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M24 #12 - formatting error

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Re: M24 #12 - formatting error [#permalink] New post 09 Feb 2010, 08:03
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 ...

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Re: M24 #12 - formatting error [#permalink] New post 11 Feb 2011, 06:20
GMAT exams are only based on real numbers.

If they allowed imaginary numbers that would only make the math more complex. Get it?!?
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Re: M24 #12 - formatting error [#permalink] New post 11 Feb 2011, 07:13
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.
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Re: M24 #12 - formatting error [#permalink] New post 12 Feb 2011, 23:35
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.
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Re: M24 #12 - formatting error [#permalink] New post 13 Feb 2011, 02:13
Expert's post
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)
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Re: M24 #12 - formatting error [#permalink] New post 13 Feb 2011, 22:38
Ahhhh i see...this makes more sense...thanks so much Bunuel!!! :)
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Re: M24 #12 - formatting error [#permalink] New post 14 Feb 2011, 05:33
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
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Re: M24 #12 - formatting error [#permalink] New post 16 Feb 2012, 17:08
I answered C, which upon further thinking was a careless mistake. To answer the question I tentatively drew out different scenarios for each equation.

With statement 1, the parabola can cross or not cross, it all depends on b and d (insufficient)

With statement 2, we don't have information on a or c, so they can still cross or not cross (insufficient)

When combining to the two statements, I made the mistake of assuming that a was positive and c was negative, which given statement 2, the two lines would not cross. I stupidly forgot about the opposite situation, where statement 1 would still be satisfied, but would give a different result.

Silly mistake.

Answer is E
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Re: M24 #12 - formatting error [#permalink] New post 27 Feb 2012, 22:04
Hi I am getting c. Please see the attached image.. please expl this solution is not why this solution is not correct
Attachments

equations intersect.jpg
equations intersect.jpg [ 23.83 KiB | Viewed 1331 times ]

equations intersect.jpg
equations intersect.jpg [ 26.78 KiB | Viewed 1332 times ]

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Re: M24 #12 - formatting error [#permalink] New post 27 Feb 2012, 22:21
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devinawilliam83 wrote:
Hi I am getting c. Please see the attached image.. please expl this solution is not why this solution is not correct


Please read the solutions above with algebraic as well as number plugging approaches showing that answer is E, not C.

The problem with your reasoning is that the case you've given is not the only possible one, there are the cases when the graphs do not intersect.

Consider the graphs y=x^2+1 and y=-x^2 to get answer NO:
Attachment:
1.gif
1.gif [ 4.4 KiB | Viewed 1313 times ]

Consider the graphs y=-x^2+1 and y=x^2 to get answer YES:
Attachment:
2.gif
2.gif [ 5.18 KiB | Viewed 1313 times ]


Hope it's clear.
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Re: M24 #12 - formatting error [#permalink] New post 27 Feb 2012, 22:42
Yes I missed that .. Thanks
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Re: M24 #12 - formatting error [#permalink] New post 15 Feb 2013, 05:17
Gr8 question.

E for me because the signs a, b, c, d are unknown even after combining both the conditions.

If a or c would had been given positive, then the answer could be determined.
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Re: M24 #12 - formatting error [#permalink] New post 15 Feb 2013, 09:09
I thought the in geometry definition, parabolas are not consider lines.
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Re: M24 #12 - formatting error [#permalink] New post 21 Apr 2014, 05:01
2 lines cross when there exists x so that (a-c)x^2=d-b (*)
1) a=-c: don't mention anything about the right side of (*) -> insufficient
2) b>d: if a<c: (*) has at least one root; if a>c: no root -> insufficient
Combine 2 stats: still insufficient coz we don't know whether a>c or not

Choose E
Re: M24 #12 - formatting error   [#permalink] 21 Apr 2014, 05:01
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