kilukilam wrote:

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

(1) The slope of line k is negative

(2) a < b

Statement 1) The slope of line k is negative

Using this and the stimulus we know that we have a line with negative slope that passes through the origin.

But the point (a,b) can lie either on Q II or on Q IV

In Q II b is positive, But in Q IV b is negative.. so INSUFFICIENT

Statement 2) a<b

Now point a less than point b - Apart from Q IV in which "point a" will always positive and "point" b is always negative, this condition "a<b" can happen in any three of Q I, Q II, Q III

After all all it is saying is magnitude of a is less than magnitude of b .. Possible in Q I, Q II and Q III

Merging the two statements

b has to be greater and line has to pass through Q II or IV, there is only one possible quadrant Q II where a is always -ve b is aways +ve. therefore b>a (always)

This satisfies both ur condition and thus we can say that YES B is positive.

Hence answer is C

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