Geometry

[mukgera]

Please help me with this problem.

[Anurag@Gurome]

Please help me with this problem.

Equation of line passing through two points origin and (x1, y1) is (y - y1) = m * (x - x1)
So, equation of line k is (y - 0) = m * (x - 0) or y = mx
Since line k passes through (a, b), so b = ma

(1) Slope of line k is negative implies b = -ma; NOT sufficient.

(2) a < b
b = ma does not imply if b is positive or negative; NOT sufficient.

Combining (1) and (2), b = ma and a < b implies that a will have to be negative to satisfy a < b. If a = negative, then b will always be positive; SUFFICIENT.

The correct answer is C.

[mukgera]

Hi Anurag,
The approach I took was very similar to the one took by you and reached till the point b = ma

1. Now since slope m < 0 so b/a < 0, means b and a have opposite signs. - Not sufficient
2. a < b. Not sufficient

Combining the two e.g ,

If I take a = +ve and b = -ve then 2 is not true.
and If i take a = -ve and b = +ve then 2 is true.

So situation in which 1 and 2 both are true will be when b > 0. So C is the answer.

Could this be the one of the way to approach this ?

Please help me with this problem.

Equation of line passing through two points origin and (x1, y1) is (y - y1) = m * (x - x1)
So, equation of line k is (y - 0) = m * (x - 0) or y = mx
Since line k passes through (a, b), so b = ma

(1) Slope of line k is negative implies b = -ma; NOT sufficient.

(2) a < b
b = ma does not imply if b is positive or negative; NOT sufficient.

Combining (1) and (2), b = ma and a < b implies that a will have to be negative to satisfy a < b. If a = negative, then b will always be positive; SUFFICIENT.

The correct answer is C.

[Anurag@Gurome]

Hi Anurag,
The approach I took was very similar to the one took by you and reached till the point b = ma

1. Now since slope m < 0 so b/a < 0, means b and a have opposite signs. - Not sufficient
2. a < b. Not sufficient

Combining the two e.g ,

If I take a = +ve and b = -ve then 2 is not true.
and If i take a = -ve and b = +ve then 2 is true.

So situation in which 1 and 2 both are true will be when b > 0. So C is the answer.

Could this be the one of the way to approach this ?

Absolutely, that's right!