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ab < 0 bc > 0

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ab < 0 bc > 0 [#permalink] New post 24 May 2017, 01:29
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66% (00:40) correct 34% (00:40) wrong based on 100 sessions



\(ab < 0\)

\(bc > 0\)

Quantity A
Quantity B
\(ac\)
\(0\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: ab < 0 bc > 0 [#permalink] New post 24 May 2017, 05:24
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Carcass wrote:


GIVEN: ab is NEGATIVE and bc is POSITIVE

So, (ab)(bc) = (NEGATIVE)(POSITIVE) = NEGATIVE
Simplify left side to get: ab²c = NEGATIVE
Rewrite as: (ac)() = NEGATIVE
Since 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
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Re: ab < 0 bc > 0 [#permalink] New post 28 Mar 2018, 15:34
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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.

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Re: ab < 0 bc > 0 [#permalink] New post 14 Jun 2019, 10:33
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Carcass wrote:



\(ab < 0\)

\(bc > 0\)

Quantity A
Quantity B
\(ac\)
\(0\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


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
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Re: ab < 0 bc > 0   [#permalink] 14 Jun 2019, 10:33
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