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# For which value of x will y=ax^2+100x+b have a maximum in the xy-pla

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 800 Q59 V59
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For which value of x will y=ax^2+100x+b have a maximum in the xy-pla [#permalink]

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28 Nov 2017, 00:55
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[GMAT math practice question]

For which value of x will $$y=ax^2+100x+b$$ have a maximum in the $$xy$$-plane?

1) $$b=100$$
2) $$a=-4$$
[Reveal] Spoiler: OA

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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 $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" PS Forum Moderator Joined: 25 Feb 2013 Posts: 1018 Location: India GPA: 3.82 For which value of x will y=ax^2+100x+b have a maximum in the xy-pla [#permalink] ### Show Tags 28 Nov 2017, 09:56 3 This post received KUDOS 2 This post was BOOKMARKED MathRevolution wrote: [GMAT math practice question] For which value of x will $$y=ax^2+100x+b$$ have a maximum in the $$xy$$-plane? 1) $$b=100$$ 2) $$a=-4$$ The maximum or minimum value of a quadratic function $$ax^2+bx+c$$ occurs at $$x=-\frac{b}{2a}$$ so if $$a>0$$ then minima will occur and the parabola will open upwards and if $$a<0$$ then maxima will occur and the parabola will open downwards so for $$y=ax^2+100x+b$$ maxima will be at $$x=-\frac{100}{2a}$$ where $$a<0$$ Statement 1: no information about $$a$$. Insufficient Statement 2: provides the value of $$a$$. Sufficient Option B Alternatively, we can use derivative (out of scope for GMAT) $$y=ax^2+100x+b$$ so $$\frac{dy}{dx} = 2ax+100$$ maximum point will be $$\frac{dy}{dx}=0 => 2ax+100=0$$ so $$x=-\frac{100}{2a}$$. We need the value of $$a$$ to get the maximum point. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5079 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: For which value of x will y=ax^2+100x+b have a maximum in the xy-pla [#permalink] ### Show Tags 30 Nov 2017, 01:19 => 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, and then recheck the numbers of variables and equations. We can modify the original condition and question as follows: If $$a < 0$$, the function will have a maximum at $$x = \frac{(-100)}{(2a)} = \frac{(-50)}{a}$$. If $$a > 0$$, the function has no maximum. So, to answer the question, we need to find the value of a. Thus, condition 2) is sufficient. Note: condition 1) cannot be sufficient as it provides no information about the value of a. Therefore, the answer is B. Answer: B _________________ 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$79 for 3 month Online Course"
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Re: For which value of x will y=ax^2+100x+b have a maximum in the xy-pla   [#permalink] 30 Nov 2017, 01:19
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