Bunuel wrote:
What is the value of x?
(1) 5x + 10y = 65
(2) 130 – 20y = 10x
Target question: What is the value of x? Statement 1: 5x + 10y = 65 All we have is ONE equation with TWO variables.
As such, there isn't just one unique solution for x.
Statement 1 is NOT SUFFICIENT
If you're not convinced, recognize that there are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 13 and y = 0. In this case, the answer to the target question is
x = 13Case b: x = 0 and y = 6.5. In this case, the answer to the target question is
x = 0Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 130 – 20y = 10x Once again, we have is ONE equation with TWO variables.
As such, there isn't just one unique solution for x.
Statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined We have the following system of linear equations.
5x + 10y = 65130 – 20y = 10xIf these two linear equations are DIFFERENT, then we have a system of TWO equations with TWO variables, which means we can solve the system for x and y.It turns out the equations are IDENTICAL.
Take:
130 – 20y = 10xAdd 20y to both sides:
130 = 10x + 20yDivide both sides by 2 to get :
65 = 5x + 10y, which is the SAME as
5x + 10y = 65So, in actuality, we have only ONE (unique) equation with TWO variables.
As such, there isn't just one unique solution for x.
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent