An easier explanation please

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An easier explanation please

by Rastis » Mon Sep 15, 2014 12:23 pm
Is d negative?

(1) e + d = -12

(2) e - d < -12

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by GMATGuruNY » Mon Sep 15, 2014 12:31 pm
Rastis wrote:Is d negative?

(1) e + d = -12

(2) e - d < -12
Clearly, neither statement is sufficient on its own.
Substituting e = -d-12 into e-d < -12, we get:
(-d-12) - d < -12
-2d - 12 < -12
-2d < 0
d > 0.
SUFFICIENT.

The correct answer is C.
Last edited by GMATGuruNY on Mon Sep 15, 2014 12:41 pm, edited 1 time in total.
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by Rastis » Mon Sep 15, 2014 12:40 pm
Thank you! Much easier to understand than what the explanation showed!

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by [email protected] » Mon Sep 15, 2014 12:41 pm
Hi Rastis,

This DS question can be solved with a bit TESTing Values and algebra:

We're asked if D is negative. This is a YES/NO question.

Fact 1: E + D = -12

If.....
E = -12, D = 0, then the answer to the question is NO
E = 0, D = -12, then the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: E - D < -12

If.....
E = 0, D = 13, then the answer to the question is NO
E = -100, D = -1, then the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we have....
E + D = -12
E - D < - 12

We can combined these items using substitution; since the question is about "D", I'm going to eliminate the E:

E = -12 - D
(-12 - D) - D < -12

-12 -2D < -12
-2D < 0
D > 0

This proves that D is ALWAYS POSITIVE, so the answer to the question is ALWAYS NO.
Combined, SUFFICIENT

Final Answer: C

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