XY-plane

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hai1: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Tue Oct 23, 2007 9:25 am; Thanked: 1 times; GMAT Score:600

by hai1 » Sun Dec 27, 2009 3:32 pm

Ans: C

My reasoning: Slope= -b/a
1. Slope is negative
For slope to be negative, b & a> 0; or b & a<0;
Hence it is not possible to tell if b is postive.

2. a<b
We cannot tell anything about this.

1 & 2 combined: Even this will not give us any information about b.
If a<b and a&b>0; -b/a will be -ve; Is b > 0? yes
If a<b and a&b<0; -b/a will be -ve; Is b < 0? No

So how is this answer right?

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Source: Beat The GMAT — Data Sufficiency | Sun Dec 27, 2009 3:32 pm

rohan_vus: Master | Next Rank: 500 Posts; Posts: 189; Joined: Thu Apr 03, 2008 2:03 pm; Location: USA; Thanked: 21 times

by rohan_vus » Sun Dec 27, 2009 3:53 pm

Slope should be b/a and not -b/a..

From (1) all u know is b/a < 0 , which means a & b are of different sign ( +ve or -ve)..so if b > 0 then a < 0 and if b<0 then a >0

From (2) a<b ... b could be anything

Combing (1) & (2) ,
If b< 0 implines a < 0 as a < b...so a has to be -ve... But from (1) u know a and b got to be of opposite signs..so b must be +ve

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Testluv: GMAT Instructor; Posts: 1302; Joined: Mon Oct 19, 2009 2:13 pmFollowed by: 164 members; Location: Toronto; Thanked: 539 times; GMAT Score:800

by Testluv » Sun Dec 27, 2009 10:01 pm

hai1 wrote:

Ans: C

My reasoning: Slope= -b/a
1. Slope is negative
For slope to be negative, b & a> 0; or b & a<0;
Hence it is not possible to tell if b is postive.

2. a<b
We cannot tell anything about this.

1 & 2 combined: Even this will not give us any information about b.
If a<b and a&b>0; -b/a will be -ve; Is b > 0? yes
If a<b and a&b<0; -b/a will be -ve; Is b < 0? No

So how is this answer right?

I think you are forgetting to include key info from the question stem: the line passes through origin.

You have to combine the info from (1) with the info in the question stem. (1) tells us the slope is negative. So, (reading from left to right) the line "falls". But if it is passing through the origin, this means the line is falling from the second quadrant (upper-left) into the fourth quadrant (lower-right). In the second quadrant, y values are positive while x values are negative; in the fourth quadrant, it is the other way around. So from (1), we know that one coordinate in (a,b) is negative while the other positive; as Rohan put it, a and b have different signs. Combining this with (2), clearly a is negative and b is positive.

____________

Takeaways: -evaluate each statement independently from each other BUT IN CONJUNCTION WITH THE QUESTION STEM!
- many coordinate geometry problems are better approached qualitatively (rather than algebraically), either visualizing or drawing out a quick coordinate plane on your scratchpaper.

Kaplan Teacher in Toronto

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Mon Dec 28, 2009 2:37 am

c att for soln

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