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

 It is currently 21 May 2019, 22:23

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

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

The shaded region in the figure above represents a rectangular frame

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55231
The shaded region in the figure above represents a rectangular frame  [#permalink]

Show Tags

12 Sep 2018, 01:00
00:00

Difficulty:

35% (medium)

Question Stats:

83% (02:12) correct 17% (01:44) wrong based on 21 sessions

HideShow timer Statistics

The shaded region in the figure above represents a rectangular frame with a length of 20 inches and a width of 16 inches. The frame encloses a rectangular picture that has same area as the frame itself. If the length and width of the picture have the same ratio as the length and width of the frame, what is the length of the picture, in inches?

A. $$5\sqrt{2}$$

B. $$\frac{5}{\sqrt{2}}$$

C. $$\frac{10}{\sqrt{2}}$$

D. 10

E. $$10\sqrt{2}$$

Attachment:

image019.gif [ 2.55 KiB | Viewed 523 times ]

_________________
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1008
WE: Supply Chain Management (Energy and Utilities)
Re: The shaded region in the figure above represents a rectangular frame  [#permalink]

Show Tags

12 Sep 2018, 02:25
Bunuel wrote:

The shaded region in the figure above represents a rectangular frame with a length of 20 inches and a width of 16 inches. The frame encloses a rectangular picture that has same area as the frame itself. If the length and width of the picture have the same ratio as the length and width of the frame, what is the length of the picture, in inches?

A. $$5\sqrt{2}$$

B. $$\frac{5}{\sqrt{2}}$$

C. $$\frac{10}{\sqrt{2}}$$

D. 10

E. $$10\sqrt{2}$$

Attachment:
image019.gif

Given, Area of frame =Area of picture
Area of frame =Area of bigger rectangular region - Area of picture
Or, Area of picture =1/2*20*16=160

Let l and w are the length and width of picture respectively.
Given l:w=20:16=5:4
Or, w=(4/5)*l

So area of picture=l*(4/5)*l=160
Or, $$l^2$$=200
Or, l=10$$\sqrt{2}$$

Ans. (E)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Director
Joined: 04 Sep 2015
Posts: 559
Location: India
WE: Information Technology (Computer Software)
Re: The shaded region in the figure above represents a rectangular frame  [#permalink]

Show Tags

14 Sep 2018, 13:01
Bunuel wrote:

The shaded region in the figure above represents a rectangular frame with a length of 20 inches and a width of 16 inches. The frame encloses a rectangular picture that has same area as the frame itself. If the length and width of the picture have the same ratio as the length and width of the frame, what is the length of the picture, in inches?

A. $$5\sqrt{2}$$

B. $$\frac{5}{\sqrt{2}}$$

C. $$\frac{10}{\sqrt{2}}$$

D. 10

E. $$10\sqrt{2}$$

Attachment:
image019.gif

Lw=20*16-lw
2lw=20*16=lw=160.

w/l=4/5

substitute l*l=200,

l=10root2.

Option E.
Re: The shaded region in the figure above represents a rectangular frame   [#permalink] 14 Sep 2018, 13:01
Display posts from previous: Sort by