BrentGMATPrepNow wrote:
Is \(\frac{x^2}{y} > 0\)
(1) \(-4 < x < 1\)
(2) \(1 < y < 4\)
No takers?
Target question: Is \(\frac{x^2}{y} > 0\)
[b] Statement 1: \(-4 < x < 1\) There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = -1 and y = 2. In this case, the answer to the target question is
YES, \(\frac{x^2}{y}\) is greater than 0Case b: x = 0 and y = 2. In this case, the answer to the target question is
NO, \(\frac{x^2}{y}\) is not greater than 0Since we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: \(1 < y < 4\) This statement also seems insufficient.
TIP: Rather than come up with new counterexamples, check whether we can repurpose the pairs of values we used for statement 1.Since the counter-examples we used in statement 1 also satisfy statement 2, let's reuse them.
Case a: x = -1 and y = 2. In this case, the answer to the target question is
YES, \(\frac{x^2}{y}\) is greater than 0Case b: x = 0 and y = 2. In this case, the answer to the target question is
NO, \(\frac{x^2}{y}\) is not greater than 0Since we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined 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 = -1 and y = 2. In this case, the answer to the target question is
YES, \(\frac{x^2}{y}\) is greater than 0Case b: x = 0 and y = 2. In this case, the answer to the target question is
NO, \(\frac{x^2}{y}\) is not greater than 0Since we can’t answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E _________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant scores NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing -
Learn more