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kkrrsshh
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Is x > 0? 15 Feb 2018, 20:23
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33% (03:06) correct 67% (01:31) wrong based on 3 sessions

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Is x > 0?
(1) | 2x − 12 | < 10
(2) x^2 − 10x ≥ − 21

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(A): (1) SUFFICIENT: Manipulate the absolute value expression to represent this inequality on a number line: | 2x − 12 | < 10 | 2( x − 6) | < 10 2 | x − 6 | < 10 | x − 6 | < 5 This can be interpreted as “The distance between x and 6 is less than 5.” On a number line, this is the region between 1 and 11: All possible values for x are positive, so the answer to the question is a definite “Yes.” (2) INSUFFICIENT: Manipulate the inequality to get 0 on one side, thenfactor the resulting quadratic: x2 − 10x ≥ − 21 x2 − 10x + 21 ≥ 0 (x − 7)( x − 3) ≥ 0 The factored quadratic on the left side will equal 0 when x = 3 and 7. These are the boundary points. On a number line, check the regions on either side of these boundary points to determine the valid region( s) for x: Note that when 3 < x < 7, (x − 7)( x − 3) = (neg)( pos) = neg. Since both positive and negative values are possible for x, the answer is “Maybe.” The correct answer is (A).



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Is x > 0? 15 Feb 2018, 20:48
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kkrrsshh
Is x > 0?
(1) | 2x − 12 | < 10
(2) x^2 − 10x ≥ − 21

Show Spoiler
(A): (1) SUFFICIENT: Manipulate the absolute value expression to represent this inequality on a number line: | 2x − 12 | < 10 | 2( x − 6) | < 10 2 | x − 6 | < 10 | x − 6 | < 5 This can be interpreted as “The distance between x and 6 is less than 5.” On a number line, this is the region between 1 and 11: All possible values for x are positive, so the answer to the question is a definite “Yes.” (2) INSUFFICIENT: Manipulate the inequality to get 0 on one side, thenfactor the resulting quadratic: x2 − 10x ≥ − 21 x2 − 10x + 21 ≥ 0 (x − 7)( x − 3) ≥ 0 The factored quadratic on the left side will equal 0 when x = 3 and 7. These are the boundary points. On a number line, check the regions on either side of these boundary points to determine the valid region( s) for x: Note that when 3 < x < 7, (x − 7)( x − 3) = (neg)( pos) = neg. Since both positive and negative values are possible for x, the answer is “Maybe.” The correct answer is (A).
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Discussed here: is-x-152912.html Hope it helps.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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Bunuel
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