NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 20:28 It is currently 25 Apr 2024, 20:28
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

What is the area of the shaded portion of this rectangle, given that A

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619043 [1]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
What is the area of the shaded portion of this rectangle, given that A [#permalink] New post   31 Jan 2016, 07:02
1
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

91% (01:20) correct 9% (01:50) wrong based on 107 sessions
Hide Show timer Statistics

What is the area of the shaded portion of this rectangle, given that AD = 6, CD = 8, and AE = x?

A. 48 − 3x
B. 48 + 3x
C. 3x + 16
D. 24 − 3x
E. 24 + 3x

Show Spoiler
Attachment:
2016-01-31_1801.png
2016-01-31_1801.png [ 2.37 KiB | Viewed 15381 times ]
ShowHide Answer
Official Answer
A
User avatar
L
EMPOWERgmatRichC
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21846
Own Kudos [?]: 11666 [1]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: What is the area of the shaded portion of this rectangle, given that A [#permalink] New post   01 Feb 2016, 11:35
1
Kudos
Expert Reply
Hi All,

This question can be solved by TESTing VALUES. Here are a couple of hints so that you can try this question on your own:

Show Spoiler
1) To find the area of the shaded region, you need to subtract the area of the white triangle from the area of the rectangle.
2) TEST a VALUE for X - remember that since AB=CD=8, X has to be less than 8).
3) Calculate the area of the triangle and subtract it from the area of the rectangle.
4) Find the 'matching' value in the answer choices.


GMAT assassins aren't born, they're made,
Rich
User avatar
L
Mo2men
RSM Erasmus Moderator
Joined: 26 Mar 2013
Posts: 2461
Own Kudos [?]: 1360 [2]
Given Kudos: 641
Concentration: Operations, Strategy
Schools: Erasmus (II)
Send PM
Reviews Badge
Re: What is the area of the shaded portion of this rectangle, given that A [#permalink] New post   02 Feb 2016, 18:23
2
Kudos
Hi Rich,

In this question particularly, I think the answer choices reveal the answer. The shaded area should be result of subtracting rectangular area from the area of triangle.

The only choice that contain area of rec (48) is choice (A)

If the choices have more 48, we may use Testing the Values
User avatar
L
EMPOWERgmatRichC
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21846
Own Kudos [?]: 11666 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: What is the area of the shaded portion of this rectangle, given that A [#permalink] New post   02 Feb 2016, 23:29
Expert Reply
Hi Mo2men,

You bring up a very good point. Whoever wrote the answer choices to this question really made it 'easy' for you to spot that pattern. However, you will likely NOT have it so easy on the multi-shape Geometry question(s) that you face on the Official GMAT. Those questions can be some of the most time-consuming and toughest questions that you face. As such, you'll still need to be practicing the proper math 'skills' and Tactics to consistently score at a high level in the Quant section.

GMAT assassins aren't born, they're made,
Rich
User avatar
TeamGMATIFY
Tutor
Joined: 20 Aug 2015
Posts: 350
Own Kudos [?]: 1393 [1]
Given Kudos: 10
Location: India
GMAT 1: 760 Q50 V44
Send PM
Re: What is the area of the shaded portion of this rectangle, given that A [#permalink] New post   04 Feb 2016, 02:54
1
Kudos
Expert Reply
Bunuel wrote:

What is the area of the shaded portion of this rectangle, given that AD = 6, CD = 8, and AE = x?

A. 48 − 3x
B. 48 + 3x
C. 3x + 16
D. 24 − 3x
E. 24 + 3x

Show Spoiler
Attachment:
2016-01-31_1801.png


Whenever you see a question with shaded area, try to find out the area of the participating figures.
In this case, we need the area of the rectangle ABCD and triangle ADE

1. Area of rectangle = AD*CD = 6*8 = 48
2. Area of triangle = \(\frac{1}{2}\)* AD*AE = \(\frac{1}{2}\) *6*x = 3x

Area of shaded region = area of rectangle - area of triangle = 48 - 3x (Option A)
avatar
davedekoos
Manager
Manager
Joined: 09 Jul 2013
Posts: 97
Own Kudos [?]: 296 [1]
Given Kudos: 8
Send PM
What is the area of the shaded portion of this rectangle, given that A [#permalink] New post   04 Feb 2016, 12:59
1
Kudos
The solutions above are perfect, and probably the easiest way to go. I agree with Rich that on the actual test you're probably not going to be so lucky as to see answer choices as straightforward as these.

Another approach would be to calculate the area of the shaded region directly using the formula for the area of a trapezoid.

\(A=\frac{l_1+l_2}{2}*h\) where \(l_1\) and \(l_2\) are the lengths of the parallel sides, and \(h\) is the height (perpendicular distance between the parallel sides)

\(A=\frac{8+(8-x)}{2}*6\)

\(A=(8-\frac{x}{2})*6\)

\(A = 48-3x\)

Answer: A
avatar
sharmilaz87
Intern
Intern
Joined: 04 May 2015
Posts: 5
Own Kudos [?]: 7 [0]
Given Kudos: 1
Send PM
Re: What is the area of the shaded portion of this rectangle, given that A [#permalink] New post   04 Feb 2016, 20:16
Area of the rectangle ABCD=6*8=48
Let AE=x, since AB=8, EB=8-x
EBCD is a trapezoid
Area of EBCD=(Base1+Base2)/2 * Height={8+(8-x)}/2 * 6=48-3x
Ans.A
User avatar
G
Sr1994
Retired Moderator
Joined: 28 Nov 2019
Posts: 223
Own Kudos [?]: 124 [0]
Given Kudos: 90
Location: India
Schools: ISB '24 Imperial
Send PM
What is the area of the shaded portion of this rectangle, given that A [#permalink] New post   27 Oct 2020, 16:34
Area of shaded portion = Total area - Area of triangle AED

Total area = 6 * 8 = 48

Area of Triangle AED = \(\frac{1}{2}\) * x * 6 = 3X

Therefore , area of shaded portion = 48 - 3X

Answer A
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18761
Own Kudos [?]: 22054 [1]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: What is the area of the shaded portion of this rectangle, given that A [#permalink] New post   31 Oct 2020, 13:50
1
Kudos
Expert Reply
Bunuel wrote:

What is the area of the shaded portion of this rectangle, given that AD = 6, CD = 8, and AE = x?

A. 48 − 3x
B. 48 + 3x
C. 3x + 16
D. 24 − 3x
E. 24 + 3x

Show Spoiler
Attachment:
2016-01-31_1801.png

Solution:

We see that the area of the shaded region is the difference between the area of rectangle ABCD and the area of triangle ADE.

Since the area of rectangle ABCD is 8 * 6 = 48 and the area of triangle ADE is ½ * 6 * x = 3x, the area of the shaded region is 48 - 3x.

Answer: A
GMAT Club Bot
gmatclubot
Re: What is the area of the shaded portion of this rectangle, given that A [#permalink]
31 Oct 2020, 13:50
Moderators:
Bunuel
Math Expert
92915 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