Subject Survey ResultsMath252Science168The table shows the results of a survey about students' favorite subjects. A total of 420 students selected...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
| Subject Survey Results | |
|---|---|
| Math | 252 |
| Science | 168 |
The table shows the results of a survey about students' favorite subjects. A total of 420 students selected at random were asked which subject they preferred. If a school with 4,620 students has the same preference distribution, by how many students would Math be more popular than Science?
\(84\)
\(924\)
\(1{,}848\)
\(2{,}772\)
1. TRANSLATE the survey information
- Given information:
- Survey results: 252 students prefer Math, 168 prefer Science
- Total surveyed: 420 students
- School population: 4,620 students
- What we need to find: The difference in preference between Math and Science in the larger school
2. INFER the scaling approach
- The key insight: Survey proportions from 420 students can predict preferences for 4,620 students
- Strategy: Find what fraction of students prefer each subject, then apply these fractions to the school population
3. SIMPLIFY the proportion calculations
- Math preference rate: \(252 \div 420 = \frac{3}{5}\) (or 0.6)
- Science preference rate: \(168 \div 420 = \frac{2}{5}\) (or 0.4)
- Check: \(\frac{3}{5} + \frac{2}{5} = 1\) ✓
4. SIMPLIFY the scaling to school population
- Math preferences in school: \(\frac{3}{5} \times 4{,}620 = 2{,}772\) students
- Science preferences in school: \(\frac{2}{5} \times 4{,}620 = 1{,}848\) students
- Check: \(2{,}772 + 1{,}848 = 4{,}620\) ✓
5. TRANSLATE 'by how many more' into subtraction
- Difference: \(2{,}772 - 1{,}848 = 924\) students
Answer: B) 924
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students don't realize they need to scale the survey data to the larger population. Instead, they work directly with the survey numbers.
They calculate: \(252 - 168 = 84\) and select Choice A (84)
This happens because they miss the critical connection that survey data must be proportionally scaled to apply to a different population size.
Second Most Common Error:
Poor TRANSLATE reasoning: Students correctly scale one preference but forget to calculate the other, or they calculate both scaled values but forget to find the difference.
For example, they might find that Math would have 2,772 preferences and stop there, selecting Choice D (2,772) without completing the comparison.
The Bottom Line:
This problem tests whether students understand that sample data must be proportionally scaled before making predictions about larger populations. The trap is thinking the raw survey numbers can be used directly.
\(84\)
\(924\)
\(1{,}848\)
\(2{,}772\)