A stock portfolio contains 300 shares, of which 75 are technology stocks. What percentage of the portfolio consists of technology...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
A stock portfolio contains \(300\) shares, of which \(75\) are technology stocks. What percentage of the portfolio consists of technology stocks?
1. TRANSLATE the problem information
- Given information:
- Total shares in portfolio: 300
- Technology stocks: 75
- Find: What percentage are technology stocks?
2. INFER the approach
- We need to find what portion the technology stocks represent of the entire portfolio
- This calls for the percentage formula: \(\frac{\mathrm{part}}{\mathrm{whole}} \times 100\%\)
- The "part" is technology stocks (75), the "whole" is total shares (300)
3. SIMPLIFY the calculation
- Set up the fraction: \(\frac{75}{300}\)
- Divide: \(75 \div 300 = 0.25\)
- Convert to percentage: \(0.25 \times 100\% = 25\%\)
Answer: A (25%)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE reasoning: Students see "75 technology stocks" and assume this directly means 75%.
They skip the crucial step of comparing the part to the whole, thinking that the number of technology stocks automatically equals the percentage. This leads them to select Choice C (75%).
Second Most Common Error Path:
Inadequate INFER skill: Students know they need to do something with both numbers but aren't sure what operation to perform.
They might try various combinations like adding \(75 + 300\), subtracting \(300 - 75\), or dividing the wrong way \(300 \div 75\). This leads to confusion and guessing among the remaining choices.
The Bottom Line:
This problem tests whether students truly understand that percentages require a comparison between a part and its corresponding whole, not just looking at the part in isolation.