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What is the difference between the areas of the squares ABCD

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What is the difference between the areas of the squares ABCD

by fskilnik@GMATH » Mon Feb 25, 2019 1:39 pm

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GMATH practice exercise (Quant Class 15)

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What is the difference between the areas of the squares ABCD and EFGC, in that order?

(1) The area of the shaded triangle CDE is 30.
(2) The ratio of the areas of the squares ABCD and EFGC, in that order, is 25/9.

Answer: [spoiler]____(C)__[/spoiler]
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Source: — Data Sufficiency |
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ABCD-EFGC

by GMATGuruNY » Mon Feb 25, 2019 2:05 pm

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fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 15)

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What is the difference between the areas of the squares ABCD and EFGC, in that order?

(1) The area of the shaded triangle CDE is 30.
(2) The ratio of the areas of the squares ABCD and EFGC, in that order, is 25/9


Statement 1:
Case 1: DC=10 and EC=6, with the result that CDE = (1/2)(10)(6) = 30
In this case, ABCD-EFGC = 10² - 6² = 100 - 36 = 64.

Case 2: DE=20 and EC=3, with the result that CDE = (1/2)(20)(3) = 30
In this case, ABCD-EFGC = 20² - 3² = 400 - 9 = 391.

Since ABCD-EFGC can be different values, INSUFFICIENT.

Statement 2:
Case 3: ABCD=25 and EFCG=9
In this case, ABCD-EFGC = 25 - 9 = 16.

Statement 2 implies the following:
DC²/EC² = 25/9
DC/EC = 5/3.
Case 1 satisfies the condition that DC/EC = 5/3.
In Case 1, ABCD-EFGC = 64.

Since ABCD-EFGC can be different values, INSUFFICIENT.

Statements combined:
Only Case 1 satisfies both statements.
In Case 1, ABCD-EFGC = 64.
SUFFICIENT.

The correct answer is C.
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What is the difference between the areas of the squares ABCD

by fskilnik@GMATH » Mon Feb 25, 2019 5:31 pm

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fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 15)

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What is the difference between the areas of the squares ABCD and EFGC, in that order?

(1) The area of the shaded triangle CDE is 30.
(2) The ratio of the areas of the squares ABCD and EFGC, in that order, is 25/9.
$$?\,\, = \,\,{S_{{\rm{ABCD}}}} - {S_{{\rm{EFGC}}}}$$

(Click on the image to have it "zoomed"!)

Image

$$\left. \matrix{
\left( {1 + 2} \right)\,\,\,\,? = \,{\left( {5k} \right)^2} - {\left( {3k} \right)^2} = 16{k^2} \hfill \cr
30 = {S_{\Delta {\rm{CDE}}}} = {{3k \cdot 5k} \over 2}\,\,\,\,\, \Rightarrow \,\,\,\,{k^2} = 4\,\,\, \hfill \cr} \right\}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 16 \cdot 4\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.$$


The correct answer is (C).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.


POST-MORTEM: this problem is presented in our Quant Class 17 (not 15)... we thank our students for the correction!
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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