Linear equation

[rahulvsd]

Given the linear equation y = kx + n, for what values of x will y < 0?

(1) n = 0

(2) k < 0

[spoiler]OA:C[/spoiler]

[GmatMathPro]

Restated: For what values of k is kx+n<0?

1. n=0. kx<0. solutions depend on the value of k. If k is positive, then all negative x values satisfy the inequality. If k is negative, all positive values satisfy the inequality, and if k=0, there is no solution. INSUFFICIENT.

2. k<0 kx<-n x>-n/k. So all values of x bigger than -n/k satisfy the inequality. However, we have no idea what n or k is, so we can't specify an exact range. INSUFFICIENT.

1&2: If we know that n=0, the inequality derived in the second statement will be true for x>0. SUFFICIENT.

[user123321]

1) if n = 0 then y = kx
depending on value of k,
if k is +ve , then if x is -ve then y is -ve
if k is -ve , then if x is -ve then y is +ve
since we dont know the sign of k we cannot say anything about it.
hence insufficient.

2) if k<0, it will have different ranges of x for different values of n.
hence insufficient.

But if we have both we can say for sure, that y<0 when x>0 & vice versa hence both are sufficient.

user123321

[bpdulog]

Went with C here, seemed pretty straightfoward.

Knowing N without K and vice versa won't tell us much about y. You can get a positive/negative Y if you plug in extreme numbers.