Bunuel
Is \(\frac{x}{y} < \frac{b}{c}\) ?
(1) \(cx - yb < 0\)
(2) \(bx - cy < 0\)
\(\frac{x}{y} - \frac{b}{c} < 0\)
Taking yc as the LCM
\(\frac{xc - yb }{ yc} < 0\)
There can be two possible cases -
Case 1: yc < 0
xc - yb > 0
xc > yb
When yc < 0, xc should be greater than yb
Case 2: yc > 0
xc - yb < 0
xc < yb
When yc > 0, xc should be less than yb
With this pre-analysis done, let's dive into the options.
Statement 1\(xc - yb < 0\)
The statement matches with a condition in case 1, however we don't know if yc < 0
Hence the statement only gives partial information, and hence is not sufficient. We can eliminate A and D.
Statement 2\(bx - cy < 0\)
This statement wouldn't help us. The coefficients of x and y are not the same as what we need. Hence this statement is not sufficient and eliminate B.
CombinationAs statement 2 didn't provide any meaningful information, the combination wouldn't help.
Option E