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# Which of following satisfies the inequality (2x-49)(x^2+6x+10) < 0?

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Math Revolution GMAT Instructor
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Which of following satisfies the inequality (2x-49)(x^2+6x+10) < 0?  [#permalink]

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01 Mar 2019, 00:58
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91% (01:22) correct 9% (01:46) wrong based on 43 sessions

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[GMAT math practice question]

Which of following satisfies the inequality $$(2x-49)(x^2+6x+10) < 0$$?

$$A. 24$$
$$B. 25$$
$$C. 50$$
$$D. 51$$
$$E. 99$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 8006 Re: Which of following satisfies the inequality (2x-49)(x^2+6x+10) < 0? [#permalink] ### Show Tags 01 Mar 2019, 01:16 MathRevolution wrote: [GMAT math practice question] Which of following satisfies the inequality $$(2x-49)(x^2+6x+10) < 0$$? $$A. 24$$ $$B. 25$$ $$C. 50$$ $$D. 51$$ $$E. 99$$ All choices are positive, so $$(x^2+6x+10)>0$$ for all positive x... For $$(2x-49)(x^2+6x+10) < 0$$, 2x-49<0 as $$(x^2+6x+10)>0$$. So, 2x-49<0....2x<49...x<49/2 or x<24.5 Only 24 is in the range .. A _________________ VP Joined: 31 Oct 2013 Posts: 1465 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) Re: Which of following satisfies the inequality (2x-49)(x^2+6x+10) < 0? [#permalink] ### Show Tags 01 Mar 2019, 01:31 MathRevolution wrote: [GMAT math practice question] Which of following satisfies the inequality $$(2x-49)(x^2+6x+10) < 0$$? $$A. 24$$ $$B. 25$$ $$C. 50$$ $$D. 51$$ $$E. 99$$ Either (2x - 49) or $$(x^2 + 6x + 10)$$ must be negative. but if you scan the answer choices , you see that there is no negative answer choices. Thus, $$( x^2 + 6x + 10)$$ can not be negative in this case. So, (2x - 49) is negative. 2x - 49<0 2x <49 scanning the option it's visible that only available value of x is 24. 2*24 <49. The correct answer is A. Senior Manager Joined: 04 Aug 2010 Posts: 477 Schools: Dartmouth College Re: Which of following satisfies the inequality (2x-49)(x^2+6x+10) < 0? [#permalink] ### Show Tags 01 Mar 2019, 05:44 MathRevolution wrote: [GMAT math practice question] Which of following satisfies the inequality $$(2x-49)(x^2+6x+10) < 0$$? $$A. 24$$ $$B. 25$$ $$C. 50$$ $$D. 51$$ $$E. 99$$ The two factors must have DIFFERENT SIGNS. Each of the answer choices will yield a positive value for x² + 6x + 10. Thus, the correct answer must yield a negative value for 2x-49. Only A is viable: (2*24) - 49 = -1 . _________________ GMAT and GRE Tutor Over 1800 followers GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8027 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of following satisfies the inequality (2x-49)(x^2+6x+10) < 0? [#permalink] ### Show Tags 03 Mar 2019, 18:36 => $$x^2+6x+10 = x^2+6x+9 + 1 = (x+3)^2+1 ≥ 1 > 0$$. Since $$x^2+6x+10 > 0$$, we have $$(2x-49)(x^2+6x+10) ≤ 0$$, which implies that $$2x – 49 < 0$$. So, $$2x < 49$$, and $$x < 24.5.$$ Therefore, the answer is A. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: Which of following satisfies the inequality (2x-49)(x^2+6x+10) < 0?   [#permalink] 03 Mar 2019, 18:36
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# Which of following satisfies the inequality (2x-49)(x^2+6x+10) < 0?

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