A rectangle measuring 6 inches by 7 inches is centered inside a larger

Question

A rectangle measuring 6 inches by 7 inches is centered inside a larger rectangle of proportional dimensions so that the perimeters of the two rectangles are separated by a uniform distance of x inches.If the difference between the areas of the two rectangles is 168 square inches, what is x?

A. 3
B. 4
C. 6
D. 8
E. 9

A. 3
B. 4
C. 6
D. 8
E. 9

Mohammadmo · Answer

The area of the smaller rectangle is 42.(6×7)
The space between the two rectangles is 168 so the area of the large rectangle is 210.
168+42=210
4x^2+26X=168
2X^2+13X=84
2(4^2)+13*(4)=32+52=84
Option B

Posted from my mobile device

Archit3110 · Answer

from given info we
can say
( 6+2x)(7+2x) - 42 = 168
solve we get
2x^2+4x=84
x=4 sufficeint
IMO B

amarsinha · Answer

Area of bigger rectangle = (6+2x)(7+2x) = 4x^2 + 26x + 42. 
Area of smaller rectangle = 42. 
Difference = 4x^2 + 26x 
So 4x^2 + 26x = 168
=> 2x^2 + 13 x - 84 = 0 
=> (x-4)*(2x+21) = 0 
x cannot be negative so x = 4

ScottTargetTestPrep · Answer

We see that the dimension of the small rectangle is 6 by 7, and so the dimension of the larger rectangle is (6 + 2x) by (7 + 2x). We can create the equation:

6 * 7 + 168 = (6 + 2x)(7 + 2x)

42 + 168 = 42 + 26x + 4x^2

4x^2 + 26x - 168 = 0

2x^2 + 13x - 84 = 0

(2x + 21)(x - 4) = 0

x = -21/2 or x = 4

Since x can’t be negative, x = 4.

Answer: B

Vinayak013 · Answer

why did we take it as "+2x" and not simply "+x"

Abhishek009 · Answer

Workout using the Options....

X inches on each side means the bigger rectangle must have the dimention (6 + 2x ) ( 7 + 2x)

We know 6*7 = 42

Now, check the options

(A) (6 + 2x ) ( 7 + 2x) - 42 = 12*13 - 42 , No need to check actual calculation, just check units digit and you will find it ends in 4.

(B) (6 + 2x ) ( 7 + 2x) - 42 = 14*15 - 42 => 168 , Answer

One may check other options just to cross check...

gvij2017 · Answer

centered inside a larger rectangle of proportional dimensions

Here we are talking about  proportional dimensions  of the larger rectangle. 
This bolded part made me assume the dimension of the larger rectangle 6a and 7a.

Besides this, I understood that problem has mentioned distance between smaller and larger circle x. 
Therefore, dimension of larger circle will be 6+2x and 7+2x.

Now I got confused between these two different dimensions of larger rectangle according to problem statement.

Please tell me where I am wrong?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A rectangle measuring 6 inches by 7 inches is centered inside a larger

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A rectangle measuring 6 inches by 7 inches is centered inside a larger

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards