Here's a different approach

-------------ASIDE--------------
KEY PROPERTY:
If \(a = b\)
and \(c = d\)
Then \(\frac{a}{c} = \frac{b}{d}\)

NOTE: This works as long as b and d do not equal zero
-------------------------------

GIVEN: \(ab < 0\) and \(bc > 0\)

In other words,
ab = some NEGATIVE number
bc = some POSITIVE number

Applying the Key Property, we can write: \(\frac{ab}{bc}=\) (some NEGATIVE number)/(POSITIVE number)

The b's cancel out, AND we know that the right side must be a NEGATIVE number

That is, \(\frac{a}{c}=\) a NEGATIVE number

This means one value (a or c) is positive, and the other value is negative.
As such, we can be certain that the product ac is negative, which means Quantity B is greater.

Answer: B

Cheers,
Brent

ab <0 < bc

if we think of b as +ve thus a is -ve for sure
and c is +ve (if it wasn't then value would not be more than zero) and b is +ve (else again the equation will change --> ab would be more than zero)

then ac < 0

Now if b is -ve

then a is +ve and c is also -ve Thus ac < 0

hence B

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