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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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New post 08 Aug 2017, 02:13
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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
[Reveal] Spoiler: OA

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

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New post 08 Aug 2017, 02:17
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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New post 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 \(= 27\)

Answer (C)...

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

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New post 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.

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

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New post 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.

Answer: C
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Re: If the average (arithmetic mean) of distinct integers x, y, and z is 1   [#permalink] 10 Aug 2017, 10:52
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