One of a planet's moons orbits the planet every 252 days. A second moon orbits the planet every 287 days....
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
One of a planet's moons orbits the planet every \(\mathrm{252}\) days. A second moon orbits the planet every \(\mathrm{287}\) days. How many more days does it take the second moon to orbit the planet \(\mathrm{29}\) times than it takes the first moon to orbit the planet \(\mathrm{29}\) times?
1. TRANSLATE the problem information
- Given information:
- First moon: orbits every \(252\) days (one complete orbit = \(252\) days)
- Second moon: orbits every \(287\) days (one complete orbit = \(287\) days)
- Need to find: difference in time for each moon to complete \(29\) orbits
2. INFER the solution strategy
- To find "how many more days," we need:
- Calculate total time for first moon to complete \(29\) orbits
- Calculate total time for second moon to complete \(29\) orbits
- Subtract to find the difference
3. SIMPLIFY the calculations
- First moon total time: \(252 \times 29 = 7,308\) days (use calculator)
- Second moon total time: \(287 \times 29 = 8,323\) days (use calculator)
- Difference: \(8,323 - 7,308 = 1,015\) days (use calculator)
Answer: \(1,015\)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students might misinterpret the question and calculate \(287 - 252 = 35\), thinking this represents the answer.
They read "how many more days" and immediately focus on the difference between the orbital periods (\(287\) vs \(252\)) rather than understanding that they need to find the difference in total time for \(29\) complete orbits. This leads to confusion about what exactly needs to be calculated and may result in guessing or selecting \(35\) if it were an answer choice.
Second Most Common Error:
Inadequate SIMPLIFY execution: Students understand the correct approach but make arithmetic errors in the large multiplication or subtraction calculations.
For example, they might calculate \(252 \times 29 = 7,208\) instead of \(7,308\), or make an error in the final subtraction step. These calculation mistakes lead to incorrect final answers that are close to but not exactly \(1,015\).
The Bottom Line:
This problem tests whether students can correctly interpret a multi-step word problem requiring them to scale up individual orbital periods before finding differences, rather than just working with the given periods directly.