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Senior Manager
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xy cordinate [#permalink] New post 30 Aug 2009, 11:04
00:00
A
B
C
D
E

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(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
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[Reveal] Spoiler:
C pls explain how....

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Re: xy cordinate [#permalink] New post 30 Aug 2009, 12:46
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I may be wrong. But the way I would think would be like that:

Let's consider statement (1) "products of the x-intercepts is positive" and possible variants of slopes:

Variant 1. Negative slope*positive slope=negative
X-intercept product is positive, y-intercept product is negative
Image

Variant 2. Negative slope * negative slope = positive
X-intercept product is positive, y-intercept product is positive
Image

Variant 3. Positive slope*positive slope=positive
X-intercept product is positive, y-intercept product is positive
Image

Variant 4. Positive slope*positive slope=positive
X-intercept product is positive, y-intercept product is positive
Image

Hence, the product of slopes can be either positive or negative. Not sufficient.

Now statement (2) "product of y-intercepts is negative". This can happen in two cases.

Variant 1. Negative slope*positive slope=negative
X-intercept product is positive, y-intercept product is negative
Image

Variant 2. Positive slope*positive slope=positive
X-intercept product is negative, y-intercept product is negative
Image

So, from statement (2) we get that positive and negative products of slopes are possible. So, insufficient.

However, when we combine the two statements, we need both two conditions to be true, that is: product of x intercepts should be positive and product of y-intercepts should be negative. There is only one case when the above conditions are true among all our charts. Only one variant (Variant 1) overlaps. Hence, we can conclude that the product is negative. Therefore, C.

My guess. May be wrong.

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Last edited by CasperMonday on 30 Aug 2009, 23:25, edited 1 time in total.
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Re: xy cordinate [#permalink] New post 30 Aug 2009, 12:58
one way is to draw various line on a paper based on these conditions..but that can be risky as chances of miising a line are more likely..

Another way is:-

Let equation L which passes through (3,4) = y = m1x + c1 where m1 is the slope of line L

or, y = m1x + 3-4m1 ( calculating c1 in terms of m1 , using (3,4) lies on L) - 1st

Similarly,

equation k = y = m2x + 3-4m2 -- 2nd where m2 is the slope of line k

1.) (4m1 - 3)(4m2 -3)/m1*m2 >0

which gives, (4m1 - 3)(4m2 -3) > 0 and m1*m2 >0

or
(4m1 - 3)(4m2 -3) < 0 and m1*m2 < 0
Insufficient

2.) (3 - 4m1)(3 - 4m2) < 0

which is also insufficient..

combinig together,
m1*m2 < 0

Hence ,C
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Re: xy cordinate [#permalink] New post 30 Aug 2009, 23:00
CasperMonday: really explained very well.. But in your second stmt condition can you explain .. both the variants as i see a lil discrepecy in them.. the line are not making postiive intercepts ( above origin) also can you give how finally combined figure will give the result..


Gmate2010: can you alaborate a little in the last stage when you combined it.??
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Re: xy cordinate [#permalink] New post 30 Aug 2009, 23:34
rohansherry wrote:
CasperMonday: really explained very well.. But in your second stmt condition can you explain .. both the variants as i see a lil discrepecy in them..

The differennce is in the sign of slopes. In one variant both slopes are positive, in the other one - one slope is positive, the other is negative. We should have considered the third variant, when both slopes are negative, but in such case the product of y-intercepts will be positive and that violates our statement.

rohansherry wrote:
the line are not making postiive intercepts ( above origin)

Statement 2 requires that the product of y-intercepts is negative. That is, we need to have one intercept below zero (negative) and one - above zero (positive). In such case negative intercept*positive intercept = negaative product of the intercepts. Therefore, we don't need only positive intercepts under statement 2.

rohansherry wrote:
also can you give how finally combined figure will give the result..

I added some more comments into my previous post, see highlighted text
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Re: xy cordinate [#permalink] New post 30 Aug 2009, 23:38
gmate2010 wrote:
one way is to draw various line on a paper based on these conditions..but that can be risky as chances of miising a line are more likely..

Another way is:-



Liked your method. Thanks!
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Re: xy cordinate [#permalink] New post 31 Aug 2009, 03:31
rohansherry wrote:
CasperMonday: really explained very well.. But in your second stmt condition can you explain .. both the variants as i see a lil discrepecy in them.. the line are not making postiive intercepts ( above origin) also can you give how finally combined figure will give the result..


Gmate2010: can you alaborate a little in the last stage when you combined it.??


from second, we have (3 - 4m1)(3 - 4m2) < 0

or, (4m1 - 3) (4m2 - 3) < 0

from first,
we know that , (4m1 - 3)(4m2 -3) > 0 and m1*m2 >0
or
(4m1 - 3)(4m2 -3) < 0 and m1*m2 < 0


now,(4m1 - 3) (4m2 - 3) < 0 then m1*m2 should be less than 0..
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Re: xy cordinate [#permalink] New post 02 Sep 2009, 04:43
Good explanation .. thank you
Re: xy cordinate   [#permalink] 02 Sep 2009, 04:43
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