Is b positive?

[Deepthi Subbu]

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

1.Slope of line k is negative .

2.a<b

OA C

[Anurag@Gurome]

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

1. Slope of line k is negative .
2. a < b

Equation of the line is of the form, y = mx
As (a, b) is on the line, b = ma => m = (b/a) = Slope of the line
Hence, equation of the line is y = (bx/a)

Statement 1: Slope of line k is negative.
As the line has a negative slope and passes through the origin, the line passes through 2nd and 4th quadrant. That means b can be either positive or negative.

Not sufficient

Statement 2: a < b
This implies either,

• 1. (b/a) > 1 if a is positive
  2. (b/a) < 1 if a is negative

Thus slope is either greater than 1 or less than 1.

Not sufficient

1 & 2 Together: From statement 1, slope is negative and thus less than 1. From statement 2 we know it is possible only if a is negative too. Thus b is positive.

Sufficient.

The correct answer is C.