GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Mar 2019, 05:48

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# What is the difference between the areas of the squares ABCD and EFGC,

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 910
What is the difference between the areas of the squares ABCD and EFGC,  [#permalink]

### Show Tags

25 Feb 2019, 14:49
1
00:00

Difficulty:

35% (medium)

Question Stats:

73% (02:04) correct 27% (01:44) wrong based on 22 sessions

### HideShow timer Statistics

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.

_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Senior Manager
Joined: 04 Aug 2010
Posts: 386
Schools: Dartmouth College
Re: What is the difference between the areas of the squares ABCD and EFGC,  [#permalink]

### Show Tags

25 Feb 2019, 15:23
fskilnik 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 = 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.

.
_________________

GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 910
What is the difference between the areas of the squares ABCD and EFGC,  [#permalink]

### Show Tags

25 Feb 2019, 18:42
fskilnik 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)
Our high-level "quant" preparation starts here: https://gmath.net

SVP
Joined: 18 Aug 2017
Posts: 2450
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: What is the difference between the areas of the squares ABCD and EFGC,  [#permalink]

### Show Tags

27 Feb 2019, 04:44
#1
side of large square * side of small square = 60
side can be ( 30,2) , ( 20,3).. so on in sufficient

#2
ratio 25/9 or say side 5/3 in sufficient

from 1 & 2
base = 10 and side = 6 ;
ratio 5/3 area 25/9
IMO C

fskilnik 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.

_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

Re: What is the difference between the areas of the squares ABCD and EFGC,   [#permalink] 27 Feb 2019, 04:44
Display posts from previous: Sort by

# What is the difference between the areas of the squares ABCD and EFGC,

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.