The table gives the distribution of votes for a new school mascot and grade level for students.MascotSixthSeventhEighthTotalBadger49922Lion92920Longho...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
The table gives the distribution of votes for a new school mascot and grade level for students.
| Mascot | Sixth | Seventh | Eighth | Total |
|---|---|---|---|---|
| Badger | 4 | 9 | 9 | 22 |
| Lion | 9 | 2 | 9 | 20 |
| Longhorn | 4 | 6 | 4 | 14 |
| Tiger | 6 | 9 | 9 | 24 |
| Total | 23 | 26 | 31 | 80 |
If one of these students is selected at random, what is the probability of selecting a student whose vote for new mascot was for a lion?
1. TRANSLATE the probability question
- The question asks: "What is the probability of selecting a student whose vote was for a lion?"
- This translates to: \(\mathrm{P(lion\ voter)} = \frac{\mathrm{Number\ of\ students\ who\ voted\ for\ lion}}{\mathrm{Total\ number\ of\ students}}\)
2. VISUALIZE the table to find lion votes
- Look at the "Lion" row in the table
- Add across all grade levels: \(9 + 2 + 9 = 20\) students voted for lion
- The total number of students is shown in the bottom right: 80 students
3. INFER the probability calculation
- We now have: \(\mathrm{P(lion\ voter)} = \frac{20}{80}\)
- This fraction needs to be simplified to match the answer choices
4. SIMPLIFY the fraction
- \(\frac{20}{80} = \frac{1}{4}\) (dividing both numerator and denominator by 20)
Answer: C. \(\frac{1}{4}\)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misunderstand what the question is asking and calculate the wrong probability.
Instead of finding \(\mathrm{P(lion\ voter)}\), they might calculate:
- \(\mathrm{P(lion\ voter\ |\ specific\ grade)}\) using just one grade level
- \(\mathrm{P(specific\ grade\ |\ lion\ voter)}\) reversing the conditional probability
This leads to incorrect calculations like \(\frac{9}{23}\) or \(\frac{2}{26}\) from individual grade columns, which don't match any answer choices. This causes them to get stuck and randomly select an answer.
Second Most Common Error:
Poor VISUALIZE execution: Students misread the table and use incorrect numbers.
Common mistakes include:
- Using 22 (total for Badger) instead of 20 for lion votes
- Using row totals instead of the specific lion data
- Confusing rows and columns when reading the table
This may lead them to select Choice A (\(\frac{1}{9}\)) if they incorrectly use \(\frac{9}{80}\) from just one grade level.
The Bottom Line:
This problem tests whether students can correctly interpret what probability is being asked for and accurately extract information from a two-way table. The key insight is recognizing that "selecting a student who voted for lion" means finding what fraction of all 80 students voted for lion, regardless of their grade level.