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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 Equation Problem This topic has 1 expert reply and 3 member replies What is the value of K if y ^2 - 12y + k = 0? (1) One root of the equation is 3. (2) One root of the equation is 6 more than the other. _________________ Philosophers have interpreted world in various ways, the point is to change it! Legendary Member Joined 20 Jun 2007 Posted: 1153 messages Followed by: 2 members Upvotes: 146 Target GMAT Score: V50 ritula wrote: What is the value of K if y ^2 - 12y + k = 0? (1) One root of the equation is 3. (2) One root of the equation is 6 more than the other. y^2 - 12y +k = 0 Statement I one root is 3 3^2 - 12*3 +k = 0 9 - 36 + k = 0 k = 36-9 = 27 Sufficient. Statement II One root is 6 more than the other. We can have infinite values for k. Therefore insufficient. Hence A is the answer. GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2475 messages Followed by: 351 members Upvotes: 1090 GMAT Score: 780 If a and b are the roots of the equation, then (y-a)(y-b) = y^2 - 12y + k so -a - b = - 12, and (-a)(-b) = k. Rewriting these, we have: a + b = 12 ab = k From 1), we can plug in b = 3 to find that a = 9, k = 27. From 2) we can plug in b = a - 6 to find that a = 9, b = 3, and k = 27. D. _________________ If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com Master | Next Rank: 500 Posts Joined 23 Jun 2008 Posted: 172 messages Followed by: 1 members Upvotes: 3 [quote="Ian Stewart"]so -a - b = - 12, and (-a)(-b) = k. Rewriting these, we have: a + b = 12 ab = k quote] How did you go from -a-b=-12 & (-a)(-b)=k? Thanks. Senior | Next Rank: 100 Posts Joined 23 Jun 2008 Posted: 35 messages Upvotes: 2 Re:[quote="Ian Stewart"]so -a - b = - 12, and (-a)(-b) = k. Rewriting these, we have: a + b = 12 ab = k quote] How did you go from -a-b=-12 & (-a)(-b)=k? Thanks.] These are standard Vi�te's formulas. x1+x2 = -b/a x1.x2 = c/a where x1,x2 are roots of euqations ax^2+bx+c=0 • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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