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08 Jul 2020, 04:42
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E
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Difficulty:
65%
(hard)
Question Stats:
57% (02:07) correct
43%
(02:29)
wrong
based on 102
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If \(x ≠ −√3\) or \(√3\), is \(\frac{3}{x^2 − 3} > 0\) ?
(1) \(\frac{1}{x^2} > 0\)
(2) \(\frac{−2}{x^2 − 2} < 0\)
Are You Up For the Challenge: 700 Level Questions
(1) \(\frac{1}{x^2} > 0\)
(2) \(\frac{−2}{x^2 − 2} < 0\)
Are You Up For the Challenge: 700 Level Questions
ArunSharma12
Joined: 25 Oct 2015
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08 Jul 2020, 06:48
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Bunuel
\(\frac{3}{x^2 − 3} > 0\)
\(x^2 − 3 > 0\) ?
x > 1.7 or x < -1.7?
statement 1: \(\frac{1}{x^2} > 0\)
\(x^2 > 0\) ; x can be anything
not sufficient
statement 2:\(\frac{−2}{x^2 − 2} < 0\)
\(x^2 − 2 > 0\)
x > 1.4 or x < -1.4
x can be 1.5 or 1.8.
not sufficient
combining both statements,
x > 1.4 or x < -1.4
not sufficient
Ans: E
08 Jul 2020, 11:51
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Bunuel
We are asking if a fraction is greater than 0, the numerator is confirmed positive so we only need the denominator to be positive as well to ensure the entire fraction is positive.
Hence we can simplify the question to "is \(x^2 - 3 > 0\)?"
If we keep simplifying we get "is \(x > \sqrt{3}\) or \(x < -\sqrt{3}\)?"
Statement 1:
Using the same logic, we can deduct \(x^2 > 0\). This does not guarantee \(x^2 > 3\) so this is insufficient. In fact, this only tells us x cannot be 0 which is very minimal information.
Statement 2:
We need the fraction to be negative now, so we must have negative/positive < 0, the denominator here must be positive.
We get \(x^2 > 2\) but we run into the same problem in statement 1. Insufficient.
Combined:
Since both statements share the same problem combining is insufficient. We only know \(x^2 > 2\) combined but that is not enough to guarantee \(x^2 > 3\).
Ans: E
