It is currently 24 Jun 2017, 15:53

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The shaded region in the figure above represents a rectangul

Author Message
TAGS:

### Hide Tags

Intern
Joined: 06 Oct 2010
Posts: 40

### Show Tags

17 Oct 2010, 13:02
2
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

71% (02:58) correct 29% (03:04) wrong based on 58 sessions

### HideShow timer Statistics

The shaded region in the figure above represents a rectangular frame with length 18 inches and width 15 inches. The frame encloses a rectangular picture that has the same area as the frame itself. If the length and width of the picture have the same ratio as the lenght and width of the frame, what is the length of the picture, in inches?

A. $$9\sqrt2$$
B. $$\frac {3}{2}$$
C. $$\frac {9}{\sqrt2}$$
D. $$15 ( 1 - \frac {1}{\sqrt2})$$
E. $$\frac {9}{2}$$

Source: Paper Test
Test Code 28
Section 5
# 15

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-shaded-region-in-the-figure-above-represents-a-135095.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Sep 2015, 23:10, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Retired Moderator
Joined: 02 Sep 2010
Posts: 803
Location: London
Re: The shaded region in the figure above represents a rectangul [#permalink]

### Show Tags

17 Oct 2010, 15:11
1
KUDOS
niheil wrote:
This is a tough one. Can anyone help me out with this:

The shaded region in the figure above represents a rectangular frame with length 18 inches and width 15 inches. The frame encloses a rectangular picture that has the 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) $$9\sqrt{2}$$

(B) $$\frac{3}{2}$$

(C) $$\frac{9}{\sqrt{2}}$$

(D) $$15(1-\frac{1}{\sqrt{2}})$$

(E) $$\frac{9}{2}$$

Source: Paper Test
Test Code 28
Section 5
# 15

Let the length of the picture be x. Since its length and width are in the same ratio as that of the frame, the width must be (5/6)x.

Area of frame = 18*15 - Area of picture.

But we know area of picture = area of frame, hence :

Area of picture = 18*15/2
x * (5/6)x = 9*15
x^2 = 27*6 = 81*2
Hence x = 9 * sqrt(2)

_________________
Intern
Joined: 06 Oct 2010
Posts: 40
Re: The shaded region in the figure above represents a rectangul [#permalink]

### Show Tags

17 Oct 2010, 16:52
I'm so sorry for forgetting to include the diagram or mentioning that the question came with one. Thanks for the help shrouded1.
Senior Manager
Joined: 13 Aug 2010
Posts: 292
Re: The shaded region in the figure above represents a rectangul [#permalink]

### Show Tags

17 Oct 2010, 20:26
hi, if its not much of a problem can you please include the diagram. thanx
Manager
Joined: 19 Aug 2010
Posts: 76
Re: The shaded region in the figure above represents a rectangul [#permalink]

### Show Tags

18 Oct 2010, 14:23
18*15-X*5/6*X=X*5/6*
X=3\sqrt{2}
Intern
Joined: 18 Jun 2010
Posts: 8
Schools: Richard Ivey, Rotman, kelley, Rice, illinois, sauder, NUS
Re: The shaded region in the figure above represents a rectangul [#permalink]

### Show Tags

14 Apr 2011, 18:28
The explanation is not proper. Can someone else explain please.

The answer is coming down to $$3/\sqrt{2}$$ and not the OA $$9/\sqrt{2}$$.
Manager
Joined: 14 Feb 2011
Posts: 194
Re: The shaded region in the figure above represents a rectangul [#permalink]

### Show Tags

14 Apr 2011, 23:05
1
KUDOS
shrouded1 wrote:
niheil wrote:
This is a tough one. Can anyone help me out with this:

The shaded region in the figure above represents a rectangular frame with length 18 inches and width 15 inches. The frame encloses a rectangular picture that has the 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) $$9\sqrt{2}$$

(B) $$\frac{3}{2}$$

(C) $$\frac{9}{\sqrt{2}}$$

(D) $$15(1-\frac{1}{\sqrt{2}})$$

(E) $$\frac{9}{2}$$

Source: Paper Test
Test Code 28
Section 5
# 15

Let the length of the picture be x. Since its length and width are in the same ratio as that of the frame, the width must be (5/6)x.

Area of frame = 18*15 - Area of picture.

But we know area of picture = area of frame, hence :

Area of picture = 18*15/2
x * (5/6)x = 9*15
x^2 = 27/6 = 9/2
Hence x = sqrt(9/2)

x^2 = 27*6=9*9*2

So, x = 9$$\sqrt{2}$$

The approach is right but there is a calculation mistake (in red above).

If you make correct calculations (in blue above), you will get right answer as A.
Retired Moderator
Joined: 02 Sep 2010
Posts: 803
Location: London
Re: The shaded region in the figure above represents a rectangul [#permalink]

### Show Tags

14 Apr 2011, 23:23
agreed, small calc mistake there ... willl correct
_________________
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2010
Re: The shaded region in the figure above represents a rectangul [#permalink]

### Show Tags

15 Apr 2011, 02:06
6
KUDOS
2
This post was
BOOKMARKED
niheil wrote:
This is a tough one. Can anyone help me out with this:

The shaded region in the figure above represents a rectangular frame with length 18 inches and width 15 inches. The frame encloses a rectangular picture that has the 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) $$9\sqrt{2}$$

(B) $$\frac{3}{2}$$

(C) $$\frac{9}{\sqrt{2}}$$

(D) $$15(1-\frac{1}{\sqrt{2}})$$

(E) $$\frac{9}{2}$$

Source: Paper Test
Test Code 28
Section 5
# 15

Attachment:

rectangular_picture_frame.PNG [ 10.34 KiB | Viewed 11773 times ]

Given:
Length of the frame(outer side of the black portion) = 18 inches
Width of the frame(outer side of the black portion) = 15 inches

Total Area of the frame(black portion) and picture(orange portion) = length*width = 18*15
$$A_t=18*15$$

Let the length of the picture(orange portion) be "l", we need to find this.
Let the width of the picture(orange portion) be "w"
Area of the picture(orange portion) = l*w
$$A_p=l*w$$

Area of the frame(black portion) = Total Area of the frame(black) and picture(orange) - Area of the picture(orange)
$$A_f=A_t-A_p$$

"The frame encloses a rectangular picture that has the same area as the frame itself"
$$A_p=A_f$$

$$A_p=A_t-A_p$$
$$A_t=2A_p$$
$$2A_p=18*15$$

$$A_p=\frac{18*15}{2}$$

$$l*w=\frac{18*15}{2}$$ -----------------------1

"length and width of the picture(orange) have the same ratio as the length and width of the frame(black)"
$$\frac{l}{w}=\frac{18}{15}$$

$$w=\frac{15}{18}*l$$ --------------------2

Substituting "w" from 2 in 1:

$$l*\frac{15}{18}*l=\frac{18*15}{2}$$
$$l^2=\frac{(18)^2}{2}$$

Taking the square root on both sides:
$$l=\frac{18}{\sqrt{2}}$$

$$l=\frac{2*9}{\sqrt{2}}$$

$$l=\frac{\sqrt{2}*\sqrt{2}*9}{\sqrt{2}}$$

$$l=9\sqrt{2}$$

Ans: "A"
_________________
Intern
Joined: 04 Jan 2014
Posts: 3
Re: The shaded region in the figure above represents a rectangul [#permalink]

### Show Tags

06 Jan 2014, 04:15
Is this one really supposed to be easy?
Math Expert
Joined: 02 Sep 2009
Posts: 39662
Re: The shaded region in the figure above represents a rectangul [#permalink]

### Show Tags

06 Jan 2014, 04:23
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
FirstScore350 wrote:
Is this one really supposed to be easy?

It's ~650 level question.

The shaded region in the figure above represents a rectangular frame with length 18 inches and width 15 inches. The frame encloses a rectangular picture that has the same area as the frame itself. If the length and width of the picture have the same ratio as the lenght and width of the frame, what is the length of the picture, in inches?

A. $$9\sqrt2$$
B. $$\frac {3}{2}$$
C. $$\frac {9}{\sqrt2}$$
D. $$15 ( 1 - \frac {1}{\sqrt2})$$
E. $$\frac {9}{2}$$

Say the length and the width of the picture are $$x$$ and $$y$$ respectively. Since they have the same ratio as the lenght and width of the frame, then $$\frac{x}{y}=\frac{18}{15}$$ --> $$y=\frac{5}{6}x$$.

Next, since the frame encloses a rectangular picture that has the same area as the frame itself and the whole area is $$18*15$$, then the areas of the frame (shaded region) and the picture (inner region) are $$\frac{18*15}{2}=9*15$$ each.

The area of the picture is $$xy=9*15$$ --> $$x*(\frac{5}{6}x)=9*15$$ --> $$x^2=2*81$$ --> $$x=9\sqrt{2}$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-shaded-region-in-the-figure-above-represents-a-135095.html
_________________
Re: The shaded region in the figure above represents a rectangul   [#permalink] 06 Jan 2014, 04:23
Similar topics Replies Last post
Similar
Topics:
1 The figure above represents a window, with the shaded regions represe 1 11 Aug 2016, 08:11
6 The figure above represents a frame; the shaded regions represent the 3 07 Mar 2017, 17:20
The figure above represents a window, with the shaded regions represen 2 27 Nov 2015, 22:37
26 The shaded region in the figure above represents a 9 12 May 2016, 11:46
4 The shaded region in the figure above represents a rectangular frame 7 28 Sep 2015, 23:11
Display posts from previous: Sort by