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What is the value of x - z? (1) The arithmetic average of x and y is

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Bunuel
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What is the value of x - z? (1) The arithmetic average of x and y is [#permalink] What is the value of x - z? (1) The arithmetic average of x and y is   13 Apr 2018, 01:15
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75% (00:46) correct 25% (01:02) wrong based on 104 sessions
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What is the value of x - z?

(1) The arithmetic average of x and y is 55.
(2) The arithmetic average of y and z is 80.
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C
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Re: What is the value of x - z? (1) The arithmetic average of x and y is [#permalink] What is the value of x - z? (1) The arithmetic average of x and y is   13 Apr 2018, 01:34
Bunuel wrote:
What is the value of x - z?

(1) The arithmetic average of x and y is 55.
(2) The arithmetic average of y and z is 80.


we are looking for the value of x-z.

statement 1: x+y/2=55
x+y=110....................equation 1

no information about z. not sufficient

statement 2: y+z/2=80
y+z=160.........................equation 2

No information regarding x is given. Not sufficient.

deduction equation 1 from equation 2: x+y-y-z=160-110=50

Thus both statement together is sufficient. Correct answer is C.
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BrentGMATPrepNow
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Re: What is the value of x - z? (1) The arithmetic average of x and y is [#permalink] What is the value of x - z? (1) The arithmetic average of x and y is   25 Mar 2020, 06:31
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Bunuel wrote:
What is the value of x - z?

(1) The arithmetic average of x and y is 55.
(2) The arithmetic average of y and z is 80.


Target question: hat is the value of x - z?

Statement 1: The arithmetic average of x and y is 55.
Since we have no information about \(z\), there's no way to answer the target question with certainty
NOT SUFFICIENT

Statement 2: The arithmetic average of y and z is 80
No information about \(x\)
NOT SUFFICIENT

Statements 1 and 2 combined
From statement 1, we can write: \(\frac{x+y}{2}=55\)
Multiply both sides of the equation by 2 to get: \(x+y=110\)

From statement 2, we can write: \(\frac{z+y}{2}=80\)
Multiply both sides of the equation by 2 to get: \(z+y=160\)

So we now have the following system of equations:
\(x+y=110\)
\(z+y=160\)

From here, if we subtract the bottom equation from the top equation we get: \(x-z=-50\)

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

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Brent
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Re: What is the value of x - z? (1) The arithmetic average of x and y is [#permalink]
25 Mar 2020, 06:31
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Bunuel
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