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If the average (arithmetic mean) of positive integers x, y,

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shamimshariq
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If the average (arithmetic mean) of positive integers x, y, [#permalink] New post   Updated on: 24 May 2014, 10:43
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If the average (arithmetic mean) of positive integers x, y, and z is 10, what is the greatest possible value of z ?

A. 8
B. 10
C. 20
D. 28
E. 30
ShowHide Answer
Official Answer
D

Originally posted by shamimshariq on 21 Jul 2009, 22:25.
Last edited by Bunuel on 24 May 2014, 10:43, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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MohitRulz
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Re: Is 0 a positive integer. [#permalink] New post   21 Jul 2009, 23:16
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0 is considered positive integer, brother
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IanStewart
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Re: Is 0 a positive integer. [#permalink] New post   22 Jul 2009, 04:45
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MohitRulz wrote:
0 is considered positive integer, brother


0 is definitely an integer, but it's definitely not positive. It's the only real number which is not positive, and not negative.

And the question in the OP: If the average of x, y and z is 10, then their sum is 30:

x + y + z = 30

If x, y and z are all positive, the smallest x and y could be is 1, so the largest z could be is 28.
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Re: Is 0 a positive integer. [#permalink] New post   22 Jul 2009, 08:54
zero is the neutral integer ; neither positive nor negative
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mad4gmat
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Re: Is 0 a positive integer. [#permalink] New post   22 Jul 2009, 08:59
0 is neither positive nor negative.

In the question, if it is mentioned Non-negative or non-positive, then you need to consider 0 also while solving the problem.
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irajeevsingh
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Re: Is 0 a positive integer. [#permalink] New post   23 Jul 2009, 00:13
and just to extend mad4gmat you can use 0 when you are asked to use integer or non-negative integer.
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Re: Is 0 a positive integer. [#permalink] New post   23 Jul 2009, 05:05
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IanStewart wrote:
MohitRulz wrote:
0 is considered positive integer, brother


0 is definitely an integer, but it's definitely not positive. It's the only real number which is not positive, and not negative.

And the question in the OP: If the average of x, y and z is 10, then their sum is 30:

x + y + z = 30

If x, y and z are all positive, the smallest x and y could be is 1, so the largest z could be is 28.

Agree with you. 0 is the only real number which is neither positive nor negative.
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Re: Is 0 a positive integer. [#permalink] New post   24 May 2014, 10:33
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shamimshariq wrote:
Is 0 a positive integer.If not,what is the solution of problem below.

Q10:
If the average (arithmetic mean) of positive integers x, y, and z is 10, what is the greatest possible value of z ?
A. 8
B. 10
C. 20
D. 28
E. 30 :


Is 0 a positive integer?
Can this be confirmed by a GMAT expert :)
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Re: Is 0 a positive integer. [#permalink] New post   24 May 2014, 10:36
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0 is not a positive integer.

It is an integer that is neither positive nor negative.
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Re: Is 0 a positive integer. [#permalink] New post   24 May 2014, 10:45
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b2bt wrote:
shamimshariq wrote:
Is 0 a positive integer.If not,what is the solution of problem below.

Q10:
If the average (arithmetic mean) of positive integers x, y, and z is 10, what is the greatest possible value of z ?
A. 8
B. 10
C. 20
D. 28
E. 30 :


Is 0 a positive integer?
Can this be confirmed by a GMAT expert :)


0 is neither positive nor negative even integer.
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Re: If the average (arithmetic mean) of positive integers x, y, [#permalink] New post   20 Nov 2016, 14:26
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D!

1 - For the average to be 10, the sum of the three positive integers has to be 30.
2 - The integers need not be distinct (not such constraint is mentioned)
3 - As the previous posters mentioned, 0 is neither positive or negative. Therefore the smallest positive integer you would use is 1.

30 = 28 + 1 + 1

Therefore the answer is D
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Re: If the average (arithmetic mean) of positive integers x, y, [#permalink] New post   21 Nov 2016, 09:39
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shamimshariq wrote:
If the average (arithmetic mean) of positive integers x, y, and z is 10, what is the greatest possible value of z ?

A. 8
B. 10
C. 20
D. 28
E. 30


\(\frac{x + y + z}{3} = 10\)

So, \(x + y + z = 30\)

We need to maximize z and minimize x and y

Given : x, y, and z are all positive integers...

If x = y = 1

We have \(x + y + z = 30 = 1 + 1 + 28\)

Thus, maximum value of z is (D) 28
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Re: If the average (arithmetic mean) of positive integers x, y, [#permalink] New post   12 Dec 2016, 11:13
Nice Question.
Here is what i did in this one.
Mean(3)=10
Sum(3)=10*3=30
x+y+z=30
for z to be max => rest of the numbers must be minimum.
But they are all positive integers.
hence x=1,y=1=> z=28
Hence max(z)=> 28

Hence D
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Re: If the average (arithmetic mean) of positive integers x, y, [#permalink] New post   18 Dec 2016, 14:24
One interesting note => If the question said x,y,z are distinct integers,then => maximum value of z=> 30-(1+2)=27
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Re: If the average (arithmetic mean) of positive integers x, y, [#permalink] New post   18 Dec 2016, 15:11
0 is definitely not positiv. Think about the very nature of positive and negative. In real life you could think of somethin positive, if it adds something for instance. And negative if it makes it less. What is zero doing ? Right, nothing! ;)
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Re: If the average (arithmetic mean) of positive integers x, y, [#permalink] New post   19 Apr 2020, 10:19
If the average (arithmetic mean) of positive integers x, y, and z is 10, what is the greatest possible value of z ?

the average of x, y and z is 10,
so,then their sum is 30:
or,x + y + z = 30
now, x, y and z are all positive integers, the smallest x and y could be is 1, so the largest z could be is 28.

correct answer D
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Re: If the average of positive integers x, y, and z is 10, what [#permalink] New post   31 Mar 2022, 03:54
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Re: If the average of positive integers x, y, and z is 10, what [#permalink]
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