Customer Purchases at a Gas StationBeverage purchasedBeverage not purchasedTotalGasoline purchased602585Gasoline not purchased351550Total9040135On Tue...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
Customer Purchases at a Gas Station
| Beverage purchased | Beverage not purchased | Total | |
|---|---|---|---|
| Gasoline purchased | 60 | 25 | 85 |
| Gasoline not purchased | 35 | 15 | 50 |
| Total | 90 | 40 | 135 |
On Tuesday, a local gas station had 135 customers. The table above summarizes whether or not the customers on Tuesday purchased gasoline, a beverage, both, or neither. Based on the data in the table, what is the probability that a gas station customer selected at random on that day did not purchase gasoline?
1. TRANSLATE the problem information
- Given information:
- Two-way table showing customer purchases at a gas station
- Total of 135 customers on Tuesday
- Table categorizes customers by gasoline purchase (yes/no) and beverage purchase (yes/no)
- What we need to find: Probability that a randomly selected customer did NOT purchase gasoline
2. INFER which numbers from the table to use
- For probability calculations: \(\mathrm{P(event)} = \frac{\mathrm{favorable\ outcomes}}{\mathrm{total\ outcomes}}\)
- Favorable outcomes = customers who did NOT purchase gasoline
- Total outcomes = all customers
- Looking at the table: "Gasoline not purchased" row shows 50 total customers
- Grand total shows 135 customers
3. Set up and calculate the probability
- Probability = (Customers who did not purchase gasoline) / (Total customers)
\(\mathrm{Probability} = \frac{\mathrm{Customers\ who\ did\ not\ purchase\ gasoline}}{\mathrm{Total\ customers}}\)
\(\mathrm{Probability} = \frac{50}{135}\)
Answer: D. \(\frac{50}{135}\)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students confuse simple probability with conditional probability and use numbers from individual cells rather than row/column totals.
Instead of using the straightforward ratio \(\frac{50}{135}\), they might look at specific cells like:
- 15 customers who bought neither gasoline nor beverage
- 35 customers who bought beverage but not gasoline
This leads them to create fractions like \(\frac{15}{50}\), \(\frac{35}{50}\), or \(\frac{15}{40}\), corresponding to Choices A, C, or B respectively.
Second Most Common Error:
Poor TRANSLATE reasoning: Students misread what the question is asking for and calculate probabilities for the wrong event.
They might calculate the probability of purchasing gasoline (\(\frac{85}{135}\)) or getting confused about which row/column totals to use. This causes them to get stuck and guess among the available choices.
The Bottom Line:
This problem tests whether students can distinguish between simple probability (what we want) and conditional probability (what the distractors represent). The key insight is recognizing that "selected at random" means we want a simple ratio of the target group to the entire population.