What is the difference between the areas of the squares ABCD

Expert replies

Previous Topic Next Topic

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

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

Timer

00:00

Answers

Stats

Difficulty—

GMATH practice exercise (Quant Class 15)

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]

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Like this post

Source: Beat The GMAT — Data Sufficiency | Mon Feb 25, 2019 1:39 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

ABCD-EFGC

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

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

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 = 10Â² - 6Â² = 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 = 20Â² - 3Â² = 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:
DCÂ²/ECÂ² = 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.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

What is the difference between the areas of the squares ABCD

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

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

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"!)

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

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)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review