ps:m24 #21

Question

How to solve it?
GMATclub test24

cipher · Answer

IMO its should be C. These are equations for parabola, now trying substituting diff values of 'a' and try to make a figure out of it ( if a= +ve then you will get a figure some thing like this which is attached and if a=-ve then its mirror image)

I hope this helped else let me know I will elaborate.
Please confirm answer as well.

Cheers

IanStewart · Answer

Recall how we find intersection points - we just solve the two equations together. So really you're just trying to determine if ax^2 + b = cx^2 + d has any solutions, or equivalently, if (a - c)x^2 = d - b has any solutions, or perhaps most simply, if x^2 = (d-b)/(a-c) has any solutions. If the right side of this equation is zero or positive, we'll be able to find one or two values of x, respectively. If the right side is negative, there will be no solutions. So we can rephrase the question: is (d-b)/(a-c)  >  0?

Since we need to know about both the numerator and denominator of (d-b)/(a-c), neither statement is sufficient alone. Combining the statements, since c = -a, our fraction becomes (d-b)/(2a). From Statement 2, d-b is negative. Still, we don't know if a is positive or negative; if a is positive, the fraction is negative, and if a is negative, the fraction is positive. Insufficient.

Of course, if you recognize that these are equations of parabolas, you can use coordinate geometry principles to solve. S1 tells us that one parabola is rising, one falling. Statement 2 tells us that the first parabola has a higher vertex than the second. Still, we have two possibilities; if the first parabola is rising, and the second falling, they don't intersect. If the first parabola is falling and the second rising, they do. Insufficient.

All that said, the wording of the question is very bad - the equations in the question clearly do not define 'lines'; they define 'curves'.

sudeep · Answer

HI Nitish,

Right approach, but I think you missed the point when a is negative, it'll not be mirror image, but there will be two intersection(because Y intercepts didn't change)

So, correct answer is E.

cipher · Answer

Hi Sudeep,

I agree that when a is -ve it wont be the mirror image but I guess in that case also it won't intersect as d< b. So, I think the figure would be some thing like this. In this case the second parabola will be inside the first parabola but I think it won't intersect.

Cheers

sudeep · Answer

Nitish,

See this:

cipher · Answer

Thanks Sudeep, I got it now

ps:m24 #21

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