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805+ (Hard)|   Graphs|   Math Related|         
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cheshire
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The graph is part of a report about land use in a certain region Updated on: 28 Jul 2025, 20:27
Originally posted by cheshire on 25 Jul 2025, 20:56.
Last edited by cheshire on 28 Jul 2025, 20:27, edited 6 times in total.
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Dropdown 1: 10 to 1 Dropdown 2: 1 to 40
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Difficulty:

95% (hard)

Question Stats:

32% (03:08) correct 68% (03:00) wrong based on 1069 sessions

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The graph is part of a report about land use in a certain region. The chart shows, for each of the designations park and vacant, the percent of the region's total area that has that designation and the percent of the total number of lots in the region that have that designation. All land in the region is divided into lots.

Select the options from the drop-down menus that complete the statement so that it most accurately reflects the information provided.

For this region, the ratio of the number of lots with the designation vacant to the number with the designation park is approximately

For this region, the ratio of the mean area of the lots with the designation vacant to the mean area of the lots with the designation park is approximately


ID: 102501


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Dropdown 1: 10 to 1 Dropdown 2: 1 to 40
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BinodBhai
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The graph is part of a report about land use in a certain region 31 Jul 2025, 12:15
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This is a very tricky question, esp the 2nd part.. You need to read the stem carefully

Mean area = Area / # of lots
Let total area and total lots = 100 each

For Park:
Total Area = 40% = 40
Total lots = 2% = 2
Mean Area of lots = 40/2 = 20

For Vacant:
Total Area = 10% = 10
Total lots = 20% = 20
Mean Area lots = 10/20 = 1/2

Required ratio: Vacant / Park = 1/2 / 20 = 1/40
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The graph is part of a report about land use in a certain region 27 Jul 2025, 09:15
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OA:


Question 1:
The graph indicates that for this region approximately 20% of the lots have the designation vacant and 2% of the lots have the designation park. Therefore, for this region the number of lots with the designation vacant \s 10 times the number with the designation park, and hence for this region the ratio of the number of lots with the designation vacant to the number with the designation park is 10 to 1.

The correct answer is 10 to 1.


Question 2:
Let 4 be the total area of the region and let N be the total number of lots in the region. The graph shows that there are approximately 0.2N (i.e., 20% of N) lots with the designation vacant and these lots together use an area of approximately 0.1A (i.e., 10% of A). Thus, the mean area of the lots with the designation vacant is approximately \(\frac{01A}{02N} =\frac{1}{2} (\frac{A}{N})\) The graph also shows that there are approximately 0.02N (i.e., 2% of N) lots with the designation park and these lots together use an area of approximately 0.4/4 (i.e., 40% of A). Thus, the mean area of the lots with the designation park is approximately \(\frac{0.4A}{0.02N} = 20(\frac{A}{N})\) Therefore, for this region the ratio of the mean area of the lots with the designation vacant to the mean area of the lots with the designation park is approximately 1/2 to 20, or equivalently, 1 to 40.

The correct answer is 1 to 40.
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The graph is part of a report about land use in a certain region 26 Jul 2025, 12:33
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Solution:

Dropdown 1 For this region, the ratio of the number of lots with the designation vacant to the number with the designation park is approximately 10:1.

Number of lots with the designation vacant 0-5, 5-10, 10-15, 15-20--> 20

Number of lots with the designation park 0-2--->2

So, the ratio would be \(\frac{20}{2}\) = 10:1

Dropdown 2 For this region, the ratio of the mean area of the lots with the designation vacant to the mean area of the lots with the designation park is approximately 4:1.

Mean area of the lots with the designation park=\(\frac{0+5+10+15+20+25+30+35+40}{900}\) = \(\frac{1}{5}\).

Mean area of the lots with the designation vacant =\(\frac{0+5+10}{300}\)=\(\frac{1}{20}\)

So, the ratio should be 4:1.


cheshire

The graph is part of a report about land use in a certain region. The chart shows, for each of the designations park and vacant, the percent of the region's total area that has that designation and the percent of the total number of lots in the region that have that designation. All land in the region is divided into lots.

Select the options from the drop-down menus that complete the statement so that it most accurately reflects the information provided.

For this region, the ratio of the number of lots with the designation vacant to the number with the designation park is approximately

For this region, the ratio of the mean area of the lots with the designation vacant to the mean area of the lots with the designation park is approximately


ID: 102501


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