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Joined: 02 Sep 2009
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If x^2  2x  15 = 0 and x > 0, which of the following must
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03 Feb 2014, 00:16
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The Official Guide For GMAT® Quantitative Review, 2ND EditionIf x^2  2x  15 = 0 and x > 0, which of the following must be equal to 0 ? I. x^2  6x + 9 II. x^2 7x + 10 III. x^2  10x + 25 (A) I only (B) II only (C) III only (D) II and III only (E) I, II, and III Problem Solving Question: 72 Category: Algebra Seconddegree equations Page: 71 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Math Expert
Joined: 02 Sep 2009
Posts: 51218

Re: If x^2  2x  15 = 0 and x > 0, which of the following must
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03 Feb 2014, 00:16



Intern
Joined: 03 Feb 2014
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Re: If x^2  2x  15 = 0 and x > 0, which of the following must
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03 Feb 2014, 01:04
Remember the formula for second degree equations and solve for x(1) x(2): x(1) + x(2) =  (2) x(1)*x(2)= 15
x(1) = 3 X(2)= 5
Now given that x>0, x must be equal to 5. only II and III include a 5 given the last terms are 10 (II) and 25 (III). Hence, we have to check if they include a positive or negative 5. => The solution for II is 2, 5. Sufficient => The solution for III is 5, 5. Sufficient
Solution: D



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Re: If x^2  2x  15 = 0 and x > 0, which of the following must
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03 Feb 2014, 01:57
Can see from the first equation that: (x5)*(x+3)=0 And since x>0 than x=5 1) 2530 = 5 2) 2535+10 = 0 2) 2550+25 = 0 so D.
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Re: If x^2  2x  15 = 0 and x > 0, which of the following must
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03 Feb 2014, 10:23
Ans. D
x^2 2x  15=0 x^2  5x + 3x 15=0 (x+3)(x5)=0 x=5 (x=3 is not possible since x>0)
II and III statements have (x5) as factors therefore will be '0'.



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Re: If x^2  2x  15 = 0 and x > 0, which of the following must
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04 Feb 2014, 00:49
Solve x^2  2x  15 = 0: (x5)(x+3) = 0; x = 3, 5.
Since x is given as positive(x > 0), x = 5 is the valid one.
Substitute the value of x = 5 in the equations: I. 25  30 + 9 = 4#0; Reject. II. 25  35 + 10 = 0; Correct. III. 25  50 + 25 = 0; Correct.
II and III only.
Ans is (D).



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Re: If x^2  2x  15 = 0 and x > 0, which of the following must
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23 Feb 2018, 05:21
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