xy-coordinate plane

[guest612]

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.

[sheetal]

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.

[guest612]

Thanks, Sheetal. You know your coordinate geometry!

[StaceyKoprince]

Thanks, Sheetal - and guest612, I assume Sheetal was right in regard to the typo?

[guest612]

yes, yes. sheetal was correct about the typo. thank you both!

[StaceyKoprince]

great, thanks for confirming!

[sfbay]

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 + )

[RonPurewal]

heh, nice three-year bump.

good solution

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 + )