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"It takes a very long time to become young."

- Pablo Picasso

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 B

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: (Mon, Aug 30, 2010 02:51:25 PM)

I don't unterstand this answer. Please any one explain.

Harika said: (Fri, Sep 10, 2010 06:50:29 AM)

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: (Thu, Sep 30, 2010 11:06:00 PM)

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: (Thu, Oct 14, 2010 03:59:36 PM)

@ 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: (Tue, Nov 30, 2010 04:45:07 AM)

@ 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: (Tue, Dec 7, 2010 02:26:30 AM)

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: (Mon, Dec 13, 2010 09:44:52 AM)

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: (Mon, Dec 13, 2010 09:51:11 AM)

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: (Thu, Dec 16, 2010 05:04:17 AM)

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: (Thu, Dec 16, 2010 08:19:20 AM)

@Tarun Your explanation is perfect...

Naim said: (Mon, Jan 3, 2011 03:16:14 AM)

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: (Thu, Jan 20, 2011 08:30:28 AM)

@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: (Mon, Jan 24, 2011 01:53:16 AM)

hi harika i understand this about ur explanation. thank you

King Praba said: (Wed, Mar 2, 2011 07:54:32 AM)

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: (Fri, May 13, 2011 06:24:57 AM)

Pravin, Harika. Thank you very much for your explanations.

Mrs Pallavi said: (Thu, May 19, 2011 09:11:18 PM)

Hey tarun you explained very nicely good keep it up.

Amit said: (Mon, May 30, 2011 05:25:07 PM)

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: (Sun, Jun 19, 2011 12:55:33 PM)

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: (Sat, Jun 25, 2011 11:00:48 AM)

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: (Thu, Jul 7, 2011 07:51:32 AM)

Thank you tarun. I can understand your explanation.

Laxmi said: (Sun, Aug 14, 2011 05:29:31 PM)

Thank you king praba. Your explanation was good.

Ameer said: (Fri, Aug 26, 2011 06:07:12 PM)

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: (Fri, Aug 26, 2011 07:27:39 PM)

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: (Sun, Sep 18, 2011 08:04:15 PM)

Am not clear vth above answers. Still I'm in dilemma. ?

Abhay said: (Tue, Sep 20, 2011 04:51:32 PM)

Praveen answer is the best one to understand this problem. Good praveen.

Shekhar said: (Sun, Oct 23, 2011 10:33:14 PM)

Absolutly right. How can age be negative?

Aishwarya said: (Thu, Nov 17, 2011 10:55:10 AM)

@ tarun your explanations seems the correct one.