Maya always ships her packages using one of two shipping companies. At Company 1, Maya pays €3.00 per kilogram based...
GMAT Two Part Analysis : (TPA) Questions
Maya always ships her packages using one of two shipping companies. At Company 1, Maya pays €3.00 per kilogram based on the total weight of the package. At Company 2, she pays a flat fee of €14.00 to ship a package of any weight. No other fees apply to ship a package at either company, and Maya always chooses the least expensive company to ship any given package. The average weight of the 27 packages Maya shipped last year using Company 1 was 2.50 kilograms.
Based on the information provided, select for Average price the average price Maya paid per package using Company 1 last year, and select for Average amount saved the average amount Maya saved per package last year by using Company 1 rather than Company 2 to ship the packages. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Visualization Selection
Since we're comparing two companies with different pricing structures, we'll use a comparison table:
| Feature | Company 1 | Company 2 |
| Pricing | \(€3.00 \text{ per kg}\) | \(€14.00\) flat fee |
| Maya's Usage | 27 packages | 0 packages (last year) |
| Avg Weight | \(2.50 \text{ kg}\) | N/A |
Key Information
- Maya shipped 27 packages using Company 1 last year
- Average weight of those packages: \(2.50 \text{ kg}\)
- She always chooses the cheaper option
Phase 2: Understanding the Question
We need to find two values:
- Average price: The average price Maya paid per package using Company 1
- Average amount saved: How much she saved on average by choosing Company 1 over Company 2
Key Insight
Since Maya chose Company 1 for these packages, it must have been cheaper than Company 2's \(€14.00\) flat fee for each of them.
Phase 3: Finding the Answer
Calculating Average Price (Company 1)
- Price formula for Company 1: \(\mathrm{Price} = \mathrm{Weight} \times €3.00/\mathrm{kg}\)
- Average weight = \(2.50 \text{ kg}\)
- Average price = \(2.50 \text{ kg} \times €3.00/\mathrm{kg} = €7.50\)
Calculating Average Savings
- Company 2 would have charged: \(€14.00\) per package (flat fee)
- Company 1 average charge: \(€7.50\) per package
- Average savings = \(€14.00 - €7.50 = €6.50\)
Verification
This makes sense because Maya chose Company 1, meaning it was cheaper. At \(2.50 \text{ kg}\) average weight, Company 1 charges \(€7.50\), which is indeed less than Company 2's \(€14.00\).
Phase 4: Solution
Final Answer:
- Average price: \(€7.50\)
- Average amount saved: \(€6.50\)