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 80No 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
Cheers,
Brent
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