GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 18 Jan 2020, 19:40

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

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

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 60480
A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure  [#permalink]

Show Tags

New post 04 May 2015, 06:09
5
29
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

30% (03:04) correct 70% (03:02) wrong based on 191 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

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 5673 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 5670 times ]



Kudos for a correct solution.

_________________
Most Helpful Community Reply
Senior Manager
Senior Manager
User avatar
Joined: 07 Aug 2011
Posts: 498
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, 10:15
6
6
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

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 4887 times ]

General Discussion
Manager
Manager
avatar
Joined: 17 Mar 2015
Posts: 113
A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure  [#permalink]

Show Tags

New post 04 May 2015, 07:06
1
1
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
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, 13:33
5
2
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
Current Student
User avatar
G
Joined: 28 Nov 2014
Posts: 813
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, 04:41
1
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: 98
Location: United States (CA)
GMAT 1: 700 Q49 V35
GMAT 2: 740 Q48 V42
WE: Programming (Computer Software)
GMAT ToolKit User
A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure  [#permalink]

Show Tags

New post 28 Oct 2016, 07:57
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)
\(=> \frac{12*13}{2}\)

\(=> 78\)
Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 417
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Reviews Badge
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, 04:55
2
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 3451 times ]

Intern
Intern
User avatar
B
Joined: 26 Jul 2016
Posts: 4
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, 05:00
3
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, 22:32
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: 9
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, 00:52
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

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?
VP
VP
avatar
P
Joined: 12 Dec 2016
Posts: 1471
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
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 24 Aug 2017, 17:25
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: 262
Location: India
Concentration: Marketing, Finance
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 16 Nov 2017, 00:30
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

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.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 60480
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, 01:20
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

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).
_________________
VP
VP
avatar
P
Joined: 12 Dec 2016
Posts: 1471
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
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 16 Nov 2017, 01:31
the key attack is to spot that DF = AF = CD => ACDF is a rhombus.
Intern
Intern
avatar
B
Joined: 20 Jan 2019
Posts: 12
Re: A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure  [#permalink]

Show Tags

New post 17 Apr 2019, 07:39
From a quick peek, can someone elaborate why CF divides the rectangle to supposedly two symmetrical trapezoids?
CF can also be more to the left or to the right.
Any clarification?
Intern
Intern
avatar
B
Joined: 03 Mar 2019
Posts: 28
GMAT 1: 640 Q45 V32
GMAT 2: 690 Q48 V37
Re: A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure  [#permalink]

Show Tags

New post 17 Apr 2019, 23:10
1
selale wrote:
From a quick peek, can someone elaborate why CF divides the rectangle to supposedly two symmetrical trapezoids?
CF can also be more to the left or to the right.
Any clarification?


As we can see in figure 2 that DF=AF, AC=CD => angle DAF=ADF, CAD=CDA. And then we have BAC+CAD+DAF=FDE+ADF+CDA=90 ==> BAC=FDE =>BC=FE
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9052
Location: United States (CA)
Re: A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure  [#permalink]

Show Tags

New post 27 May 2019, 05:28
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

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.


We can let BC = x and thus CD = 18 - x. We see that triangle DBC (in figure 2) is a right triangle and thus we have:

(DB)^2 + (BC)^2 = (CD)^2

12^2 + x^2 = (18 - x)^2

144 + x^2 = 324 - 36x + x^2

36x = 180

x = 5

Likewise, if we let FE = y and thus AF = 18 - y. We see that triangle AEF (in figure 2) is a right triangle. Since side AE of triangle AEF is now same as DE, AE = 12 and we have:

(AE)^2 + (FE)^2 = (AF)^2

12^2 + y^2 = (18 - y)^2

This is equivalent to the equation above, so y = 5.

Now we can argue that:

Area of triangle DBC + Area of triangle AEF + 2(Area of triangle CAF) = Area of rectangle ABDE

(½)(12)(5) + (½)(12)(5) + 2(Area of triangle CAF) = 12(18)

30 + 30 + 2(Area of triangle CAF) = 216

2(Area of triangle CAF) = 156

Area of triangle CAF = 78

But the area of triangle CAF is the area of the shaded region, so the area of the shaded region is 78.

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure   [#permalink] 27 May 2019, 05:28
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  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne