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geometry ds

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
Expert replies
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.

Explain this question


(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;

Explain
(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
Attachments
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Source: — Quantitative Reasoning |

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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