Javier rates his work - readiness on a scale from 0 to 10, with 10 being maximum readiness. He wants...
GMAT Two Part Analysis : (TPA) Questions
Javier rates his work - readiness on a scale from \(0\) to \(10\), with \(10\) being maximum readiness. He wants his rating to be as high as possible when he arrives at his office and has found that the rating is being affected by how late he sleeps and how long he spends preparing for work. His alarm clock sounds at \(6\)am, at which time he has a work - readiness of \(10\). He needs to leave for work at exactly \(6:40\)am. During these \(40\) mins, Javier's only activities are sleeping or preparing for work. If Javier spends more than \(25\) mins or less than \(10\) mins to prepare, his rating is reduced by \(5\) points. To sleep past \(6\)am, however, Javier must use the snooze button on his alarm clock, which delays the alarm by \(4\) mins. Each press of the snooze button after the third will decrease Javier's efficiency rating by \(1\) point.
In the following table, select for Rating the greatest work - readiness rating that Java can achieve and select for Snoozes the number of times he must press the snooze button to achieve that rating. Make only 2 selections, one in each column.
Phase 1: Owning the Dataset
Timeline Visualization
6:00am ----[Sleep Time]----[Prep Time]---- 6:40am
(snoozes × 4 min) (remaining) = 40 min total
Key Constraints:
- Initial rating: 10 points
- Total time available: 40 minutes
- Each snooze: 4 minutes
- Preparation penalty: -5 points if >25 min OR <10 min
- Snooze penalty: -1 point for each press after 3rd
Phase 2: Understanding the Question
We need to find:
- Rating: The maximum work-readiness rating achievable
- Snoozes: The number of snooze button presses to achieve that rating
The relationship is: \(\mathrm{Preparation\ time} = 40 - (\mathrm{snoozes} \times 4)\)
Phase 3: Finding the Answer
Let's systematically check each possible number of snoozes:
0 snoozes: Sleep = 0 min, Prep = 40 min
- Prep > 25 → -5 points
- \(\mathrm{Rating} = 10 - 5 = 5\)
1 snooze: Sleep = 4 min, Prep = 36 min
- Prep > 25 → -5 points
- \(\mathrm{Rating} = 10 - 5 = 5\)
2 snoozes: Sleep = 8 min, Prep = 32 min
- Prep > 25 → -5 points
- \(\mathrm{Rating} = 10 - 5 = 5\)
3 snoozes: Sleep = 12 min, Prep = 28 min
- Prep > 25 → -5 points
- \(\mathrm{Rating} = 10 - 5 = 5\)
4 snoozes: Sleep = 16 min, Prep = 24 min
- Prep = 24 (between 10-25) → no prep penalty ✓
- 4 > 3 → -1 point for extra snooze
- \(\mathrm{Rating} = 10 - 1 = 9\) ← Maximum found!
5 snoozes: Sleep = 20 min, Prep = 20 min
- Prep = 20 (between 10-25) → no prep penalty ✓
- 5 > 3 → -2 points for 2 extra snoozes
- \(\mathrm{Rating} = 10 - 2 = 8\)
6 snoozes: Sleep = 24 min, Prep = 16 min
- Prep = 16 (between 10-25) → no prep penalty ✓
- 6 > 3 → -3 points for 3 extra snoozes
- \(\mathrm{Rating} = 10 - 3 = 7\)
Phase 4: Solution
The maximum rating Javier can achieve is 9, obtained by pressing the snooze button 4 times.
This gives him:
- 16 minutes of extra sleep
- 24 minutes to prepare (within the optimal 10-25 minute range)
- Only 1 penalty point for the 4th snooze press
Final Answer:
- Rating: 9
- Snoozes: 4