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# If the average (arithmetic mean) of distinct integers x, y, and z is 1

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If the average (arithmetic mean) of distinct integers x, y, and z is 1  [#permalink]

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08 Aug 2017, 02:13
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78% (00:40) correct 22% (00:54) wrong based on 91 sessions

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If the average (arithmetic mean) of distinct positive integers x, y, and z is 10, what is the greatest possible value of z ?

A)30
B)28
C)27
D)26
E)10

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Re: If the average (arithmetic mean) of distinct integers x, y, and z is 1  [#permalink]

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08 Aug 2017, 02:17
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stonecold wrote:
If the average (arithmetic mean) of distinct positive integers x, y, and z is 10, what is the greatest possible value of z ?

A)30
B)28
C)27
D)26
E)10

x+y+z = 30
to maximize z we need to minimize x & y
since they are distinct positive integers x and y can take 1 and 2 respectively or vice versa

hence z will be 27
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Re: If the average (arithmetic mean) of distinct integers x, y, and z is 1  [#permalink]

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08 Aug 2017, 02:46
stonecold wrote:
If the average (arithmetic mean) of distinct positive integers x, y, and z is 10, what is the greatest possible value of z ?

A)30
B)28
C)27
D)26
E)10

Average of distinct positive integers $$x,y$$ and $$z = 10$$

$$\frac{x + y + z}{3} = 10$$

$$x + y + z = 10*3 => 30$$

For '$$z$$' to have greatest value, '$$x$$' and '$$y$$' should have minimum values.

Given the integers are distinct positive integers. Hence '$$x$$' and '$$y$$' could take values $$1$$ and $$2$$.

$$1 + 2 + z = 30 => 3 + z = 30$$

$$z = 30 - 3 => 27$$

Therefore the greatest possible value of $$z$$ is $$= 27$$

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Re: If the average (arithmetic mean) of distinct integers x, y, and z is 1  [#permalink]

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08 Aug 2017, 03:06
stonecold wrote:
If the average (arithmetic mean) of distinct positive integers x, y, and z is 10, what is the greatest possible value of z ?

A)30
B)28
C)27
D)26
E)10

If the average of the 3 numbers is 10, effectively each is 10. To maximise one number, the other two should be minimum. Since they must be positive integers and distinct, they would be 1 and 2.
The deviation of 9 and 8 would then be added to 10 to give 10+9+8 = 27.
Hence maximum value of z must be 27.

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Re: If the average (arithmetic mean) of distinct integers x, y, and z is 1  [#permalink]

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10 Aug 2017, 10:52
stonecold wrote:
If the average (arithmetic mean) of distinct positive integers x, y, and z is 10, what is the greatest possible value of z ?

A)30
B)28
C)27
D)26
E)10

We can create the following equation, using the formula sum/number = average:

(x + y + z)/3 = 10

x + y + z = 30

If we let x = 1 and y = 2, then z = 30 - 3 = 27.

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Re: If the average (arithmetic mean) of distinct integers x, y, and z is 1  [#permalink]

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21 Sep 2018, 12:44
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Re: If the average (arithmetic mean) of distinct integers x, y, and z is 1 &nbs [#permalink] 21 Sep 2018, 12:44
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