Bunuel wrote:
What is the value of (x - 2)(2 + y) ?
(1) xy = 6
(2) x + y = 5
Target question: What is the value of (x - 2)(2 + y) ? Statement 1: xy = 6 Let's TEST some values.
There are many values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 and y = 3. In this case, the answer to the target question is
(x - 2)(2 + y) = (2 - 2)(2 + 3) = 0Case b: x = 3 and y = 2. In this case, the answer to the target question is
(x - 2)(2 + y) = (3 - 2)(2 + 2) = 4Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x + y = 5Important: Noticed that I can use the same two pairs of values I used to show that statement 1 is not sufficient
That is....
Case a: x = 2 and y = 3. In this case, the answer to the target question is
(x - 2)(2 + y) = (2 - 2)(2 + 3) = 0Case b: x = 3 and y = 2. In this case, the answer to the target question is
(x - 2)(2 + y) = (3 - 2)(2 + 2) = 4Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
IMPORTANT: Notice that I was able to use the
same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: x = 2 and y = 3. In this case, the answer to the target question is
(x - 2)(2 + y) = (2 - 2)(2 + 3) = 0Case b: x = 3 and y = 2. In this case, the answer to the target question is
(x - 2)(2 + y) = (3 - 2)(2 + 2) = 4Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent