Bunuel wrote:

Official Solution:

Notice that we can get the equation of line \(k\) which is perpendicular to line \(y=2x\) if we know ANY point that line \(k\) passes through. So, to get the equation of line \(k\) we need the values of \(a\) and \(b\).

(1) \(a = -b\). Not sufficient.

(2) \(a - b = 1\). Not sufficient.

(1)+(2) \(a = -b\) and \(a - b = 1\), we have two distinct linear equations with two unknowns so we can solve for \(a\) and \(b\). Sufficient.

Answer: C

Hi, Bunuel!

Is it necessary to find the equation of line in absolute values of 'a' and 'b'? I mean the point (a,b) is given. Can't we just take 'a' and 'b' as known values because point (a,b) is mentioned?

My first thought while solving this question was that slope is given and point (a,b) is given through which the line passes. Only 'c' is unknown to find the equation of line. Taking each of the statements one by one, i was able to find the value of 'c' in terms of 'a' or 'b' and hence the equation of line in terms of all the known values i.e 'a' and 'b' was obtained.

So, this way each statement was sufficient according to me and I thought D to be the answer.

Please, clarify my this doubt.Thank you.