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The pages of a book are 24 centimeters high and 15 centimeters wide.

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The pages of a book are 24 centimeters high and 15 centimeters wide. [#permalink]

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New post 06 Nov 2017, 21:55
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The pages of a book are 24 centimeters high and 15 centimeters wide. Each page has a margin of 3 centimeters at the top and at the bottom, and a 2-centimeter margin on each side. What is the total area, in square centimeters, occupied by the margins on each page?

(A) 138
(B) 162
(C) 180
(D) 186
(E) 198
[Reveal] Spoiler: OA

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Re: The pages of a book are 24 centimeters high and 15 centimeters wide. [#permalink]

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New post 06 Nov 2017, 22:50
Area of complete page (including margins) = 24*15 = 360 square cm

Now, if we exclude the margins, then:
Height = 24-3-3 = 18 cm and Width = 15-2-2 = 11 cm
So, Area of page excluding margins = 18*11 = 198 square cm

Hence Area of margins = Total area - Area excluding margins = 360 - 198 = 162 square cm

Hence B answer

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Re: The pages of a book are 24 centimeters high and 15 centimeters wide. [#permalink]

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New post 07 Nov 2017, 05:02
We need to solve backwards: Entire page area - unwanted area

Any area = width * length

Entire page = 15 * 24 = 360

Unwanted area:
length: 24 - 3 - 3 = 18 (two subtractions for the top and bottom of the page)
width: 15 - 2 -2 = 11 (two subtractions for the right and left part of the page)
11 * 18 = 198

360 - 198 = 162

B is the answer

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Re: The pages of a book are 24 centimeters high and 15 centimeters wide. [#permalink]

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New post 07 Nov 2017, 17:27
Bunuel wrote:
The pages of a book are 24 centimeters high and 15 centimeters wide. Each page has a margin of 3 centimeters at the top and at the bottom, and a 2-centimeter margin on each side. What is the total area, in square centimeters, occupied by the margins on each page?

(A) 138
(B) 162
(C) 180
(D) 186
(E) 198

Attachment:
margins.png
margins.png [ 6.63 KiB | Viewed 252 times ]

I segmented off four parts, see diagram.

Top and bottom margins': length = 15, width = 3
Area for top and bottom = 3 * 15 = 45 sq cm each

The left and right margins:
Length of page is 24. Top and bottom margins together are 3 + 3 = 6
Length of page is truncated for left and right margins: length for them is 24 - 6 = 18

Left and right segments' length: 18. Width: 2
Area for left and right segments: (18 * 2) = 36 sq cm each

In square centimeters, total margin area is 45 + 45 + 36 + 36 = 162

Answer B

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Re: The pages of a book are 24 centimeters high and 15 centimeters wide. [#permalink]

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New post 08 Nov 2017, 16:38
Bunuel wrote:
The pages of a book are 24 centimeters high and 15 centimeters wide. Each page has a margin of 3 centimeters at the top and at the bottom, and a 2-centimeter margin on each side. What is the total area, in square centimeters, occupied by the margins on each page?

(A) 138
(B) 162
(C) 180
(D) 186
(E) 198



The total area of the page is 24 x 15 = 360.

The area of the page inside the margins is:

[24 - (2 x 3)] x [15 - (2 x 2)] = 18 x 11 = 198

So, the area of the margins is 360 - 198 = 162.

Answer: B
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Kudos [?]: 980 [0], given: 5

Re: The pages of a book are 24 centimeters high and 15 centimeters wide.   [#permalink] 08 Nov 2017, 16:38
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The pages of a book are 24 centimeters high and 15 centimeters wide.

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