QUESTION STEM:A museum's audio tour lasts 80 minutes in total.Each narrated segment lasts 7 minutes, and each musical interlude lasts...
GMAT Algebra : (Alg) Questions
- A museum's audio tour lasts \(\mathrm{80}\) minutes in total.
- Each narrated segment lasts \(\mathrm{7}\) minutes, and each musical interlude lasts \(\mathrm{2}\) minutes.
- If the tour includes \(\mathrm{6}\) narrated segments, how many musical interludes does it include?
Answer Format Instructions: Enter your answer as an integer.
1. TRANSLATE the problem information
- Given information:
- Total tour duration: 80 minutes
- Each narrated segment: 7 minutes
- Each musical interlude: 2 minutes
- Number of narrated segments: 6
- Need to find: Number of musical interludes
2. INFER the solution strategy
- This is a "parts make up the whole" problem
- Strategy: Find how much time the narrated segments use, then the remaining time must be used by musical interludes
- We can then divide the remaining time by the length of each interlude
3. SIMPLIFY through calculations
- Calculate time used by narrated segments:
\(6 \times 7 = 42\) minutes
- Find remaining time for musical interludes:
\(80 - 42 = 38\) minutes
- Calculate number of musical interludes:
\(38 \div 2 = 19\) interludes
Answer: 19
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret what they're solving for and try to find the total time instead of the number of interludes.
They might calculate something like: \(6 \times 7 + 2 = 44\), thinking they need to find total time with one interlude, leading to confusion and guessing.
Second Most Common Error:
Poor INFER reasoning: Students don't recognize the "remainder" structure and attempt to directly divide total time by something.
They might try \(80 \div 7 = 11.4\) or \(80 \div 2 = 40\), not understanding they need to account for the narrated segments first. This leads to confusion and abandoning systematic solution.
The Bottom Line:
This problem requires students to see the two-part structure: some time is already allocated (narrated segments), and the remaining time gets divided among interludes. Missing this partition concept is what derails most solution attempts.