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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 ## cd? ##### This topic has 1 expert reply and 4 member replies Is the product of cd positive? 1) 3c= -8d^3 2) d> c + 4 OA is A Master | Next Rank: 500 Posts Joined 03 Jun 2012 Posted: 101 messages Followed by: 1 members Upvotes: 10 Prepare a table for 1) and check for all signs for c and d c 3c d -8d^3 - - - + + + + - + + - + - - + - You can see that 3c = -8d^3 only if the signs of c and d are different. So cd will not be positive for 1). Consider 2) d > c +4 Let d = 6 and c = 1 6 > 1 + 4 Let d = 6 and c = -1 6 > -1 + 4 So c and d can have same sign or different signs. Therefore we do not know cd is +ve or -ve. Choose A Master | Next Rank: 500 Posts Joined 03 Jun 2012 Posted: 101 messages Followed by: 1 members Upvotes: 10 Sorry I always go wrong in aligning. Please prepare the table in your notebook and you will understand Master | Next Rank: 500 Posts Joined 16 Nov 2011 Posted: 435 messages Followed by: 16 members Upvotes: 48 grandh01 wrote: Is the product of cd positive? 1) 3c= -8d^3 2) d> c + 4 For questions like this, the easiest thing to do (in my opinion) is just plug in simple numbers. QUESTION: is cd positive? For cd to be positive that means they have to have the same sign (++ or --) STATEMENT ONE: 3c=-8d^3 Solve for either c or d^3. we get: -(8/3)*c = d^3. Now say c=1, plug and go. If c=1 than d^3= -(8/3) You don't need to solve for D. Just notice when c is +, D is -. That means CD = a - number. Remember any number x raised to an odd number (ie x^3) preserves the sign of x. This statement is sufficient. STATEMENT TWO: d> c + 4 This doesn't really help if c is -3, then d is +, but if c is -100, then d is -. We don't know for sure, insufficient. The correct answer is thus A. Hope this helps _________________ A useful website I found that has every quant OG video explanation: https://www.beatthegmat.com/useful-website-with-og-video-explanations-t112985.html#475231 Junior | Next Rank: 30 Posts Joined 09 Jul 2011 Posted: 24 messages Upvotes: 2 Target GMAT Score: 750 Here we go, lets start fith the 2nd option that seems prettier:-) 2. d>c+4, let c=-1 then d>3, hence cd<0 let c=0 then d>4, hence cd=0 let c=2 then d>6, hence cd>0 Thus, Cross B and D out as the 2nd option is Insufficient 1. 3C=-8D^3, here we get -0.375*C = D^3 Obviously the only way for the equation set forth above to be veracious C and D must have different signs. For example, let C=1000---->>>>>> D^3 = -375, hence cd<0 let C=-100 -->>>>>>> D^3 = 37.5, hence cd<0 From above we might conclude that the answer can be (A) Please, correct me if I went awry _________________ Life begins at the End of your Comfort Zone... ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13043 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 grandh01 wrote: Is the product of cd positive? 1) 3c = -8d^3 2) d > c + 4 OA is A Target question: Is the product cd positive? Statement 1: 3c = -8d³ Divide both sides by d to get: 3c/d = -8d² Divide both sides by 3 to get: c/d = -8d²/3 Rewrite as: c/d = (-8/3)(d²) Since d² is greater than or equal to zero for all values of d, and since -8/3 is NEGATIVE, we can rewrite our equation as: c/d = (NEGATIVE)(some number greater than or equal to zero) (NEGATIVE)(some number greater than or equal to zero) = some number that is less than or equal to zero So, c/d = some number less than or equal to zero This means the quotient c/d CANNOT be positive It also mean the product cd CANNOT be positive Since we can answer the target question with certainty, statement 1 is SUFFICIENT ASIDE: the important concept here is that, if c/d is positive, then cd is also positive. Likewise, if c/d is negative, then cd is also negative. Statement 2: d > c + 4 There are several values of c and d that satisfy statement 2. Here are two: Case a: c = 1 and d = 10. Here, cd = (1)(10) = 10, so the answer to the target question is YES, cd IS positive Case b: c = -1 and d = 5. Here, cd = (-1)(5) = -5, so the answer to the target question is NO, cd is NOT positive Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer: A Cheers, Brent _________________ Brent Hanneson – 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 GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! • FREE GMAT Exam Know how you'd score today for0

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