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guest612
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Post subject: xy-coordinate plane  Posted: Sat Mar 15, 2008 3:46 pm |
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GMATPREP CAT 2 #9
In the xy-plane, the line k passes through the origin and through point (a, b), where ab does not equal zero. Is b positive?
1. The slope of k is negative
2. a<c
Correct answer is C. Can you please tell me how to derive a solution (or how to rephrase this and get the answer to the rephrasing)? I lucky guessed C but I don't know why it's right.
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sheetal
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Post subject: Posted: Sat Mar 15, 2008 7:54 pm |
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I assume that the statement (2) has a a typo error otherwise the ans will be E.
I will consider statement (2) a < b
We are given that slope(m) = (b/a); ab != 0
Question : Is b > 0?
(1) says (b/a) < 0
This could mean 2 things
a) Either a > 0 & b < 0 OR
b) a < 0 & b > 0
Both are of opposite signs.
This is not sufficient to ans the question. This eliminated A & D
(2) a < b
This could mean
a) a < 0 & b > 0 (eg -1 < 1)
b) a > 0 & b > 0 (eg. 2 < 3)
c) a < 0 & b < 0 (eg -2 < -1)
This is also not sufficnet. WE can eliminate B.
If we combine (1) and (2), we get
1(b) and 2(a) give a definite solution. We can ans the question. So C is the ans.
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guest612
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Post subject: got it Posted: Sun Mar 16, 2008 1:58 pm |
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Thanks, Sheetal. You know your coordinate geometry!
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StaceyKoprince
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Post subject: Posted: Mon Mar 17, 2008 4:05 pm |
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| ManhattanGMAT Staff |
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Posts: 6077
Location: San Francisco
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Thanks, Sheetal - and guest612, I assume Sheetal was right in regard to the typo?
_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
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guest612
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Post subject: yes yes Posted: Mon Mar 17, 2008 7:34 pm |
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yes, yes. sheetal was correct about the typo. thank you both!
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StaceyKoprince
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Post subject: Posted: Wed Mar 19, 2008 4:42 pm |
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| ManhattanGMAT Staff |
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Posts: 6077
Location: San Francisco
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great, thanks for confirming!
_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
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sfbay
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Post subject: Re: xy-coordinate plane Posted: Fri Mar 25, 2011 9:14 pm |
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Posts: 26
Location: San Francisco
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Graphical solution
given a line going through 0,0 and not vertical (no slope) or horizontal (slope =0)
is b - ?
1) negative sloping line going through 0,0. therefore line is in quad 2 and quad 4. quad 2 a is - and b is + . quad 4 a is + and b is -
so b can be either + or - , not suff
2) a<b can be true in quad 1 , quad 2 and quad 3 and again b can be + or - , not suff
combined
negative slope gives quad 2 or 4, and statement 2 only true in quad 2 (since quad 2 b is + and a - and in quad 4 b is - and a + )
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RonPurewal
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Post subject: Re: xy-coordinate plane Posted: Fri Mar 25, 2011 10:44 pm |
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| ManhattanGMAT Staff |
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heh, nice three-year bump. good solution munnynarang wrote: Graphical solution
given a line going through 0,0 and not vertical (no slope) or horizontal (slope =0)
is b - ?
1) negative sloping line going through 0,0. therefore line is in quad 2 and quad 4. quad 2 a is - and b is + . quad 4 a is + and b is -
so b can be either + or - , not suff
2) a<b can be true in quad 1 , quad 2 and quad 3 and again b can be + or - , not suff
combined
negative slope gives quad 2 or 4, and statement 2 only true in quad 2 (since quad 2 b is + and a - and in quad 4 b is - and a + )
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