Go to GMAT Club Tests http://gmatclub.com/tests

Economist · **Posted:** Sun Apr 05, 2009 1:43 am

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.

abhishekik wrote:

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.

Prometoh · **Posted:** Fri Nov 06, 2009 10:56 pm

if cross ax2 + b = cx2 + d
x2(a - c) = d – b
x2 = (d-b)/(a-c)
Thus, three criteria occur:
(1) a != c
(2) if a > c, d > b
(3) if a < c, d < b

1. a = -c, we do not know about b and d  insufficient
2. b > d, what about a and c?  insufficient
Both are still insufficient because a can be either more or less than c

run4run · **Posted:** Mon Feb 08, 2010 10:14 am

Statement 1: It states that each parabola has a different sign (or they both equal 0). If one slope is positive with an intercept that is positive and one is negative with an intercept that is negative the lines will never cross. (There is nothing defining which line has a positive or negative slope).

Statement 2: Obviously not sufficient says nothing about the slopes.

Together: Since we don't know which line is positive and which is negative or rather if there both not zero than the y intercept can either mean they cross or don't so still not definitive.

E

dmetla · **Posted:** Mon Feb 08, 2010 12:46 pm

I get A

if product of two slops =-1 then the lines are perpendicular to each other so they cross. Not sure why OA is E can anyone explain

dmetla · **Posted:** Mon Feb 08, 2010 12:49 pm

I get E

only if product of two slops =-1 then the lines are perpendicular to each other so they cross.

varun2410 · **Posted:** Mon Feb 08, 2010 8:24 pm

i have thought : if two line are not parallel then they cross each other ,if we can prove this to line are not parallel ( i don’t know how?) then they intersect each other at some x point.

dzyubam · **Posted:** Tue Feb 09, 2010 8:03 am

Wow. Bunuel, fantastic explanation, as always

.

Bunuel wrote:

zoinnk wrote:

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

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

[Reveal] Spoiler: OA

E

Source: GMAT Club Tests - hardest GMAT questions

What am I supposed to do w/ #2?

I'd like to comment on this one:

First of all: equations given ARE NOT ...

themule1406 · **Posted:** Fri Feb 11, 2011 6:20 am

GMAT exams are only based on real numbers.

If they allowed imaginary numbers that would only make the math more complex. Get it?!?

321kumarsushant · **Posted:** Fri Feb 11, 2011 7:13 am

A would have been the answer provided a=c not equal to zero
since, no condition is given hence, we cant its A.
and by using both statement together also we cant say whether it will cross or not.
if constants are not equal to zero, then the curve will cross each other.
if constants(a&C) are zero, then it is line with different value. wont cross each other.
and if, constant (all) are zero they will over lap.

so, the best answer is E.

rongali · **Posted:** Fri Feb 11, 2011 3:21 pm

agree ans is E

144144 · **Posted:** Sat Feb 12, 2011 2:02 am

agree with E. thanks.

saswani · **Posted:** Sat Feb 12, 2011 11:35 pm

Please explain as to how did you get from 2ax^2 + (b-d) = 0 ----> to d=0 - 8a(b-d) >= 0....
and from (a-c)x^2 +(b-a) = 0 -----> to d = 0 - 4(a-c)(b-d) >= 0

This would help me see what I am missing. I understood the explanation but stuck at how the above equation for 'd' was derived.

Bunuel · **Posted:** Sun Feb 13, 2011 2:13 am

saswani wrote:

Please explain as to how did you get from 2ax^2 + (b-d) = 0 ----> to d=0 - 8a(b-d) >= 0....
and from (a-c)x^2 +(b-a) = 0 -----> to d = 0 - 4(a-c)(b-d) >= 0

This would help me see what I am missing. I understood the explanation but stuck at how the above equation for 'd' was derived.

Second d (red part) stands here for the discriminant of a quadratic expression not the variable d.

Check this for more: math-coordinate-geometry-87652.html (Parabola chapter)

saswani · **Posted:** Sun Feb 13, 2011 10:38 pm

Ahhhh i see...this makes more sense...thanks so much Bunuel!!!

maelstroem · **Posted:** Mon Feb 14, 2011 5:33 am

These are 2 paraboles.
Statement 1 (one of the paraboles is inverted depending on a negative or positive) ==> alone insufficient
Statement 2 Parobole 1 crosses 0 above Parabole 2 ==> alone insufficient
They would cross each other if a was negative. But as this information is not there ==> both statement insufficient

E

Similar topics	Author	Replies	Views	Last post
Error Log format in Share Your GMAT Experience	dm2824	5	751	Thu Mar 01, 2007 11:31 am
m24 - 19 in GMAT Math Questions and Intellectual Discussions	chengliu	3	219	Sat May 24, 2008 5:59 pm
M24 #4 in GMAT Club Tests	snowy2009	22	3442	Sat Oct 04, 2008 12:50 pm
M24#34 in GMAT Club Tests	ventivish	15	1974	Fri Nov 28, 2008 11:19 pm

Go to GMAT Club Tests http://gmatclub.com/tests | What are GMAT Club Tests?

M24 #12 - formatting error

Get Started:
Two Free Trial Tests

Get All GMATClub Tests

Who is online

Main Navigation

GMAT Resources

Partners

MBA Resources