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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 ## Algebra tagged by: Brent@GMATPrepNow ##### This topic has 3 expert replies and 0 member replies ## Algebra If $$\left(3+a\right)\left(\frac{a}{10}-0.4\right)=-1$$ , then a could be A. -4 B. -2 C. 1 D. 2 E. 4 What is the correct solution to this to get the right Option? Can any expert help out here? ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13046 messages Followed by: 1252 members Upvotes: 5254 GMAT Score: 770 Roland2rule wrote: If $$\left(3+a\right)\left(\frac{a}{10}-0.4\right)=-1$$ , then a could be A. -4 B. -2 C. 1 D. 2 E. 4 The decimals make this equation hard to solve . So, let's first multiply both sides by 10. We get: (3 + a)(10)(a/10 - 0.4) = (10)(-1) Expand to get: (3 + a)(a - 4) = -10 Expand and simplify to get: aÂ² - a - 12 = -10 Add 10 to both sides: aÂ² - a - 2 = 0 Factor: (a - 2)(a + 1) = 0 So EITHER a = 2 OR a = -1 Check the answer choices.... Answer: D Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hi Roland2rule, Lets take a look at your question. $$\left(3+a\right)\left(\frac{a}{10}-0.4\right)=-1$$ In the first step, we will simplify the equation, $$\left(3+a\right)\left(\frac{a-4}{10}\right)=-1$$ Multiply both sides of the equation by 10, $$\left(3+a\right)\left(a-4\right)=-1\left(10\right)$$ $$\left(3+a\right)\left(a-4\right)=-10$$ Simplify the left hand side by multiplying the binomials, $$3a-12+a^2-4a=-10$$ $$-a-12+a^2=-10$$ $$-a-12+a^2+10=0$$ $$a^2-a-2=0$$ Factorizing by grouping, $$a^2-2a+a-2=0$$ $$a\left(a-2\right)+1\left(a-2\right)=0$$ $$\left(a-2\right)\left(a+1\right)=0$$ $$Either\ \left(a-2\right)=0\ or\ \left(a+1\right)=0$$ $$Either\ a=2\ or\ a\ =\ -1$$ If we see on the options given, we can only find 2 in the answer choices. Therefore, Option D is correct. 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. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 497 members Upvotes: 2867 GMAT Score: 800 Hi Roland2rule, This question can be solved by TESTing THE ANSWERS. You can also take advantage of a particular Number Property to help you eliminate some of the answer choices. Since the product of the two parentheses is -1, one of those parentheses has to be POSITIVE while the other is NEGATIVE. (3+A)(A/10 - .4) = -1 Answer A will make BOTH negative, while Answer E will make the second one equal 0. Thus, you can eliminate both of those options. From the remaining 3 choices, you just have to 'plug in' until you find the match. Based on these 3 remaining answers, the second parenthesis will be a one-decimal-place FRACTION, and the sum in the first will either be 1, 4 or 5, the correct answer will likely be the 5 (since we need the product to be an integer). TEST A=2 and you'll have your match. Final Answer: D GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • Award-winning private GMAT tutoring Register now and save up to$200

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