GIVEN: ab is NEGATIVE and bc is POSITIVE

So, (ab)(bc) = (NEGATIVE)(POSITIVE) = NEGATIVE
Simplify left side to get: ab²c = NEGATIVE
Rewrite as: (ac)(b²) = NEGATIVE
Since b² must be positive, we can write: (ac)(POSITIVE) = NEGATIVE
This tells us that ac must be NEGATIVE

So, we get:
Quantity A: NEGATIVE
Quantity B: 0

0 is greater than a NEGATIVE number
Answer: B

Cheers,
Brent
_________________

Answer: B
ab< 0 a is negative and b is positive or a is positive and b is negative
bc > 0 both b and c are positive. or both b and c are negative.

If both b and c are positive, then because ab is negative, a is negative. So ac is negative.
If both b and c are negative, then because ab is negative, a is positive, and ac is negative.
In both situations, ac is negative and less than 0.
B is bigger than A.
_________________

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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