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TAGS: Founder  Joined: 18 Apr 2015
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ab < 0 bc > 0 [#permalink]
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Expert's post 00:00

Question Stats: 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

_________________ GRE Instructor Joined: 10 Apr 2015
Posts: 2022
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Kudos [?]: 1841  , given: 9

Re: ab < 0 bc > 0 [#permalink]
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Expert's post
Carcass wrote:

ab < 0

bc > 0

 Quantity A Quantity B ac 0

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

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com  Manager Joined: 22 Feb 2018
Posts: 163
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Re: ab < 0 bc > 0 [#permalink]
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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.

_________________ GRE Instructor Joined: 10 Apr 2015
Posts: 2022
Followers: 62

Kudos [?]: 1841  , given: 9

Re: ab < 0 bc > 0 [#permalink]
1
KUDOS
Expert's post
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.

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com  Re: ab < 0 bc > 0   [#permalink] 14 Jun 2019, 10:33
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