Riya plans to order 95 custom shirts for the participants of a fundraising event she is organizing. She is considering...
GMAT Two Part Analysis : (TPA) Questions
Riya plans to order 95 custom shirts for the participants of a fundraising event she is organizing. She is considering two options for ordering the shirts—a local option where she would have no shipping costs and an option to order the shirts online and have them shipped to her. If she uses the local option, each shirt will cost \(\mathrm{\$x}\). If she uses the online option, each shirt will cost slightly less, at \(\mathrm{\$y}\), but she will have to pay a flat shipping fee of \(\mathrm{\$22}\). These are the only costs associated with ordering the shirts. Riya correctly determined that by ordering the 95 shirts using the online option rather than the local option, she will spend exactly \(\mathrm{\$16}\) less.
Select a value for \(\mathrm{x}\) and a value for \(\mathrm{y}\) that are jointly consistent with the information provided. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Visual Representation
Since we're comparing two options with different cost structures, let's use a comparison table:
| Option | Per Shirt Cost | Shipping | Total Cost (95 shirts) |
| Local | $x | $0 | \(95\mathrm{x}\) |
| Online | $y | $22 | \(95\mathrm{y} + 22\) |
Key constraint: Online total is exactly $16 less than Local total
Phase 2: Understanding the Question
Breaking Down the Relationship
We're told that ordering online saves exactly $16. Let's translate this:
- Local cost = \(95\mathrm{x}\)
- Online cost = \(95\mathrm{y} + 22\)
- Online is $16 less, so: Online cost = Local cost - 16
This gives us: \(95\mathrm{y} + 22 = 95\mathrm{x} - 16\)
Simplifying to Find the Key Relationship
\(95\mathrm{y} + 22 = 95\mathrm{x} - 16\)
\(95\mathrm{y} = 95\mathrm{x} - 16 - 22\)
\(95\mathrm{y} = 95\mathrm{x} - 38\)
\(\mathrm{y} = \mathrm{x} - \frac{38}{95}\)
Using calculator for precision: \(38 ÷ 95 = 0.4\)
Key insight: \(\mathrm{y} = \mathrm{x} - 0.40\)
This means the online per-shirt price is exactly $0.40 less than the local price.
Phase 3: Finding the Answer
Systematic Check of Options
Given choices: 12.04, 12.10, 12.25, 12.33, 12.50
We need x and y where \(\mathrm{y} = \mathrm{x} - 0.40\). Let's check each potential x value:
- If x = 12.04 → y = 12.04 - 0.40 = 11.64 (not in choices)
- If x = 12.10 → y = 12.10 - 0.40 = 11.70 (not in choices)
- If x = 12.25 → y = 12.25 - 0.40 = 11.85 (not in choices)
- If x = 12.33 → y = 12.33 - 0.40 = 11.93 (not in choices)
- If x = 12.50 → y = 12.50 - 0.40 = 12.10 ✓ (12.10 is in choices!)
? Stop here - we found our answer.
Verification
Let's confirm our answer works:
- Local cost: \(95 × \$12.50 = \$1,187.50\)
- Online cost: \(95 × \$12.10 + \$22 = \$1,149.50 + \$22 = \$1,171.50\)
- Savings: \(\$1,187.50 - \$1,171.50 = \$16\) ✓
Phase 4: Solution
Final Answer:
- \(\mathrm{x} = \$12.50\) (local per-shirt cost)
- \(\mathrm{y} = \$12.10\) (online per-shirt cost)
These values satisfy our requirement that \(\mathrm{y} = \mathrm{x} - 0.40\) and result in exactly $16 savings when ordering 95 shirts online versus locally.