• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

A framed picture is shown above. The frame, shown shaded, is

This topic has 2 expert replies and 0 member replies

A framed picture is shown above. The frame, shown shaded, is

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Source: Official Guide



A framed picture is shown above. The frame, shown shaded, is 6 inches wide and forms a border of uniform width around the picture. What are the dimensions of the viewable portion of the picture?

1. The area of the shaded region is 24 square inches.
2. The frame is 8 inches tall.

The OA is C.

  • +1 Upvote Post
  • Quote
  • Flag
Post
BTGmoderatorLU wrote:
Source: Official Guide



A framed picture is shown above. The frame, shown shaded, is 6 inches wide and forms a border of uniform width around the picture. What are the dimensions of the viewable portion of the picture?

1. The area of the shaded region is 24 square inches.
2. The frame is 8 inches tall.

The OA is C.
Say the uniform width of the frame = a inches and the height of the frame = X inches

Dimensions of the picture: Width = 6 - 2a and Height = X - 2a

We have to get the values of (6 - 2a) and (X - 2a).

Question rephrased: What's the value of a and X?

Let's take each statement one by one.

1. The area of the shaded region is 24 square inches.

=> 2[6*a + (X - 2a)*a] = 24
6a + Xa - 2a^2 = 12
Can't get the value of a and X. Insufficient.

2. The frame is 8 inches tall.
=> X = 8.

But, we don't have the value of a. Insufficient.

(1) and (2) together

Plugging-in the value of X = 8 in 6a + Xa - 2a^2 = 12, we get

6a + Xa - 2a^2 = 12 => 6a + 8a - 2a^2 = 12 => 14a - 2a^2 = 12 => a^2 - 7a + 6 = 0 => (a - 6)(a - 1) = 0 => a = 6 or 1.

a cannot be 6 because if it were 6, then there would be no border at all as the width itself = 6 inches.

=> a = 1

So, we have X = 8 and a = 1. Sufficient.

The correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Jayanagar | Dilsukhnagar | Himayatnagar | Visakhapatnam | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
BTGmoderatorLU wrote:
Source: Official Guide



A framed picture is shown above. The frame, shown shaded, is 6 inches wide and forms a border of uniform width around the picture. What are the dimensions of the viewable portion of the picture?

1. The area of the shaded region is 24 square inches.
2. The frame is 8 inches tall.
Statement 1:
Test one case that also satisfies Statement 2.

Case 1: The frame is 8 inches tall, with the result that the total area of the frame and picture combined = 6*8 = 48
Area of the picture = (total area) - (shaded region) = 48-24 = 24.
Implication:
The width of the frame is 1 inch, yielding for the picture a base of 4 and a height of 6.

Cases 2: The frame is MORE than 8 inches tall
Here, the area of the picture will be MORE than 24, with the result that the dimensions of the picture will NOT be 4 inches by 6 inches.

Since the dimensions of the picture can be different values. INSUFFICIENT.

Statement 2:
Since the width of the frame is unknown, the area of the picture can be different values.
As a result, the dimensions of the picture can be different values.
INSUFFICENT.

Statements combined:
Only Case 1 satisfies both statements, with the result that the picture has a base of 4 and a height of 6.
SUFFICIENT.

The correct answer is C.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

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

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep

Top First Responders*

1 Brent@GMATPrepNow 41 first replies
2 Ian Stewart 37 first replies
3 Jay@ManhattanReview 32 first replies
4 GMATGuruNY 26 first replies
5 Scott@TargetTestPrep 14 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

199 posts
2 image description Max@Math Revolution

Math Revolution

92 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

74 posts
4 image description GMATGuruNY

The Princeton Review Teacher

45 posts
5 image description Ian Stewart

GMATiX Teacher

43 posts
See More Top Beat The GMAT Experts