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04 May 2022, 02:00
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
71% (01:27) correct
29%
(01:53)
wrong
based on 106
sessions
History
Date
Time
Result
Not Attempted Yet
If x is a positive number, is x less than 1?
(1) \(x > \sqrt{x}\)
(2) \(−\sqrt{x} > −x\)
(1) \(x > \sqrt{x}\)
(2) \(−\sqrt{x} > −x\)
04 May 2022, 07:05
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Bunuel
Key properties:
Property #1: If \(0 < x < 1\), then \(x < \sqrt{x}\). For example, \(\frac{1}{4} < \sqrt{\frac{1}{4}}\)
Property #2: If \(x > 1\), then \(x > \sqrt{x}\). For example, \(9 > \sqrt{9}\)
Target question: Is x less than 1?
Statement 1: \(x > \sqrt{x}\)
This statement is identical to Property #2, which means x > 1
So, the answer to the target question is NO, x is not less than 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: \(−\sqrt{x} > −x\)
Multiply both sides of the inequality by \(-1\) to get: \(\sqrt{x} < x\) [Whenever we multiply both sides of an inequality by a negative value, we must REVERSE the direction of the inequality symbol]
Since the resulting inequality is identical to the statement 1 inequality, statement 2 must also be SUFFICIENT
Answer: D
Cheers,
Brent
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