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11 Jun 2018, 02:47
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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:
35%
(medium)
Question Stats:
69% (01:28) correct
31%
(01:46)
wrong
based on 39
sessions
History
Date
Time
Result
Not Attempted Yet
11 Jun 2018, 02:47
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Official Solution:
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.
Modifying the question:
\(x^3 - x^2 + x < 0\)
⇔ \(x(x^2 - x + 1) < 0\)
⇔ \(x < 0\) since \(x^2 - x + 1 > 0\) always.
So, the question becomes, 'is \(x < 0?\)'.
Condition 1) is certainly sufficient.
Condition 2), \(x^5 + x < 0\), is equivalent to \(x(x^4 + 1) < 0\) or \(x < 0\), since \(x^4 + 1 > 0\) is always true. So, condition 2) is also sufficient.
Therefore, D is the answer.
Answer: D
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.
Modifying the question:
\(x^3 - x^2 + x < 0\)
⇔ \(x(x^2 - x + 1) < 0\)
⇔ \(x < 0\) since \(x^2 - x + 1 > 0\) always.
So, the question becomes, 'is \(x < 0?\)'.
Condition 1) is certainly sufficient.
Condition 2), \(x^5 + x < 0\), is equivalent to \(x(x^4 + 1) < 0\) or \(x < 0\), since \(x^4 + 1 > 0\) is always true. So, condition 2) is also sufficient.
Therefore, D is the answer.
Answer: D
13 Sep 2018, 04:14
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Didnt understand this part - ⇔ x<0x<0 since x2−x+1>0x2−x+1>0 always. How is x2−x+1>0 ?
Please can someone explain ?
Please can someone explain ?
