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# If a < b and c < 0, which of the following are true?

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Retired Moderator
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If a < b and c < 0, which of the following are true? [#permalink]

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19 Jan 2010, 15:47
2
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Difficulty:

55% (hard)

Question Stats:

56% (01:18) correct 44% (00:59) wrong based on 332 sessions

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If a < b and c < 0, which of the following are true?

I. ac > bc
II. a + c < b + c
III. a - c > b - c

A. I only
B. II only
C. III only
D. I and II only
E. Neither
[Reveal] Spoiler: OA

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Last edited by Bunuel on 26 Sep 2014, 00:19, edited 1 time in total.
Edited the question and added the OA.

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Re: If a < b and c < 0, which of the following are true? [#permalink]

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19 Jan 2010, 19:05
no idea if can be graphed but I say the answer is B

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Re: If a < b and c < 0, which of the following are true? [#permalink]

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19 Jan 2010, 23:01
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1. AC > BC

=> AC-BC >0
(A-B) C > 0 true

as C< 0
and A-B < 0...thus true.

2. Its also true

Thus I and II only
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Re: If a < b and c < 0, which of the following are true? [#permalink]

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20 Jan 2010, 09:41
gurpreetsingh wrote:

1. AC > BC

=> AC-BC >0
(A-B) C > 0 true

as C< 0
and A-B < 0...thus true.

2. Its also true

Thus I and II only

Nice explanation!! Kudos!!

OA is "D".
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Re: If a < b and c < 0, which of the following are true? [#permalink]

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19 Dec 2011, 12:22
if a<b and c<0
then: a+c<b+0
can someone explain, how ii is true?

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Re: If a < b and c < 0, which of the following are true? [#permalink]

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20 Dec 2011, 11:11
since c<0 and a<b so if we multiply a negative quantity to a smaller quantity then it turns out to be bigger in value(in both cases when a,b are negative or positive).so a is correct..simmilarly for b

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Re: If a < b and c < 0, which of the following are true? [#permalink]

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06 Jan 2012, 21:25
Nice question. Its easy to miss that even statement 1 is be true. Thanks gurpreetsingh.
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Re: If a < b and c < 0, which of the following are true? [#permalink]

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25 Sep 2014, 22:57

Try with values. 2nd statement fails for a=-1, b=1, c=-1

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Re: If a < b and c < 0, which of the following are true? [#permalink]

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25 Sep 2014, 23:25
prabhakarsharma wrote:

Try with values. 2nd statement fails for a=-1, b=1, c=-1

a + c = -1 -1 = -2
b + c = 1 -1 = 0

=> a + c < b + c
(II) is correct.

Hope it helps
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Re: If a < b and c < 0, which of the following are true? [#permalink]

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26 Sep 2014, 00:03
D is correct. as it works for both +ve and -ve numbers

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Re: If a < b and c < 0, which of the following are true? [#permalink]

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26 Sep 2014, 00:25
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Hussain15 wrote:
If a < b and c < 0, which of the following are true?

I. ac > bc
II. a + c < b + c
III. a - c > b - c

A. I only
B. II only
C. III only
D. I and II only
E. Neither

Multiply a < b by c and don't forget to flip the sign of the inequality since we are multiplying by negative value: ac > bc. So, I must be true.

As for II. Cancel c on both sides: a < b. II is true.

The same for III. Cancel -c on both sides: a > b. So, III is not true.

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Re: If a < b and c < 0, which of the following are true? [#permalink]

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13 May 2016, 12:30
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Re: If a < b and c < 0, which of the following are true? [#permalink]

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02 Jun 2017, 22:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If a < b and c < 0, which of the following are true?   [#permalink] 02 Jun 2017, 22:20
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