NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 16:30 It is currently 26 Apr 2024, 16:30
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

In the figure, the area of rectangle EFGH is 3 units greater than the

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619239 [1]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
In the figure, the area of rectangle EFGH is 3 units greater than the [#permalink] New post   Updated on: 15 Jul 2019, 04:24
1
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

79% (02:09) correct 21% (02:41) wrong based on 43 sessions
Hide Show timer Statistics

In the figure, the area of rectangle EFGH is 3 units greater than the area of rectangle ABCD. What is the value of ab if a + b = 8?

(A) 9
(B) 12
(C) 15
(D) 18
(E) 21

Source: Nova GMAT
Difficulty Level: 600

Show Spoiler
Attachment:
recs.jpg
recs.jpg [ 15.7 KiB | Viewed 3451 times ]
ShowHide Answer
Official Answer
C

Originally posted by Bunuel on 09 Oct 2018, 23:41.
Last edited by Sajjad1994 on 15 Jul 2019, 04:24, edited 1 time in total.
Added Source
User avatar
L
Chethan92
Director
Director
Joined: 18 Jul 2018
Posts: 926
Own Kudos [?]: 1288 [0]
Given Kudos: 95
Location: India
Concentration: Operations, General Management
Schools: IIMB EPGP'22 (M)
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE:Engineering (Energy and Utilities)
Send PM
Reviews Badge
Re: In the figure, the area of rectangle EFGH is 3 units greater than the [#permalink] New post   10 Oct 2018, 00:02
area of rectangle EFGH = 3 + area of rectangle ABCD

(x+a)(x+b) = 3+(x+2)(x+6)

\(x^2\)+x(a+b)+ab = \(x^2\)+8x+15

Given a+b = 8.

Solving gives ab = 15.

C is the answer.
User avatar
G
Salsanousi
Senior Manager
Senior Manager
Joined: 19 Oct 2013
Posts: 412
Own Kudos [?]: 307 [1]
Given Kudos: 117
Location: Kuwait
GPA: 3.2
WE:Engineering (Real Estate)
Send PM
GMAT ToolKit User
Re: In the figure, the area of rectangle EFGH is 3 units greater than the [#permalink] New post   10 Oct 2018, 04:57
Bunuel wrote:

In the figure, the area of rectangle EFGH is 3 units greater than the area of rectangle ABCD. What is the value of ab if a + b = 8?

(A) 9
(B) 12
(C) 15
(D) 18
(E) 21

Show Spoiler
Attachment:
recs.jpg


\((x+a) * (x+b) = 3 + (x+6)*(x+2)\)

\(x^2 + xb + xa + ab = 3 + x^2 + 2x + 6x + 12\)

\(x^2\) cancel from both side.

take x as a common factor

\(x (a+b) + ab = 3 + x (2+6) + 12\). we are given a+b = 8
\(8x + ab = 15 +8x\)

\(ab = 15\)

Answer choice C
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6072
Own Kudos [?]: 4690 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
GMAT ToolKit User
Re: In the figure, the area of rectangle EFGH is 3 units greater than the [#permalink] New post   10 Oct 2018, 07:47
Bunuel wrote:

In the figure, the area of rectangle EFGH is 3 units greater than the area of rectangle ABCD. What is the value of ab if a + b = 8?

(A) 9
(B) 12
(C) 15
(D) 18
(E) 21

Show Spoiler
Attachment:
recs.jpg


\((x+a)(x+b) - (x+2)(x+6) = 3\)

Or, \((ab +ax + bx +x^2) - (x^2 +8x + 12) = 3\)

Or, \(ab + x (a + b) - 8x - 12 = 3\)

Or, \(ab + 8x - 8x - 12 = 3\)

Or, \(ab = 15\), Answer must be (C)
User avatar
L
pushpitkc
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 2873
Own Kudos [?]: 5206 [0]
Given Kudos: 47
Location: India
GPA: 3.12
Send PM
Re: In the figure, the area of rectangle EFGH is 3 units greater than the [#permalink] New post   11 Oct 2018, 01:00


Formula used: Area(Rectangle) = Length * Breadth.
Given: Area(Rectangle EFGH) is 3 units greater than the Area(Rectangle ABCD)

Area(Rectangle ABCD) = \((x+2)(x+6) = x^2 + 8x + 12\) units.
Area(Rectangle EFGH) = \((x+a)(x+b) = x^2 + (a+b)x + ab\) units.

Therefore, the area of the rectangle ABCD is \((x^2 + 8x + 12) + 3 = x^2 + 8x + 15\) and value of ab is 15(Option C)
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18767
Own Kudos [?]: 22064 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: In the figure, the area of rectangle EFGH is 3 units greater than the [#permalink] New post   13 Oct 2018, 18:13
Expert Reply
Bunuel wrote:

In the figure, the area of rectangle EFGH is 3 units greater than the area of rectangle ABCD. What is the value of ab if a + b = 8?

(A) 9
(B) 12
(C) 15
(D) 18
(E) 21

Show Spoiler
Attachment:
recs.jpg


We can create the equation:

3 + (x + 2)(x + 6) = (x + a)(x + b)

3 + x^2 + 8x + 12 = x^2 + ax + bx + ab

15 + 8x = ax + bx + ab

15 + 8x = x(a + b) + ab

Since a + b = 8, we have:

15 + 8x = 8x + ab

15 = ab

Answer: C
GMAT Club Bot
gmatclubot
Re: In the figure, the area of rectangle EFGH is 3 units greater than the [#permalink]
13 Oct 2018, 18:13
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions