Brent@GMATPrepNow wrote:Is 2 < xy < 20?
(1) -2 < x < 4
(2) -1 < y < 5
Target question: Is 2 < xy < 20?
Statement 1: -2 < x < 4
Since we have no information about the value of y, there's no way to the
target question with certainty.
So, statement 1 is NOT SUFFICIENT
Statement 2: -1 < y < 5
There are several values of x and y that satisfy statement 2. Here are two:
Since we have no information about the value of y, there's no way to the
target question with certainty.
So, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that -2 < x < 4
Statement 2 tells us that -1 < y < 5
ASIDE: some students will attempt to combine the two inequalities by multiplying the 3 parts to get: 2 < xy < 20. However, doing this does not necessarily yield a new inequality that is accurate. In fact, if we do this here, we'll arrive at the wrong answer.
To see why, let's TEST some numbers.
There are several values of x and y that satisfy BOTH statements. Here are two:
Case a: x = 3 and y = 4. In this case, xy = (3)(4) = 12. So, the answer to the target question is
YES, it IS the case that 2 < xy < 20
Case b: x = 0 and y = 0. In this case, xy = (0)(0) = 0. So, the answer to the target question is
NO, it is NOT the case that 2 < xy < 20
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
