In a clinical trial, 420 patients received a new medication. At the end of the trial, 35% of the patients...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
In a clinical trial, 420 patients received a new medication. At the end of the trial, \(35\%\) of the patients showed no improvement in their condition. How many patients showed improvement in their condition?
Enter your answer as a whole number.
1. TRANSLATE the problem information
- Given information:
- 420 total patients
- 35% showed no improvement
- Find: number who showed improvement
- What this tells us: We have the percentage for one group and need to find the size of the complementary group.
2. INFER the relationship between the groups
- If 35% showed no improvement, the remaining patients must have shown improvement
- Since all percentages must add to 100%: improvement percentage = \(100\% - 35\% = 65\%\)
3. SIMPLIFY the calculation
- Convert 65% to decimal: \(65\% = 0.65\)
- Calculate: \(0.65 \times 420 = 273\) patients
Answer: 273
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students may misread the problem and calculate 35% of 420 instead of finding the complement.
They think: "The problem asks about patients who showed improvement, and it mentions 35%, so I need 35% of 420."
This leads them to calculate \(0.35 \times 420 = 147\) and answer 147 instead of the correct 273.
Second Most Common Error:
Poor INFER reasoning: Students may correctly identify that they need the complement but make an arithmetic error in finding it.
They might calculate \(100\% - 35\% = 75\%\) instead of 65%, then compute \(0.75 \times 420 = 315\).
This causes them to arrive at 315 as their answer.
The Bottom Line:
This problem tests whether students can recognize complement relationships in percentage problems. The key insight is that when given information about one group, you often need to find the "opposite" group by using the fact that all groups together represent 100%.