A car dealership tracks the inventory of its new sedans and SUVs, which are available in black, silver, or white....
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
A car dealership tracks the inventory of its new sedans and SUVs, which are available in black, silver, or white. The partially completed table below summarizes the 200 new vehicles in stock.
| Black | Silver | White | Total | |
|---|---|---|---|---|
| Sedan | 40 | 30 | 100 | |
| SUV | 50 | 20 | 30 | 100 |
| Total | 90 | 50 | 60 | 200 |
If one of these new vehicles is selected at random, what is the probability that it is a silver sedan?
Express your answer as a simplified fraction or decimal.
1. TRANSLATE the problem information
- Given information:
- 200 total vehicles (sedans and SUVs)
- Vehicles come in black, silver, or white
- Need probability of selecting a silver sedan
- Table has missing value for silver sedans
- What this tells us: We need both the number of silver sedans AND the total number of vehicles
2. INFER the approach
- Strategic insight: Before calculating probability, we must find the missing table value
- The Sedan row shows: 40 black + ??? silver + 30 white = 100 total
- This means we can solve for the missing silver sedan count
3. Find the missing value
- Silver sedans = Total sedans - (Black sedans + White sedans)
- Silver sedans = 100 - (40 + 30) = 30
\(\mathrm{Silver\ sedans} = \mathrm{Total\ sedans} - (\mathrm{Black\ sedans} + \mathrm{White\ sedans})\)
\(\mathrm{Silver\ sedans} = 100 - (40 + 30) = 30\)
4. TRANSLATE the probability setup
- Probability formula: P(event) = Number of favorable outcomes / Total outcomes
- Favorable outcomes: 30 silver sedans
- Total outcomes: 200 vehicles
\(\mathrm{P(event)} = \frac{\mathrm{Number\ of\ favorable\ outcomes}}{\mathrm{Total\ outcomes}}\)
5. SIMPLIFY the calculation
- P(silver sedan) = 30/200
- Divide both numerator and denominator by 10: = 3/20
- Convert to decimal: 3 ÷ 20 = 0.15 (use calculator)
\(\mathrm{P(silver\ sedan)} = \frac{30}{200}\)
\(= \frac{3}{20}\)
\(3 \div 20 = 0.15\)
Answer: 3/20, 0.15, or 15%
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misread what "silver sedan" means and calculate probability using incorrect values from the table.
For example, they might use all silver vehicles (50) instead of just silver sedans (30), giving them \(\frac{50}{200} = \frac{1}{4} = 0.25\). Or they might use all sedans (100) instead of just silver sedans, getting \(\frac{100}{200} = \frac{1}{2} = 0.5\).
This leads to confusion about which numbers to use in the probability formula.
Second Most Common Error:
Poor INFER reasoning: Students don't recognize they need to find the missing table value first and instead try to work with incomplete information.
They see the empty cell for silver sedans and either guess a value or attempt to calculate probability without it. This causes them to get stuck and abandon systematic solution, leading to guessing.
The Bottom Line:
This problem tests whether students can work systematically with incomplete data tables - the key insight is that probability requires complete information, so missing values must be calculated first using the given totals.