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On a construction map of a certain college campus, 1/3 of the area of

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Bunuel
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On a construction map of a certain college campus, 1/3 of the area of [#permalink] New post   20 Nov 2022, 23:37
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On a construction map of a certain college campus, 1/3 of the area of the campus is marked by landscaping. Of the part of the campus that is not marked by landscaping, 1/8 of the area is marked for gym buildings. What fraction of the area of the campus is not marked for either landscaping or gym buildings?

A. 1/12
B. 1/4
C. 5/12
D. 7/12
E. 11/12
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D
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Re: On a construction map of a certain college campus, 1/3 of the area of [#permalink] New post   21 Nov 2022, 03:30
let total area be 90

so 1/3 is landscape
i.e=30

remaining 1/8 for gym
i.e 90-30=60
1/8(60)= 7.5

now fraction 37.5/90

gives 5/12
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On a construction map of a certain college campus, 1/3 of the area of [#permalink] New post   23 Nov 2022, 10:57
Let total area = x
Area marked by landscaping = 1/3 = x/3 area
Of the part of the campus that is not marked by landscaping = x-x/3 = 2x/3
1/8 of the area is marked for gym buildings = 1/8 * 2x/3 = x/12 area

Total area marked by both = x/3 + x/12 = 5x/12
So area not marked = x- 5x/12 = 7x/12

Fraction of area not marked = 7x/12 / x = 7/12
Correct ans is D
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Re: On a construction map of a certain college campus, 1/3 of the area of [#permalink] New post   23 Nov 2022, 11:20
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Bunuel wrote:
On a construction map of a certain college campus, 1/3 of the area of the campus is marked by landscaping. Of the part of the campus that is not marked by landscaping, 1/8 of the area is marked for gym buildings. What fraction of the area of the campus is not marked for either landscaping or gym buildings?

A. 1/12
B. 1/4
C. 5/12
D. 7/12
E. 11/12


Solution:

  • Landscaping \(=\frac{1}{3}\)
  • Remaining \(=1-\frac{1}{3}=\frac{2}{3}\)
  • Gym \(=\frac{1}{8}\times \frac{2}{3}=\frac{1}{12}\)
  • Area marked \(=\frac{1}{3}+\frac{1}{12}=\frac{5}{12}\)
  • Area not marked \(=\frac{12-5}{12}=\frac{7}{12}\)

Hence the right answer is Option D
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Re: On a construction map of a certain college campus, 1/3 of the area of [#permalink]
23 Nov 2022, 11:20
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