ruwan_s wrote:What is x?
1) x = 4y - 4
2) xy = 8
In Mitch's approach, he replaced x with 4y-4 and solved for y (and then solved for x)
Another approach is to replace the y-value and then solve for x.
Here's what I mean....
Target question: What is the value of x?
Statement 1: x = 4y - 4
This statement doesn't
FEEL sufficient, so I'm going to TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: y = 1 and x = 0. In this case
x = 0
Case b: y = 2 and x = 4. In this case
x = 4
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: xy = 8
This statement doesn't feel sufficient either. So, let's test some values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: y = 1 and x = 8. In this case
x = 8
Case b: y = 2 and x = 4. In this case
x = 4
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 2: xy = 8
Solve
for y, to get:
y = 8/x
Statement 1: x = 4y - 4
Replace y with
8/x to get: x = 4(
8/x) - 4
Now, we need only solve for x
Simplify to get: x = 32/x - 4
Multiply both sides by x to get: x² = 32 - 4x
Rearrange to get: x² + 4x - 32 = 0
Factor: (x + 8)(x - 4) = 0
So,
x = -8 OR
x = 4
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer =
E
Cheers,
Brent
