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27 Nov 2020, 14:21
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Dropdown 1: 6% less
Dropdown 2: 117
The graph shows the percentages for 9,000 commuter rail stations in Dalvarnie with connections to other modes in communities where both commuter rail and the other mode operate.
A. If half of the commuter rail stations operate in areas with all four bus services and one fifth operate in areas with all three rail services, then a given commuter rail traveler is approximately likely to be able to connect to travel to another city by rail than by bus.
B. The maximum number of possible commuter rail stations with connections to both transit and intercity ferry service is
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Official Answer
Dropdown 1: 6% less
Dropdown 2: 117
27 Nov 2020, 14:21
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Official Solution:
First, calculate the number of stations that have access to each of the other modes of transportation.
The problem states that 1/2 of the 9,000 stations operate in areas with all four bus services, or 4,500, and of these 36.7% have access to intercity bus service or approximately 1,651.5.
Then, the problem states that 1/5 of the 9,000 stations operate in areas with all three rail services, or 1,800, and of these 86% have access to intercity rail service or approximately 1,548.
Either estimate or use the calculator to determine that the percent difference will be 1,651.5 - 1,548 = 103.5 / 1,651.5 or approximately 6% less.
A) 30% less
B) 6% less
C) 12% more
D) 142% more
First, find the number of stations with access to any other mode of transit by taking 86.8% of the 9,000 stations to find that 7,812 stations have access to any other mode of transit. Then, assume that every such station with access also has access to both modes of ferry service, therefore 61.5% of the 7,812 or 4,804 (rounded) have transit ferry access and 40% of the 7,812 or 3,125 (rounded) have intercity ferry access.
Now, set up a group equation for overlapping sets to determine the maximum possible overlap as 7,812 = 4,804 + 3,125 - overlap + neither. Therefore, 7,812 = 7,929 - overlap + neither. Subtract 7,812 to find that the neither - overlap = 117, which is the maximum possible value for the overlapping set which will have both transit and intercity ferry access.
A) 0
B) 117
C) 130
D) 998
Correct answer:
Dropdown 1: "6% less"
Dropdown 2: "117"
bb
First, calculate the number of stations that have access to each of the other modes of transportation.
The problem states that 1/2 of the 9,000 stations operate in areas with all four bus services, or 4,500, and of these 36.7% have access to intercity bus service or approximately 1,651.5.
Then, the problem states that 1/5 of the 9,000 stations operate in areas with all three rail services, or 1,800, and of these 86% have access to intercity rail service or approximately 1,548.
Either estimate or use the calculator to determine that the percent difference will be 1,651.5 - 1,548 = 103.5 / 1,651.5 or approximately 6% less.
A) 30% less
B) 6% less
C) 12% more
D) 142% more
First, find the number of stations with access to any other mode of transit by taking 86.8% of the 9,000 stations to find that 7,812 stations have access to any other mode of transit. Then, assume that every such station with access also has access to both modes of ferry service, therefore 61.5% of the 7,812 or 4,804 (rounded) have transit ferry access and 40% of the 7,812 or 3,125 (rounded) have intercity ferry access.
Now, set up a group equation for overlapping sets to determine the maximum possible overlap as 7,812 = 4,804 + 3,125 - overlap + neither. Therefore, 7,812 = 7,929 - overlap + neither. Subtract 7,812 to find that the neither - overlap = 117, which is the maximum possible value for the overlapping set which will have both transit and intercity ferry access.
A) 0
B) 117
C) 130
D) 998
Correct answer:
Dropdown 1: "6% less"
Dropdown 2: "117"
20 Feb 2023, 20:09
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abhimahna explanation is not clear; Why did you chose 36.7% & 86% for the calculations ?
