geometry ds

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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geometry ds

by rupsk » Sun Nov 13, 2011 3:13 pm
What is the area of triangle EBC?

(1) The area of ΔAED is 16.

(2) The area of ΔDEC is 12.

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(1)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
(2)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
(3)bOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked;

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(4)

EACH statement ALONE is sufficient to answer the question asked;

(5)

statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Image
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Source: — Quantitative Reasoning |

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by neelgandham » Mon Nov 14, 2011 4:28 am
Area of triangle EBC ?
1)Area of triangle AED = 16
Area of ADC = Area of BDC (common base(BC) and equal height (AD) -(1)

Area(BEC) = Area(BDC) - Area(EDC)
Area(AED) = Area(ADC) - Area(EDC)
Subtracting the left hand and right hand sides
Area(BEC) - Area(AED) = Area(BDC) - Area(EDC) - Area(ADC) + Area(EDC)
Area(BEC) - Area(AED) = Area(BDC) - Area(ADC) = 0 (from (1) above)

So, Area(BEC) - Area(AED) = 0 and Area(BEC) = Area(AED) =16
Sufficient!
(2) The area of �"DEC is 12.
Insufficient!

IMO A
Anil Gandham
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