Co-ordinate Geometry #2

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yankee.musk: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Fri Feb 23, 2007 1:35 pm; GMAT Score:610

by yankee.musk » Sat May 22, 2010 2:14 pm

In the xy-plane, the line 'k' passes through the origin and through point (a,b) where (ab NOT EQUAL 0). IS 'b' positive?

(1) The slope of the line is negative
(2) a < b

My understanding leaves me with options (C) or (E). But I'm having trouble translating Statement (2). Any help ?

OA:[spoiler]C[/spoiler]

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Source: Beat The GMAT — Data Sufficiency | Sat May 22, 2010 2:14 pm

clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Sat May 22, 2010 2:30 pm

yankee.musk wrote:In the xy-plane, the line 'k' passes through the origin and through point (a,b) where (ab NOT EQUAL 0). IS 'b' positive?

(1) The slope of the line is negative
(2) a < b

My understanding leaves me with options (C) or (E). But I'm having trouble translating Statement (2). Any help ?

OA:C

hi friend
try to use spoiler properly please
as to the problem
the slope of line=y/x=b/a-in our case, we need to know does b>0
(1) slope<0, b/a<0 but we don`t know for sure does b or a -ve or +ve
it can be
a>0, b<0, or
a<0, b>0
so 1 st insufficient
(2) a<b-alone gives us almost nothing
together
if a<b,then a<0 and b>0 as they must have different signs for b/a<0
so C is the answer

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yankee.musk: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Fri Feb 23, 2007 1:35 pm; GMAT Score:610

by yankee.musk » Sat May 22, 2010 2:36 pm

Thanks clock60

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Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Sat May 22, 2010 10:59 pm

Drawing may prove helpful here. We're asked whether the y coordinate of the point is positive. In other words, Reprhase to "is (a,b) above the x axis?"

(1) a negative slope goes down and to the right. Since the line goes through the origin, the point (a,b) can be in the top left or bottom right of the graph. we don't know whether it's above the x axis.

(2) gives us no information on the location of the point except that the point cannot be in the bottom right (all points in that quadrant have a positive x and negative y, so x > y).

Together, the statements limit us to the top left quadrant, so they answer the rephrase definitively. C is correct.

To better understand, have a look at the video solution. This is GMATPrep question 1108

If yo have trouble with Geometry questions, you can use the Solutions Engine to search for and practice similar questions from GMATPrep

-Patrick

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