Bunuel wrote:
What is the value of \(8x + y\)?
(1) \(3x – 2y + z = 10\)
(2) \(2(x + 3y) – (y + 2z) = –25\)
Target question: What is the value of \(8x + y\)? Statement 1: \(3x – 2y + z = 10\) Notice that z can have infinitely many values, and each of those z-values will change the values of x and y, making it impossible to answer the
target questionStatement 1 is NOT SUFFICIENT
Statement 2: \(2(x + 3y) – (y + 2z) = –25\)When we apply the same logic we applied for statement 1, we can conclude that statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined From the two statements we have the following system pf equations:
(1) \(3x – 2y + z = 10\)
(2) \(2(x + 3y) – (y + 2z) = –25\)
Simplify equation (2) as follows:
(1) \(3x – 2y + z = 10\)
(2) \(2x + 5y - 2z = –25\)
In order to eliminate the z-terms, let's take equation (1) and multiply both sides by 2 to get the following equivalent equation:
(1) \(6x – 4y + 2z = 20\)
(2) \(2x + 5y - 2z = –25\)
From here, something nice happens when we add the two equations.
We get:
\(8x + y = 5\)Since we can’t answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: C
Cheers,
Brent