In a certain geographic area, bus companies set their ticket prices based on the number of kilometers that a passenger...

Owning The Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

Company C charges exactly twice as much as Company E (\(0.6\) vs \(0.3\) euros per kilometer). Company C is a strong outlier with the highest fare, while Company B has the lowest. The per-kilometer prices among the five companies range from approximately \(0.28\) to \(0.6\) euros, showing substantial variation. The chart arranges companies alphabetically, so price relationships require visual attention.

Step-by-Step Solution

Question 1: Identifying the Company That Charges Twice as Much

Complete Statement:

Company [BLANK 1] charges twice as much per kilometer traveled as does Company [BLANK 2].

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: charges twice as much per kilometer
    • Meaning: The fare of one company must be exactly double that of another company.
    • Relation to Chart: Look for two companies where one's bar is precisely two times the other in height (value).
    • Important Implications: We're searching for an exact \(2:1\) ratio between two companies' prices, not an estimate.
• Statement Breakdown 2:
  • Key Phrase: Company [BLANK 1]
    • Meaning: The company with the higher price per kilometer within the \(2:1\) pair.
    • Relation to Chart: This will be the taller (higher value) bar of the two that form the \(2:1\) ratio.
    • Important Implications: Once this company is found, the company it is twice as expensive as can also be identified.
• What is needed: The company whose fare is exactly twice that of another company.

Solution:

• Condensed Solution Implementation:
  Scan the chart for pairs of companies and calculate if any have an exact \(2:1\) ratio in fares. This can be done by dividing the fare of each company by the fares of all other companies.
• Necessary Data points:
  Company fares: A (\(0.35\) Euro/km), B (\(0.28\) Euro/km), C (\(0.60\) Euro/km), D (\(0.47\) Euro/km), E (\(0.30\) Euro/km).
  • Calculations Estimations:
    C \((0.60) / E (0.30) = 2\), which is an exact \(2:1\) ratio.
  • Comparison to Answer Choices:
    Only Company C's fare is exactly twice that of another company (E). Therefore, the answer for [BLANK 1] is C.

FINAL ANSWER Blank 1: C

Question 2: Identifying the Company That Is Half as Expensive

Complete Statement:

Company C charges twice as much per kilometer traveled as does Company [BLANK 2].

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: Company C charges twice as much
    • Meaning: Company C has a fare exactly two times higher than the company in [BLANK 2].
    • Relation to Chart: Find the company whose fare, when doubled, equals Company C's fare.
• Statement Breakdown 2:
  • Key Phrase: as does Company [BLANK 2]
    • Meaning: The company with half the fare rate of Company C.
    • Relation to Chart: This will be the shortest bar with a value such that \(2 \times\) its value = Company C's value.
• What is needed: Which company charges half the fare of Company C.

Solution:

• Condensed Solution Implementation:
  Divide Company C's fare by 2 and see which company has that fare.
• Necessary Data points:
  Company C: \(0.60\) Euro/km. \(0.60 / 2 = 0.30\) Euro/km.
  • Calculations Estimations:
    Company E charges \(0.30\) Euro/km, which matches the calculation.
  • Comparison to Answer Choices:
    Company E is the only company whose fare is half of Company C's fare. So, [BLANK 2] is E.

FINAL ANSWER Blank 2: E

Summary

By inspecting the fares, we find that Company C (\(0.60\) Euro/km) is exactly twice as expensive as Company E (\(0.30\) Euro/km). No other company pair fits this exact \(2:1\) relationship.

Question Independence Analysis

The blanks are not independent: once we identify that C charges exactly twice as much as E, both answers are determined by this unique \(2:1\) relationship.