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Difficulty:
55%
(hard)
Question Stats:
51% (01:42) correct
49%
(01:27)
wrong
based on 52
sessions
History
Date
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Not Attempted Yet
11 Jul 2017, 01:41
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Is x greater than zero?
(1) \(x^6>x^2\). First of all notice that this implies that \(x \neq 0\). Next, since x^2 is always non-negative (and in this case because \(x \neq 0\), x^2 is positive), we can safely divide the entire inequality by x^2 and we'll get: \(x^4 > 1\). Taking the 4th root from both sides will give us |x| > 1, so x > 1 or x < -1. Not sufficient.
(2) \(x^5<x^2\). By the similar logic after reducing by x^2 we'll get: \(x^3 < 1\), which is the same as \(x < 1\) (\(x \neq 0\)). Not sufficient.
(1)+(2) Intersection of the ranges from the statements is x < -1, so the answer to the question whether x is greater than zero is a definite NO. Sufficient.
Answer: C.
Hope it's clear.
(1) \(x^6>x^2\). First of all notice that this implies that \(x \neq 0\). Next, since x^2 is always non-negative (and in this case because \(x \neq 0\), x^2 is positive), we can safely divide the entire inequality by x^2 and we'll get: \(x^4 > 1\). Taking the 4th root from both sides will give us |x| > 1, so x > 1 or x < -1. Not sufficient.
(2) \(x^5<x^2\). By the similar logic after reducing by x^2 we'll get: \(x^3 < 1\), which is the same as \(x < 1\) (\(x \neq 0\)). Not sufficient.
(1)+(2) Intersection of the ranges from the statements is x < -1, so the answer to the question whether x is greater than zero is a definite NO. Sufficient.
Answer: C.
Hope it's clear.
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