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In the xy-plane, the line K passes through the origin and

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In the xy-plane, the line K passes through the origin and [#permalink]

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In the xy-plane, the line K passes through the origin and through the point (a,b), where ab not equal to zero,
Is b positive?

1) The slope of line k is negative

2) a<b

Please explain

Thanks

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Re: DS: GMAT Prep - Geometry [#permalink]

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New post 02 Nov 2008, 19:19
johnpeter wrote:
In the xy-plane, the line K passes through the origin and through the point (a,b), where ab not equal to zero,
Is b positive?

1) The slope of line k is negative

2) a<b

Please explain

Thanks


IMO C

Clearly each option alone is not sufficient.
However if we considered them together, then we have a situation where slope is negative and x coord < y coord

Now line with negative slope passes thru origin and point (a,b)
ie line passes thru second and fourth quadrant via (0, 0)
ie the terms could be (-, +) (0, 0) or (+,-)

It is given that a < b and ab is not 0
This is possible only if the point on line was located in second quadrant
ie x is negative whereas y is positive
ie B is positve

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Re: DS: GMAT Prep - Geometry [#permalink]

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New post 03 Nov 2008, 03:17
johnpeter wrote:
In the xy-plane, the line K passes through the origin and through the point (a,b), where ab not equal to zero,
Is b positive?

1) The slope of line k is negative

2) a<b

Please explain

Thanks


line passes through the points (0,0) and (a,b)

slope = (b-0)/(a-0) = b/a

(1) b/a < 0
for b/a to be negative, either b or a has to be negative ..... b can be positive or negative.

(2) a < b
b can be positive or negative and still be smaller than a

(1) and (2)
if a < b and we know b/a < 0 then clearly a has to be negative and b is positive...
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Re: DS: GMAT Prep - Geometry [#permalink]

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New post 03 Nov 2008, 16:52
amitdgr, I agree with you until the last line. if a < b then doesn't that mean that b/a > 0 rather than b/a < 0?

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Re: DS: GMAT Prep - Geometry [#permalink]

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New post 03 Nov 2008, 19:59
smarinov wrote:
amitdgr, I agree with you until the last line. if a < b then doesn't that mean that b/a > 0 rather than b/a < 0?


smarinov ...

statement 1 says b/a < 0 ---> this means either a or b has to be negative
statement 2 says a < b ----> this means b is greater than a

combined we get -- either one of them has to be negative, and since b>a , b has to be the one with positive sign and a with the negative sign ...
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Re: DS: GMAT Prep - Geometry   [#permalink] 03 Nov 2008, 19:59
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In the xy-plane, the line K passes through the origin and

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