M24 #12 - formatting error

Do lines y = ax^2 + b and y = cx^2 + d cross?

1. a = -c
2. b \gt d


Source: GMAT Club Tests - hardest GMAT questions

What am I supposed to do w/ #2?

Do the lines cross is another way of asking if they are parallel.

Statement 1 is sufficient. We know that if a = 1 and -c = a, then c = -1. These are not parallel. Also keep in mind the forumula for a line. Is y = [slope]x + [y-intercept] (or minus y-intercept).

Statement 2 is telling us information about the y-intercept. It is saying that no matter what d is, b is greater than d. This doesn't tell us any information about a or c, which are the most important because these two variables determine the slope of the line. Without knowing the slope of the lines, we cannot know if the lines cross.

Answer is A, and the anwer with the info in A is "Yes, the lines do cross."

I posted this during the rendering engine problem and (2) showed up as bd instead of b>d.

Thanks for the help, though.

what if a and c are both 0??? then we can't confidently say that the lines will cross. I think it should be E.

You guys might have forgotten that we are dealing with quadratic equations here. The upward and downward parabolas may not cross even if the "slope" is different for the two equations. See the OE for more info.

The right answer is E.

A

We can rewrite the question as 'are two lines y=ax^2+b and y=cx^2+d NOT parralel?'
They can be parralel only if have the same slope.

1) Slopes are different, so lines must cross, Suff.
2) there is no info about slopes, Insuff.

ssss

i get C..

one is an inverted parabola and we just need to make sure they dont have the same y intercept..

How about if a = -c = 0?

Answer should be E. We know (given S1) that one of them is upward parabola, the other is inverted. However, we don't know which one is inverted and which one is upward. I.e. - we dont know the sign of "a", it can be a=2 or a=-2

Hello, would someone pls answer my question here, thank you.

I believe it was several times in past test answers that you only need slopes of lines to determine whether or not they cross, the angle they form together or whether or not they are perpendicular. Assuming that S1 stated "a=-1/c" would we then know that two lines cross are perpendicular and therefore cross?
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Do lines ax^2 + b and cx^2 + d cross?

1) a= -c
2) b > d

Answer: E

Would someone pls explain this question's answer further: What do we really need to know if two lines cross? The answer just gives examples. Also, if we have both slopes and know that one is the negative reciprocal of the other, do we then know they are perpendicular? Thankyou

This question is a bit different than a normal line equation. A normal line equation is y = [slope]x + [y intercept], but here the X is actually squared. This will lead to a curve similar to a parabola rather than a straight light. I don't think this is avery good question, but that's just me. I have not seen this before becuase I only did the first 12 or 13 math tests before my GMAT.

As for your questions prior to the DS question. Yes, generally, all you need to know for lines that cross is the slope. Remember that a Cartesian plane extends to infinity, so if the slopes are not IDENTICAL, then the lines will cross at some point. The y-intercept doesn't matter because at some point, the lines will cross unless they are EXACTLY parallel. To determine perpendicular lines, you are correct, the opposite sign (positive or negative) and reciprocal will be the test for perpendicular.

If slope is -\frac{1}{C} then the perpendicular slope will be C because we take the reciprocal so \frac{C}{1} and it's positive because the other was negative.

Can some one explain this parabola and how to figure these out similar to normal lines?

I will feel good if I see such Q on the GMAT

Both statements required to answer this question.

Explanation:
Lets equate these two equations first.
We have no idea about the signs of a,b,c or d. so we cant say anything about the nature of the graph whether it is concave or convex.
After equating these equation we can get x^2 = (d-b)/(a-c).
For getting real values of x, the above result must satisfy that a!=c!=0.
Also, (d-b)/(a-c) must always be positive.
To find this we must have both the conditions. i.e, if a=-c and b>d then x^2 will be equal to a negative value so we can't have real values of x. Thus we can say that these two lines are not crossing each other.

How did you derive x^2= (d-b)/(a-c)?

Hi icandy

If we equate the two given equations, we get x^2=(d-b)/(a-c).
We need to equate these two equations, because if they cross each other, they must satisfy(must have equal values of y) for a specific value of x. we get this value of x from x^2=(d-b)/(a-c).

Or try this way:
y=ax^2+b
and
y=cx^2+d

equating these equations will give:
ax^2+b = cx^2+d
ax^2 - cx^2=d-b
x^2(a-c)=(d-b)
x^2=(d-b)/(a-c)

Hope this will help.

What is the OA for this question?

1. a = -c
2. b > d

1) If a = -c then first equation will become as follow,

1) -cx2 –y + b = 0
2) Cx2 –y + b = 0
As per rule two lines are parallel (if a1/a2 = b1/b2) but here a1/a2 = -1 and b1/b2 = 1 and so they are not equal and so line must intercept.

2) b > d, does not give enough information about a and c and so it is not sufficient.

Answer is A.

The OA is E.

Hi abhishekik,
If we dont have real values then how do we say that lines dont intersect !! Imaginary numbers can also be plotted on plane and they can also be an intersection point??!!
http://en.wikipedia.org/wiki/Imaginary_number

Or my understanding is not correct? Please explain.