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 _________________
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05 Jun 2022, 07:58
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