Bunuel wrote:
5x + 3y = 17, what is the value of x?
(1) x is a positive integer
(2) y = 4x
Target question: What is the value of x? Given: 5x + 3y = 17 Statement 1: x is a positive integer Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 1 and y = 4 (these values satisfy the given equation,
5x + 3y = 17). In this case, the answer to the target question is
x = 1Case b: x = 2 and y = 7/3 (these values satisfy the given equation,
5x + 3y = 17). In this case, the answer to the target question is
x = 2Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y = 4xWhen we add this equation to the given equation
5x + 3y = 17, we have a system of two linear equations with 2 variables. Since we COULD solve that system for x and y, we COULD answer the
target question with certainty.
So, statement 2 is SUFFICIENT
If you're not convinced, take
5x + 3y = 17 and replace y with 4x to get:
5x + 3(4x) = 17Expand:
5x + 12x = 17Simplify:
17x = 17 Solve:
x = 1So, the answer to the target question is
x = 1Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
_________________