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Bunuel
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sumit99kr

we cannont multiply variables without knowing their signs in inequalities

xy<bcxy<bc
or say
is xc<yb

no we cannot do this


IMO option E
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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.

Combination

As statement 2 didn't provide any meaningful information, the combination wouldn't help.

Option E
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