The front of a 6-foot-by-8-foot rectangular door has brass

Question

Door.png The front of a 6-foot-by-8-foot rectangular door has brass rectangular trim, as indicated by the shading in the figure above. If the trim is uniformly 1 foot wide, what fraction of the door's front surface is covered by the trim? (A) 13/48 (B) 5/12 (C) 1/2 (D) 7/12 (E) 5/8

Bunuel · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=18896 
 The front of a 6-foot-by-8-foot rectangular door has brass rectangular trim, as indicated by the shading in the figure above. If the trim is uniformly 1 foot wide, what fraction of the door's front surface is covered by the trim?

(A) 13/48
(B) 5/12
(C) 1/2
(D) 7/12
(E) 5/8

First let's find the area of unshaded region.

The two unshaded regions have a width of 4 feet: 6 feet minus 1 foot wide trim on each side.
The two unshaded regions have a height of 5 feet: 8 feet minus 1 foot at the top, 1 foot in the middle and 1 foot at the bottom.

Thus the area of the two unshaded regions is 4*5=20 square feet.

Therefore, the area of the trim is 6*8-20=28 square feet, which is 28/48=7/12 of the total area.

Answer: D.

Hope it's clear.

PareshGmat · Answer

Segmented the shaded region in 2 as shown below:

Attachment:

Door.png [ 5.29 KiB | Viewed 48069 times ]

Yellow region area = 2 * 8*1 = 16

Pink region area = 3 * 4*1 = 12

Total shaded region = 28

Total frame area = 8*6 = 48

Ratio \(= \frac{28}{48} = \frac{7}{12}\)

Answer = D

Bigred2008 · Answer

Thank you for this. I accidently chose the trap answer of  \frac{5}{12} , and found the area of the door not covered by trim

JeffTargetTestPrep · Answer

To solve this problem we can view it as a type of “shaded region” problem, in which we first determine the area of the entire figure and then subtract the area of the unshaded (white) space from the total area to determine the area of the shaded region, which, in this case, is the area of the trim. Let’s start with the area of the entire figure. We see from the diagram that the shape is a rectangle 6 feet by 8 feet. Since the area of a rectangle is width x length, we know:

area = 6 x 8 = 48

We can determine the area of the trim by first finding the area of the white spaces. We can use a diagram to illustrate this:

https://i.imgur.com/92fDB4Z.png

We can see that, to determine the total area of the two white spaces, we can subtract a total of 2 feet from the 6 foot width and 3 feet from the 8 foot length. Thus, the combined area of the two white spaces is:

(6 – 2) x (8 – 3) = 4 x 5 = 20.

Thus, we know that the area of shaded region, i.e., the trim, is:

48 – 20 = 28

Finally, we can determine the fraction of the door's front surface that is covered by the trim.

Because the area of the trim is 28 and the area of the entire door is 48, the fraction of the door that is covered by the trim is 28/48 = 7/12.

Answer: D

Giampa · Answer

I solved the problem in the same way. IMO the most comprehensive and quick way!

dave13 · Answer

Guys i simply counted total 7 shaded lines. so i chose 7/12

is my approach correct ?

generis · Answer

dave13 , I doubt that approach is correct . . . because we need a part-whole relationship where all the parts are the same size and I cannot see how counting segments ("lines") achieves same-size parts. And - which seven segments did you count? (There are a lot of ways to divide the door trim.

)

dave13 · Answer

Guys i simply counted total 7 shaded lines. so i chose 7/12

is my approach correct ?

dave13 , I doubt that approach is correct . . . because we need a part-whole relationship where all the parts are the same size and I cannot see how counting segments ("lines") achieves same-size parts. And - which seven segments did you count? (There are a lot of ways to divide the door trim.

) generis

pushpitkc · Answer

Hi dave13

As generis already pointed out, the approach you have used is not correct.

The right way to solve this problem will be as follow:

The solid door with dimensions 6ft by 8ft will have an area of 48ft.

Attachment:

Door.png [ 8.58 KiB | Viewed 34535 times ]

The brass part shaded in black(with a uniform thickness or width of 1 ft) will cover an
area of 8*1 or 8 ft for shaded regions 1 and 2 have an area of 2*8 = 16ft.

Similarly, the three horizontal regions(3,4, and 5), each with an area of 4*1 or 4 ft will
have an area of 3*4 = 12ft

Hence, the brass part will have an area of 16 + 12 = 28 ft

Therefore, the ratio is \(\frac{28}{48} = \frac{7}{12}\) (Option D)

Hope this helps you!

Pritishd · Answer

1. We can also start by finding the area of the two white rectangles

2. The vertical height (width) of each white rectangle is  \frac{(8 - 3)}{2} = 2.5   ft

3. The length of each white rectangle is  6 - 2 = 4   ft

4. The combined area of both the white rectangles is  2.5 * 4 * 2 = 20

5. The area of the door (trim + white rectangles) is  6 * 8 = 48

6. Fraction covered by the white rectangles (non trim) is  \frac{20}{48} = \frac{5}{12}   ( Do not mark B. It's a trap answer )

7. Hence, the fraction covered by the trim is  1 - \frac{5}{12} = \frac{7}{12}

Ans.  D

Fdambro294 · Answer

Area of Shaded Region = Entire Rectangle - Whole White Rectangle in the middle (from top of white to bottom of white) + Add back the black trim in between the 2 White Rectangles.

(6 * 8) - (4 * 6) + (4 * 1) = Area of ENTIRE Black Trim/Shaded Area

= 48 - 24 + 4 = 28

As a fraction of the entire door area = (Shaded Area) / (Entire Rectangular Door Area) = 28/48 = 7/12

-D-

Posted from my mobile device

Hoozan · Answer

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Mizan42 · Answer

(8×1)+(8×1)+(4×3)=28

Hence, 28/(6×8)
=7/12

It’s clear.

Posted from my mobile device

bumpbot · Answer

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The front of a 6-foot-by-8-foot rectangular door has brass

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