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

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The average (arithmetic mean) of 3 positive integers, x, y, and z, is [#permalink] The average (arithmetic mean) of 3 positive integers, x, y, and z, is   23 May 2020, 08:38
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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
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Re: The average (arithmetic mean) of 3 positive integers, x, y, and z, is [#permalink] The average (arithmetic mean) of 3 positive integers, x, y, and z, is   23 May 2020, 09:21
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Bunuel
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

Question: \(\frac{y+z}{2} =\) ?

Given: x+y+z = 20*3 = 60 and x+y = 18 i.e. z = 42

So we need either x or y to answer the question

Statement 1: x+z = 45

i.e. x = 3
i.e. y = 15

SUFFICIENT

Statement 2: y = 5x

x+y = 18
i.e. 6x = 18 and x = 3
i.e. y = 15

SUFFICIENT

Answer: Option D
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Re: The average (arithmetic mean) of 3 positive integers, x, y, and z, is [#permalink] The average (arithmetic mean) of 3 positive integers, x, y, and z, is   24 May 2020, 05:51
Bunuel
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


Given x + y + z = 60.
x + y = 18
y + z = ?

Statement 1: The average (arithmetic mean) of x and z is 22.5
=> x + z = 45
=> y = 15.
=> x = 3
=> z = 42.
Since we have all the values, we can easily calculate the value of y+ z, thus, the average of the same.

So Sufficient.



Statement 2: y = 5x.
x + y = 18
=> 6x = 18.
=> x = 3.
=> y = 15.
=> z = 42.
Since we have all the values, we can easily calculate the value of y+ z, thus, the average of the same.

So Sufficient.


Answer D.
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Re: The average (arithmetic mean) of 3 positive integers, x, y, and z, is [#permalink] The average (arithmetic mean) of 3 positive integers, x, y, and z, is   25 May 2020, 13:48
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

D
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Re: The average (arithmetic mean) of 3 positive integers, x, y, and z, is [#permalink] The average (arithmetic mean) of 3 positive integers, x, y, and z, is   26 Nov 2020, 17:50
Bunuel
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.

Answer is D.
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Re: The average (arithmetic mean) of 3 positive integers, x, y, and z, is [#permalink] The average (arithmetic mean) of 3 positive integers, x, y, and z, is   21 Nov 2022, 10:51
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Re: The average (arithmetic mean) of 3 positive integers, x, y, and z, is [#permalink]
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