23, 2018)  
How can you say 20th number is negative?

It may have 10 positive and 10 negative numbers or may be any other combinations.

Please clarify for me.

Shreeshail Karajol said: (Sep 2, 2018)  
Very simple.

Consider the sum of all 19 number =150.
If 20th is - 150 then,
150+(-150)=0,
Now 0/20=0.

Jeevitha S K said: (Sep 20, 2018)  
If it is asked as "atleast" the answer will be 1 right.

Vinay said: (Sep 29, 2018)  
The positive numbers from 1 to 14 addition is 105.

The negative numbers i.e. 15, 16, 17, 18, 19, 20 is -105;.

So, the sum of these numbers is 0. And average is zero hence It can only 14 positive numbers.

Chandu said: (Oct 10, 2018)  
Please, anybody, explain it in an easy way.

Jyothi said: (Nov 3, 2018)  
Thanks @Tarun & @Prabha.

Jeet said: (Nov 9, 2018)  
I am not getting this. Please, anyone explain me clearly.

Bharath said: (Dec 6, 2018)  
Thanks for the answer @Praveen.

Roopa Naidu said: (Dec 12, 2018)  
Awesome, Thanks for the answer @Praveen.

Parag said: (Jan 12, 2019)  
Thanks @Praveen.

Ram said: (Feb 28, 2019)  
Thanks @Praveen.

Akshay said: (Apr 8, 2019)  
Here,

If we take 20 numbers in this way.

-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9,10.

Sum = 0,
Avg = Sum/no however Avg= 0/20,
Answer should be option C.

Yama said: (Apr 27, 2019)  
Thanks @Harika.

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