It is currently 24 Sep 2020, 23:32

### 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

# A ﬂat rectangular picture, represented by the unshaded regio

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 13358
Followers: 288

Kudos [?]: 3391 [0], given: 12193

A ﬂat rectangular picture, represented by the unshaded regio [#permalink]  30 Jan 2016, 16:53
Expert's post
00:00

Question Stats:

62% (02:23) correct 37% (02:47) wrong based on 81 sessions
Attachment:

#GREpracticequestion A ﬂat rectangular picture, represented by the unshaded.jpg [ 7.52 KiB | Viewed 4848 times ]

A ﬂat rectangular picture, represented by the unshaded region in the ﬁgure above, is mounted in a ﬂat rectangular frame, represented by the shaded region. The frame is 1 inch wide on all sides. For what value of x, in inches, is the area of the frame equal to the area of the picture?

A. 4

B. 5

C. 6

D. 7

E. 8

Practice Questions
Question: 16
Page: 469
Difficulty: hard
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Founder
Joined: 18 Apr 2015
Posts: 13358
Followers: 288

Kudos [?]: 3391 [1] , given: 12193

Re: A ﬂat rectangular picture, represented by the unshaded regio [#permalink]  30 Jan 2016, 17:01
1
KUDOS
Expert's post
Solution

The area of the picture is the area of the inner rectangle, and the area of the frame is the area of the outer rectangle minus the area of the inner rectangle.
Since the area of a rectangle is the length times the width, you need to know the length and width of the inner and outer rectangles.

In the figure, you are given that the length of the inner rectangle is x inches, but the width is not given. However, since you know that the width of the frame is 1 inch, it follows that the width of the inner rectangle is equal to the width of the outer rectangle minus 2 inches, or x−2 inches. Thus, the area of the inner rectangle is x(x−2) square inches. In the figure, you are given that the width of the outer rectangle is x inches, but the length is not given. However, since you know that the width of the frame is 1 inch, it follows that the length of the outer rectangle is equal to the length of the inner rectangle plus 2 inches, or x+2 inches. Thus, the area of the outer rectangle is x(x+2) square inches. Since the area of the frame is the area of the outer rectangle minus the area of the inner rectangle, the area of the frame is $$x(x+2) - x(x-2)=x^2+2x-x^2+2x=4x$$ square inches. Now you are ready to set up the equation. Set the expression for the area of the picture equal to the expression for the area of the frame and solve the resulting equation for x, as follows.

$$x(x-2)=4x$$

$$x^2-2x=4x$$

$$x^2-6x=0$$

$$x(x-6)=0$$

There are two solutions to the equation, x=0 and x=6. Since x represents the length of a picture, in inches, the solution $$x=0$$ does not make sense in this context. Therefore, when $$x=6$$, the area of the picture equals the area of the frame.

The correct answer is $$C.$$
_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

GRE Instructor
Joined: 10 Apr 2015
Posts: 3834
Followers: 148

Kudos [?]: 4489 [2] , given: 69

Re: A ﬂat rectangular picture, represented by the unshaded regio [#permalink]  14 Jul 2016, 13:53
2
KUDOS
Expert's post
Carcass' solution is perfect.
However, if you didn't come up with that approach, another approach is to check each answer choice to see which one yields the correct dimensions.
It's a tedious approach, but it works.

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 09 May 2016
Posts: 161
Location: United States
Followers: 8

Kudos [?]: 195 [1] , given: 0

Re: A ﬂat rectangular picture, represented by the unshaded regio [#permalink]  03 Aug 2018, 14:09
1
KUDOS
Expert's post
Carcass wrote:

A ﬂat rectangular picture, represented by the unshaded region in the ﬁgure above, is mounted in a ﬂat rectangular frame, represented by the shaded region. The frame is 1 inch wide on all sides. For what value of x, in inches, is the area of the frame equal to the area of the picture?

 A 4
 B 5
 C 6
 D 7
 E 8

We see that the area of the picture (without the frame) is x(x - 2) and the total area of the picture and the frame is x(x + 2). Since the area of the picture is equal to the area of the frame, the total area of the picture and the frame is thus twice the area of the picture. That is, we have:

x(x + 2) = 2x(x - 2)

x^2 + 2x = 2x^2 - 4x

x^2 - 6x = 0

x(x - 6) = 0

x = 0 or x = 6

Since x can’t be 0, x must be 6.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
41 Reviews

5-star rated online GRE quant
self study course

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

Re: A ﬂat rectangular picture, represented by the unshaded regio   [#permalink] 03 Aug 2018, 14:09
Display posts from previous: Sort by