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# Is d negative? (1) e + d = -12 (2) e d < -12 OA=C

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Manager
Joined: 25 May 2009
Posts: 145
Concentration: Finance
GMAT Date: 12-16-2011
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Kudos [?]: 61 [0], given: 2

Is d negative? (1) e + d = -12 (2) e d < -12 OA=C [#permalink]  13 Jul 2009, 04:06
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Is d negative?

(1) e + d = -12
(2) e – d < -12

[Reveal] Spoiler:
OA=C
Current Student
Joined: 20 Jun 2009
Posts: 168
Schools: Yale SOM Class of 2013
Followers: 4

Kudos [?]: 24 [0], given: 0

Re: Negative D [#permalink]  13 Jul 2009, 05:03
I3igDmsu wrote:
Is d negative?

(1) e + d = -12
(2) e – d < -12

[Reveal] Spoiler:
OA=C

From statement 1, we know that d = -12 - e. Thus, d < 0 if and only if e > -12. Not sufficient.

From statement 2, d > e + 12. As e can be either positive or negative, the statement is insufficient.

Taken together, the statements are sufficient. From 1 and 2, we know the following:

d = -12 -e
e < -12 + d

Thus, d < 0 if and only if e > -12. Plugging equation 1 into the inequality yields the following:

e < -24-e
2e < -24
e < -12

Becase e < -12, -12-e will always yield a positive result for d. Thus, from 1 and 2 we know that d cannot be negative.
Manager
Joined: 07 Apr 2009
Posts: 145
Followers: 1

Kudos [?]: 9 [0], given: 3

Re: Negative D [#permalink]  13 Jul 2009, 06:01
One more similar solution would be substitue value for e in the second eqn.

From 1 , e=-12-d
in 2 , d > e+ 12
d > -12-d + 12

2d >0
d >0, thus d is positive.

Re: Negative D   [#permalink] 13 Jul 2009, 06:01
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