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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] New post 10 Nov 2005, 07:04
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A
B
C
D
E

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In the xy plane, the line k passes through the origin and through the point (a, b), where ab is not qual to 0. Is b positive?

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






c
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 [#permalink] New post 10 Nov 2005, 07:18
it is C.

if it passes through the origin and ab is not equal to zero that leaves 4 possibilities a and b both possitive , a and b both negetative, a positive and b negative, and a negative and b positive.


now statement a says the sope of line k is negative.

that means a will be positive , b wil be negative or a will be negative b will be positive. so 1 alone deos not solve it.

now using statement 2 a<b we can not solve whether b is positive or negative.

but if we combine both. since a is less than b. b must be positive and a must be negative.

so the Answer is C.
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Re: Coordinate Geo GPrep DS [#permalink] New post 10 Nov 2005, 07:27
desiguy wrote:
In the xy plane, the line k passes through the origin and through the point (a, b), where ab is not qual to 0. Is b positive?

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


Surely C.

we have (b-0)/(a-0)= k ( ab<>0 ---> a AND b <>0 ---> we can have a fraction with denominator of a) ----> b/a=k
(1) k<0 ---> (b<0 AND a>0) OR (b>0 AND a<0 ) ---> can't conclude---> insuff
(2) a<b , can't conclude anything--> insuff

(1) and (2), a<b and b/a=k<0 ---> a<0<b-->suff
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 [#permalink] New post 11 Nov 2005, 20:42
(1) Insufficient

(a,b) can be in either the 2nd or 4th quandrant

(2) Insufficient

(a, b) can be in either the 1st, 2nd or 3rd quadrant

(1/2)

(a,b) can only be in the 2nd quadrant

I pick C.
  [#permalink] 11 Nov 2005, 20:42
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