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# The average (arithmetic mean) of 3 positive integers, x, y, and z, is

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Re: The average (arithmetic mean) of 3 positive integers, x, y, and z, is [#permalink]
Lets analyze the question stem and get the inferences::

AM (x,y,z) = 20 or (x+y+z)/3 = 20 or x+y+z =60. -- eq 1
AM (x,a) = 9 or (x+y)/2 =9 or x+y = 18. --eq 2

Putting value for eq 2 in eq 1, we get
z = 42 --eq 3

Find AM (y,z) or (y+z)/2; We know the value of z (from eq 3) ==> we need to find: (y+42)/2
So qtn is asking to find the value of y.

Lets analyze the statements now:
I: AM(x,z) = 22.5.==> (x+z)/2 = 22.5
From eq 3: (x+42) = 45. => x= 3

We know values of x,z and from eq 1 we can get value for y. SUFFICIENT

II: y = 5x; We know value of z from eq 3. Putting values of z and y=5x in eq 1; we can get value for x and hence the value of y. SUFFICIENT

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Re: The average (arithmetic mean) of 3 positive integers, x, y, and z, is [#permalink]
Bunuel wrote:
The average (arithmetic mean) of 3 positive integers, x, y, and z, is 20. If the average (arithmetic mean) of x and y is 9, what is the average (arithmetic mean) of y and z ?

(1) The average (arithmetic mean) of x and z is 22.5
(2) y = 5x

DS20412

Based on the information provided, we can conclude that z = 42. To determine the average of y and z, we need to figure out either the value of y or x.

(1) We're given the mean of x and z. Since we already have the value of z from the question stem, we can determine the value of x, which will then lead us to the mean of y and z. SUFFICIENT.

(2) $$y = 5x$$
$$\frac{6x}{2} = 9$$
$$6x = 18$$
$$x = 3$$

We can determine the mean of y and z. SUFFICIENT.

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Re: The average (arithmetic mean) of 3 positive integers, x, y, and z, is [#permalink]
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Re: The average (arithmetic mean) of 3 positive integers, x, y, and z, is [#permalink]
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