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

It is currently 18 Jun 2019, 00:25

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

The shaded region in the figure above represents a frame shaped as a

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55648
The shaded region in the figure above represents a frame shaped as a  [#permalink]

Show Tags

New post 13 Sep 2018, 04:50
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

50% (03:08) correct 50% (03:31) wrong based on 36 sessions

HideShow timer Statistics

Image
The shaded region in the figure above represents a frame shaped as a right triangle with sides 10 inches and 13 inches. The frame encloses a picture, shaped also as a right triangle, which has the same area as the frame itself. If the sum of the 2 legs of the picture is 17 inches, what is the length of the hypotenuse of the triangular picture?


A. \(\sqrt{29}\)

B. \(\sqrt{159}\)

C. 13

D. \(\sqrt{269}\)

E. 17

Attachment:
image052.jpg
image052.jpg [ 4.88 KiB | Viewed 733 times ]

_________________
Senior Manager
Senior Manager
avatar
P
Joined: 15 Oct 2017
Posts: 309
GMAT 1: 560 Q42 V25
GMAT 2: 570 Q43 V27
GMAT 3: 710 Q49 V39
Reviews Badge
Re: The shaded region in the figure above represents a frame shaped as a  [#permalink]

Show Tags

New post 13 Sep 2018, 20:57
Hi Bunuel, can you please share the OE or better, your approach? Thanks!
Manager
Manager
avatar
S
Joined: 19 Apr 2017
Posts: 82
Concentration: General Management, Sustainability
Schools: ESSEC '22
GPA: 3.9
WE: Operations (Hospitality and Tourism)
The shaded region in the figure above represents a frame shaped as a  [#permalink]

Show Tags

New post 15 Sep 2018, 02:16


Frame has the same area as the picture itself means -> Area of ABC – Area of picture = Area of the picture

Area of ABC= 2*area of picture

Area of ABC = (1/2) *10 * 13 = 65

\(65 = 2*1/2(ab)\)

ab=65 -> 130 = 2ab
(a+b) = 17 (GIVEN)

\((a+b)^2 = a^2+b^2+2ab\)
length of the hypotenuse \(c=> c^2=a^2+b^2=289-130=159\)
\(c=\sqrt{159}\) B
Director
Director
User avatar
P
Joined: 04 Sep 2015
Posts: 564
Location: India
WE: Information Technology (Computer Software)
Premium Member Reviews Badge
Re: The shaded region in the figure above represents a frame shaped as a  [#permalink]

Show Tags

New post 15 Sep 2018, 12:22
Bunuel wrote:
Image
The shaded region in the figure above represents a frame shaped as a right triangle with sides 10 inches and 13 inches. The frame encloses a picture, shaped also as a right triangle, which has the same area as the frame itself. If the sum of the 2 legs of the picture is 17 inches, what is the length of the hypotenuse of the triangular picture?


A. \(\sqrt{29}\)

B. \(\sqrt{159}\)

C. 13

D. \(\sqrt{269}\)

E. 17

Attachment:
image052.jpg



Given tha the area of the picture is equal to the area of the frame, then

1/2*B*H=(10*13)/2=65.


also area of the inner trianlge(picture)=1/2*b*h=65/2,

this gives b*h=65.


given b+h=17,squaring both sides,


bsquare+hsquare+2bh=289


substituting bh value we get


hypotenus theorm and ans as root 159.


Option B is correct.
GMAT Club Bot
Re: The shaded region in the figure above represents a frame shaped as a   [#permalink] 15 Sep 2018, 12:22
Display posts from previous: Sort by

The shaded region in the figure above represents a frame shaped as a

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


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