Question:The daily high temperatures, in degrees Fahrenheit, for a certain week are consecutive integers from 72 to 78 inclusive.What is...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
The daily high temperatures, in degrees Fahrenheit, for a certain week are consecutive integers from 72 to 78 inclusive.
What is the mean daily high temperature, in degrees Fahrenheit, for that week?
- 72
- 74
- 75
- 76
- 78
1. TRANSLATE the problem information
- Given information:
- Daily high temperatures are consecutive integers from \(\mathrm{72}\) to \(\mathrm{78}\) inclusive
- Need to find the mean temperature for the week
- What this tells us: We have the temperatures \(\mathrm{72, 73, 74, 75, 76, 77, 78}\) (\(\mathrm{7}\) values total)
2. INFER the solution approach
- Since we need the mean, we need: sum of all temperatures \(\div\) number of temperatures
- We can either add directly or use the arithmetic series formula since these are consecutive integers
- Direct addition is straightforward: add all seven values and divide by 7
3. SIMPLIFY by calculating the sum
- Sum \(\mathrm{= 72 + 73 + 74 + 75 + 76 + 77 + 78}\)
- Adding step by step (use calculator): \(\mathrm{72 + 73 + 74 + 75 + 76 + 77 + 78 = 525}\)
4. SIMPLIFY to find the mean
- Mean \(\mathrm{= \text{Total sum} \div \text{Number of values}}\)
- Mean \(\mathrm{= 525 \div 7 = 75}\)
Answer: C) 75
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret "consecutive integers from 72 to 78 inclusive" and either:
- Miss that "inclusive" means 78 is included, so they only use \(\mathrm{72, 73, 74, 75, 76, 77}\) (6 numbers)
- Don't realize these are consecutive integers filling the gap: \(\mathrm{72, 73, 74, 75, 76, 77, 78}\)
If they use only 6 numbers, their sum would be 447, giving mean \(\mathrm{= 447 \div 6 = 74.5}\), which isn't an answer choice. This leads to confusion and guessing.
Second Most Common Error:
Poor SIMPLIFY execution: Students correctly identify all seven temperatures but make arithmetic errors when adding them up or dividing by 7. Small calculation mistakes can lead them to select Choice B (74) or Choice D (76) instead of the correct answer.
The Bottom Line:
This problem tests careful reading (understanding "inclusive") and systematic arithmetic. The key insight is that consecutive integers from A to B inclusive means you include both endpoints and everything in between.