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# In the x-y plane, y = f(x) = ax^2+bx+c passes through (1,0) an

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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In the x-y plane, y = f(x) = ax^2+bx+c passes through (1,0) an  [#permalink]

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06 Jul 2018, 01:43
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Difficulty:

85% (hard)

Question Stats:

17% (01:51) correct 83% (01:43) wrong based on 23 sessions

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[GMAT math practice question]

In the x-y plane, $$y = f(x) = ax^2+bx+c$$ passes through $$(1,0)$$ and $$(2,0)$$. Is $$f(3)>0?$$

$$1) a > 0$$
$$2) f(0) > 0$$

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The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 04 Aug 2010 Posts: 278 Schools: Dartmouth College Re: In the x-y plane, y = f(x) = ax^2+bx+c passes through (1,0) an [#permalink] ### Show Tags 06 Jul 2018, 04:08 MathRevolution wrote: [GMAT math practice question] In the x-y plane, $$y = f(x) = ax^2+bx+c$$ passes through $$(1,0)$$ and $$(2,0)$$. Is $$f(3)>0?$$ $$1) a > 0$$ $$2) f(0) > 0$$ $$f(x) = ax^2+bx+c$$ will be a U-shaped parabola if a>0. $$f(x) = ax^2+bx+c$$ will be a -shaped parabola if a<0. Since $$f(x) = ax^2+bx+c$$ has x-intercepts at (1, 0) and (2, 0), $$f(3)>0$$ if the parabola is U-shaped. Question stem, rephrased: Is the parabola U-shaped? Statement 1: Since a>0, the parabola is U-shaped. SUFFICIENT. Statement 2: x=0 is to the LEFT of the x-intercept at (1, 0). Since x=0 yields a POSITIVE y-value, the parabola must be U-shaped. SUFFICIENT. _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6242 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: In the x-y plane, y = f(x) = ax^2+bx+c passes through (1,0) an [#permalink] ### Show Tags 08 Jul 2018, 04:17 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. Since f(x) passes through (1,0) and (2,0), 1 and 2 are roots of f(x) and we have f(x) = a(x-1)(x-2). If f(x) is concave up, then f(3) > 0. Thus, knowing that f(x) is concave up will allow us to answer the question. In addition, since we have 3 variables (a, b, c) and 2 conditions, D is most likely to be the answer. Condition 1) If a > 0, then f(x) is concave up. Thus, condition 1) is sufficient. Condition 2) Since 1 and 2 are roots of f(x) = 0, f(0) > 0 implies that f(x) is concave up. Thus, condition 2) is sufficient, too. Therefore, D is the answer. Answer: D Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2). _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: In the x-y plane, y = f(x) = ax^2+bx+c passes through (1,0) an &nbs [#permalink] 08 Jul 2018, 04:17
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# In the x-y plane, y = f(x) = ax^2+bx+c passes through (1,0) an

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