Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

We have 2 curves with so these caracteristics:
> a and c represent how much "narrow" the curve will be. For instance:
- if a is very negative (-100, -10000), the montain created by the curve will be very narrow (even a pic).
- if a is very positive (100, 10000), the valley created by the curve will be very narrow (even a fail).

> b and d are the Y-interceptors and so gives the positions of the extremum of the 2 curves, maximum or minimum, depending on the sign of a and c.

From 1 a=-c. Thus, the 2 curves represents a montain (the negative one from a and c) and a mirror of it, a valley.

o If the Y interceptor of the montain is equal to the one of the valley, there is 1 crossing point, their extremum
o If the Y interceptor of the montain is superior to the one of the valley, there are 2 crossing points.
o If the Y interceptor of the montain is inferior to the one of the valley, there is no crossing points.

INSUFF.

From 2 b > d. We have to know a relationship between a and c.

o If a > c, there is no crossing point.
o If 0 < a < c, there are 2 crossing points

INSUFF.

From 1 and 2 b > d and a=-c

We have:
o If a > 0 > c, the valley a,b never crosses the montain c,d.
o If c > 0 > a, the montain a,b crosses the valley c,d at 2 points.

We have 2 curves with so these caracteristics:
> a and c represent how much "narrow" the curve will be. For instance:
- if a is very negative (-100, -10000), the montain created by the curve will be very narrow (even a pic).
- if a is very positive (100, 10000), the valley created by the curve will be very narrow (even a fail).

i am not able to understand your point.

y = a*x^2 + b

x=+-sqrt((y-b)/a);

Is in not that as a increases curve will have lesser width.

Re: Do the lines cross each other ? DS Question [#permalink]
24 May 2007, 01:48

kamal.gelya wrote:

Do lines y = a*x^2 + b and y = c*x^2 + d cross each other ?

1) a = -c 2) b > d

Can someone add details to the explanation below.. Thanks

Explanation

S1 + S2 is not sufficient. Consider y = -x^2 + 1, y = x^2 + 0 (the answer is YES) and y = x^2 + 1, y = -x^2 + 0 (the answer is NO).

It is deceiving to call these lines, by the way!
They will cross if and only if (a-c)x^2= d-b has more than one solution i.e if (d-b)/(a-c) > 0. (2) tells us that the numerator is >0, but if a= -c as per (1), the denominator can be positive or negative. (1) and (2) together are insufficient

We have 2 curves with so these caracteristics: > a and c represent how much "narrow" the curve will be. For instance: - if a is very negative (-100, -10000), the montain created by the curve will be very narrow (even a pic). - if a is very positive (100, 10000), the valley created by the curve will be very narrow (even a fail).

i am not able to understand your point.

y = a*x^2 + b

x=+-sqrt((y-b)/a);

Is in not that as a increases curve will have lesser width.

Yes.... The absolute value of a gives the width ... I mean a very high increase, a = a +100000 (a montain) or a very high decrease, a = a -100000 (a valley) both can decrease the width and oddly mirror the montain to a valley or the valley to a montain

hrmm. this question seems odd, where did it come from? i thought lines had to be straight? i said A for the same reason as Himalayan.... if they aren't parallel they will intersect at some point in space.

We have 2 curves with so these caracteristics: > a and c represent how much "narrow" the curve will be. For instance: - if a is very negative (-100, -10000), the montain created by the curve will be very narrow (even a pic). - if a is very positive (100, 10000), the valley created by the curve will be very narrow (even a fail).

> b and d are the Y-interceptors and so gives the positions of the extremum of the 2 curves, maximum or minimum, depending on the sign of a and c.

From 1 a=-c. Thus, the 2 curves represents a montain (the negative one from a and c) and a mirror of it, a valley.

o If the Y interceptor of the montain is equal to the one of the valley, there is 1 crossing point, their extremum o If the Y interceptor of the montain is superior to the one of the valley, there are 2 crossing points. o If the Y interceptor of the montain is inferior to the one of the valley, there is no crossing points.

INSUFF.

From 2 b > d. We have to know a relationship between a and c.

o If a > c, there is no crossing point. o If 0 < a <c> d and a=-c

We have: o If a > 0 > c, the valley a,b never crosses the montain c,d. o If c > 0 > a, the montain a,b crosses the valley c,d at 2 points.

INSUFF.

I could not understant what you and Kevincan are telling?

From 1 a=-c. Thus, the 2 curves represents a montain (the negative one from a and c) and a mirror of it, a valley.

o If the Y interceptor of the montain is equal to the one of the valley, there is 1 crossing point, their extremum CASE A o If the Y interceptor of the montain is superior to the one of the valley, there are 2 crossing points. CASE B o If the Y interceptor of the montain is inferior to the one of the valley, there is no crossing points. CASE C

INSUFF.

---------

CASE A: Arbitrarly, I take a=1 and so c=-1. This way, a,b will be the valey and c,d the montain. I choose also b=d=1. (Fig A)

CASE B: Arbitrarly, I take a=1 and so c=-1. Then, we have b < d for this case and so I take b=1 and d=2. (Fig B)

CASE C: Arbitrarly, I take a=1 and so c=-1. Then, we have b > d for this case and so I take b=2 and d=1. (Fig C)

Attachments

Fig A_a equal 1_c equal -1_b & d equal 1.gif [ 3.95 KiB | Viewed 1119 times ]

We have:
o If a > 0 > c, the valley a,b never crosses the montain c,d. CASE F o If c > 0 > a, the montain a,b crosses the valley c,d at 2 points. CASE G

INSUFF.

-------

CASE F: I choose b=2 and d=1 as well as a=1 and c=-1. (Fig F)

CASE G: I choose b=2 and d=1 as well as a=-1 and c=1. (Fig G)

hrmm. this question seems odd, where did it come from? i thought lines had to be straight? i said A for the same reason as Himalayan.... if they aren't parallel they will intersect at some point in space.

i know they are parabola. i just answered the Question as A because I thought lines had to be straight, therefore they would intersect if not parallel... the question did not say they were curves. it was a time saving method... ya know, don't do the whole problem if you don't have to kinda thing..

i am curious if this is an official question... if someone could point me to the definition of what a line is within the context of coordinate geometry i would be thankful; i want to know what other quirks 'lines' might have so i don't make a similar mistake again.

I think this question is from one of the early challenges. This question is supposed to be for straight lines, not a curve. We apologize for this mistake.

The correct version should read:

Do lines $$y = a*x_1 + b$$ and $$y = c*x_2 + d$$ cross each other ?

1) a = -c
2) b > d

The specific property we were trying to test was the following:

Two lines are perpendicular if their respective slopes are negative reciprocals of one another. Thus, the line $$ y= a * x_1 +b $$ would be perpendicular to any line whose slope is $$ -1/a $$ .

so can i stop wetting my pants and trembling in the fetal posistion in a corner now at the thought of having to relearn what a line can and cant be? lines *are* straight on the GMAT? right?

so can i stop wetting my pants and trembling in the fetal posistion in a corner now at the thought of having to relearn what a line can and cant be? lines *are* straight on the GMAT? right?

::right??::

Yes, you may stop wetting your pants. Lines are straight. If you want to be more formal, horizontal and vertical are special cases of straight lines.

As a side note, thank you for taking the problem apart.