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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote If x^2 + 12x + 20 < 0, how many integer values can x be? tagged by: VJesus12 This topic has 1 expert reply and 0 member replies If x^2 + 12x + 20 < 0, how many integer values can x be? If x^2 + 12x + 20 < 0, how many integer values can x be? (A) 6 (B) 7 (C) 8 (D) 9 (E) 10 The OA is B. Hello experts. Do I need to get the solutions of the quadratic equation to know how many integers can x be? Is there another way to solve it? GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: If x^2 + 12x + 20 < 0, how many integer values can x be? (A) 6 (B) 7 (C) 8 (D) 9 (E) 10 The OA is B. Hello experts. Do I need to get the solutions of the quadratic equation to know how many integers can x be? Is there another way to solve it? Hi VJesus12, Let's take a look at your question. $$x^2+12x+20<0$$ $$x^2+2x+10x+20<0$$ $$x\left(x+2\right)+10\left(x+2\right)<0$$ $$\left(x+2\right)\left(x+10\right)<0$$ The product can only be negative if any one of the binomial is less than zero. There can be two cases: Case I: $$x+2>0,\ x+10<0$$ $$x>-2,\ x<-10$$ No value lie in this range. Case II: $$x+2<0,\ x+10>0$$ $$x<-2,\ x>-10$$ Therefore, values of x lie between -2 and -10 and both of end values will not include. The values of x will be: $$_{\left\{-3,\ -4,\ -5,\ -6,\ -7,\ -8,\ -9\right\}}$$ 7 values of x. Hence option B is correct. Hope it helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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