It is currently 19 Feb 2018, 11:52

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure

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

Hide Tags

Expert Post
4 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43810
A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure [#permalink]

Show Tags

New post 04 May 2015, 05:09
4
This post received
KUDOS
Expert's post
24
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

41% (02:38) correct 59% (03:07) wrong based on 228 sessions

HideShow timer Statistics

ImageImage
A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure 1. The sheet is then folded along the segment CF so that points A and D coincide after the paper is folded, as shown in Figure 2 (The shaded area represents a portion of the back side of the paper, not visible in Figure 1). What is the area, in square inches, of the shaded triangle shown?

A) 72
B) 78
C) 84
D) 96
E) 108

[Reveal] Spoiler:
Attachment:
Screen-Shot-2013-10-25-at-12.13.36-PM.png
Screen-Shot-2013-10-25-at-12.13.36-PM.png [ 13.42 KiB | Viewed 3290 times ]


Attachment:
Screen-Shot-2013-10-25-at-12.13.45-PM.png
Screen-Shot-2013-10-25-at-12.13.45-PM.png [ 14.78 KiB | Viewed 3287 times ]



Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

1 KUDOS received
Manager
Manager
avatar
Joined: 17 Mar 2015
Posts: 121
A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure [#permalink]

Show Tags

New post 04 May 2015, 06:06
1
This post received
KUDOS
Image
Fix the first picture by drawing the lines which correspond to the way we folded our paper.
\(AF = FD, AC = CD\) so angle \(CAD = CDA\) and \(DAF = ADF => FDE = CAB => DFE = BCD => AFD = ACD => CAD = DAF\) and \(CDA = FDA => ACDF\) is parallelogram with equal sides => \(AC = X\) and \(BC = 18 - X\)
Now our question is the area of triangle CFD: the area of this triangle equals to the area of triangle ACD which equals to the difference between areas of triangle ABD and triangle ABC, lets find those.
triangle ABD: \(12 * 18 * 0.5 = 108\)
for triangle ABC: hypothenuse = \(x\), legs are \(18 - x\) and \(12\)
\((18-x)^2 + 144 = x^2\)
\(324 - 36*x + x^2 + 144 = x^2\)
\(X = 13\) which means that \(BC = 5\) and that means that area of triangle ABC = \(12*5*0.5 = 30\) which means that the resulting area is \(108 - 30 = 78\)

B
4 KUDOS received
Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 578
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure [#permalink]

Show Tags

New post 04 May 2015, 09:15
4
This post received
KUDOS
3
This post was
BOOKMARKED
Bunuel wrote:
ImageImage
A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure 1. The sheet is then folded along the segment CF so that points A and D coincide after the paper is folded, as shown in Figure 2 (The shaded area represents a portion of the back side of the paper, not visible in Figure 1). What is the area, in square inches, of the shaded triangle shown?

A) 72
B) 78
C) 84
D) 96
E) 108

[Reveal] Spoiler:
Attachment:
The attachment Screen-Shot-2013-10-25-at-12.13.36-PM.png is no longer available


Attachment:
The attachment Screen-Shot-2013-10-25-at-12.13.45-PM.png is no longer available



Kudos for a correct solution.



From fig. 1 in attached image , \(BC=FE\) as triangle ABC and DEF are congruent (as shown in fig. ).
From fig 2. in attached image \((18-x)^2= 12^2 + x^2\) =====> \(x=5\)

Area of shaded region = \(\frac{1}{2}*12*(18-5)\) = 78 = B
Attachments

gmatclub.jpg
gmatclub.jpg [ 27.37 KiB | Viewed 2747 times ]


_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the Image to appreciate my post !! :-)

5 KUDOS received
Intern
Intern
avatar
Joined: 16 Mar 2015
Posts: 2
Re: A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure [#permalink]

Show Tags

New post 04 May 2015, 12:33
5
This post received
KUDOS
2
This post was
BOOKMARKED
The above answers are definitely correct, but a little overwrought for me.

The first thing you need to notice is that the shaded region is a triangle, thus the area will be 1/2 base * height. We already know the height is 12, since it is the same as the height of the paper. What we need to figure out is the base of the shaded region: line AF. Noticing that line AF is the hypotenuse of triangle AEF, we can calculate it with the information we have.

AF+FE = 18, so if you set FE = x, then AF = 18-x.

Using the Pythagorean theorem:
12^2+x^2=(18-x)^2
144+x^2=324-36x+x^2
36x=180
x=5

Thus, the base, AF=18-5=13.
And the area of the triangle is 1/2*13*12=78
Answer is B
1 KUDOS received
Current Student
User avatar
S
Joined: 28 Nov 2014
Posts: 916
Concentration: Strategy
Schools: Fisher '19 (M)
GPA: 3.71
Reviews Badge
Re: A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure [#permalink]

Show Tags

New post 08 Oct 2016, 03:41
1
This post received
KUDOS
Bunuel Can we even expect such questions on the GMAT even if I consider it to be a 51 level geometry question? Apparently, what I have seen is that the GMAT tests more of logic than laborious method/calculations.

Can we have your view on the same. Thanks.
Manager
Manager
User avatar
B
Joined: 17 Feb 2014
Posts: 112
Location: United States (CA)
GMAT 1: 700 Q49 V35
GMAT 2: 740 Q48 V42
WE: Programming (Computer Software)
GMAT ToolKit User Premium Member
A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure [#permalink]

Show Tags

New post 28 Oct 2016, 06:57
Keats wrote:
Bunuel Can we even expect such questions on the GMAT even if I consider it to be a 51 level geometry question? Apparently, what I have seen is that the GMAT tests more of logic than laborious method/calculations.

Can we have your view on the same. Thanks.


Just adding my thoughts here.

I would imagine that it is not totally out of the question. It all boils down to how quickly you can figure out the pythagorean relation for sides in triangle DEF (which requires logical deduction).

From the question we know, \(AF = DF\) and that angle DEF = 90, so for the triangle DEF, we can write:

\(=> AE^2 + (18-DF)^2 = DF^2\) --- this is the key relation that you have to find out; from this point onwards it should take about 30 sec to solve the rest and get to the answer.
\(=> 12^2 + (18-DF)^2 = DF^2\)
\(=> DF = \frac{12^2}{2*18} + \frac{18^2}{2*18}\)
(No laborious calculations here as DF^2 cancels out and you do not even need to find values of 12^2, 18^2 or 2*18. Just leave them as is and cancel out all the common factors and you will be left with 4 and 9)
\(=> DF = 4 + 9\)
\(=> DF = 13\)

Once you have DF, you can apply \(\frac{AB*DF}{2}\) to get the area of the triangle in question. (Another deduction required here is that height of the triangle is AB)
\(=> \frac{12*13}{2}\)

\(=> 78\)
2 KUDOS received
Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 499
GMAT 1: 570 Q49 V19
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure [#permalink]

Show Tags

New post 19 Aug 2017, 03:55
2
This post received
KUDOS
Answer is B 78 is the answer
Attachments

File comment: Clearly ans is shown in pic
IMG_4369.JPG
IMG_4369.JPG [ 1.15 MiB | Viewed 1312 times ]


_________________

Give Kudos for correct answer and/or if you like the solution.

3 KUDOS received
Intern
Intern
User avatar
B
Joined: 26 Jul 2016
Posts: 8
Location: India
GMAT 1: 680 Q49 V34
GPA: 4
Re: A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure [#permalink]

Show Tags

New post 19 Aug 2017, 04:00
3
This post received
KUDOS
sahilvijay wrote:
Answer is B 78 is the answer

Good One Sahil...excellent approach..
Intern
Intern
avatar
Joined: 19 Aug 2017
Posts: 1
Re: A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure [#permalink]

Show Tags

New post 19 Aug 2017, 21:32
BC+CD=18
and sum of their squares is CD square pythogoras theorm
BE=5
CD=13
similarly same approach for AF and FE
AF=13 and FE =5

area = 0.5x12x13=78
Intern
Intern
avatar
B
Joined: 27 Mar 2017
Posts: 12
CAT Tests
Re: A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure [#permalink]

Show Tags

New post 23 Aug 2017, 23:52
Lucky2783 wrote:
Bunuel wrote:
ImageImage
A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure 1. The sheet is then folded along the segment CF so that points A and D coincide after the paper is folded, as shown in Figure 2 (The shaded area represents a portion of the back side of the paper, not visible in Figure 1). What is the area, in square inches, of the shaded triangle shown?

A) 72
B) 78
C) 84
D) 96
E) 108

[Reveal] Spoiler:
Attachment:
Screen-Shot-2013-10-25-at-12.13.36-PM.png


Attachment:
Screen-Shot-2013-10-25-at-12.13.45-PM.png



Kudos for a correct solution.



From fig. 1 in attached image , \(BC=FE\) as triangle ABC and DEF are congruent (as shown in fig. ).
From fig 2. in attached image \((18-x)^2= 12^2 + x^2\) =====> \(x=5\)

Area of shaded region = \(\frac{1}{2}*12*(18-5)\) = 78 = B


hey can u help me with my query?
I solved till getting x=5 but then i took area of small two triangles (not shaded) and tried subtracting it from area of rectangle, which come like 216-30-30 = 156
so where am I going wrong?
SVP
SVP
avatar
P
Joined: 12 Dec 2016
Posts: 1905
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
GMAT ToolKit User Premium Member
Re: A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure [#permalink]

Show Tags

New post 24 Aug 2017, 16:25
simply enough, A and D reflect through CF, but ABCD is rectangle => AFDC is rhombus.
Also, to find the value of area of shaded triangle, we need to know AF.
Use 2 numbers 12 & 18 => B
Senior Manager
Senior Manager
User avatar
G
Joined: 03 Apr 2013
Posts: 290
Location: India
Concentration: Marketing, Finance
Schools: Simon '20
GMAT 1: 740 Q50 V41
GPA: 3
GMAT ToolKit User
Re: A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure [#permalink]

Show Tags

New post 15 Nov 2017, 23:30
Bunuel wrote:
ImageImage
A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure 1. The sheet is then folded along the segment CF so that points A and D coincide after the paper is folded, as shown in Figure 2 (The shaded area represents a portion of the back side of the paper, not visible in Figure 1). What is the area, in square inches, of the shaded triangle shown?

A) 72
B) 78
C) 84
D) 96
E) 108

[Reveal] Spoiler:
Attachment:
Screen-Shot-2013-10-25-at-12.13.36-PM.png


Attachment:
Screen-Shot-2013-10-25-at-12.13.45-PM.png



Kudos for a correct solution.


Bunuel
can you please explain how exactly the paper has been folded? has it been folded twice? The question does not look tough, but imagining how exactly the folding process took place is giving me nightmares. Please explain this. And if there are other questions like this out there then please also point them out. Thanks for your help.
_________________

Spread some love..Like = +1 Kudos :)

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43810
Re: A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure [#permalink]

Show Tags

New post 16 Nov 2017, 00:20
ShashankDave wrote:
Bunuel wrote:
ImageImage
A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure 1. The sheet is then folded along the segment CF so that points A and D coincide after the paper is folded, as shown in Figure 2 (The shaded area represents a portion of the back side of the paper, not visible in Figure 1). What is the area, in square inches, of the shaded triangle shown?

A) 72
B) 78
C) 84
D) 96
E) 108

[Reveal] Spoiler:
Attachment:
Screen-Shot-2013-10-25-at-12.13.36-PM.png


Attachment:
Screen-Shot-2013-10-25-at-12.13.45-PM.png



Kudos for a correct solution.


Bunuel
can you please explain how exactly the paper has been folded? has it been folded twice? The question does not look tough, but imagining how exactly the folding process took place is giving me nightmares. Please explain this. And if there are other questions like this out there then please also point them out. Thanks for your help.


I don;t know what can I add to what is already given there: The sheet is folded along the segment CF so that points A and D coincide after the paper is folded, as shown in Figure 2 (The shaded area represents a portion of the back side of the paper, not visible in Figure 1).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

SVP
SVP
avatar
P
Joined: 12 Dec 2016
Posts: 1905
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
GMAT ToolKit User Premium Member
Re: A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure [#permalink]

Show Tags

New post 16 Nov 2017, 00:31
the key attack is to spot that DF = AF = CD => ACDF is a rhombus.
Re: A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure   [#permalink] 16 Nov 2017, 00:31
Display posts from previous: Sort by

A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.