In a certain factory, five different machines-Machines A through E-produce ceramic figurines, each at different rates. The machines were all...
GMAT Two Part Analysis : (TPA) Questions
In a certain factory, five different machines-Machines A through E-produce ceramic figurines, each at different rates. The machines were all brought online at different times, each continuously producing figurines at its own constant rate until 8:00 p.m.:
- Machine A at 1:00 p.m., producing \(\mathrm{1,000\,figurines\,per\,hour}\)
- Machine B at 1:15 p.m., producing \(\mathrm{500\,figurines\,per\,hour}\)
- Machine C at 1:45 p.m., producing \(\mathrm{1,500\,figurines\,per\,hour}\)
- Machine D at 2:00 p.m., producing \(\mathrm{400\,figurines\,per\,hour}\)
- Machine E at 2:45 p.m., producing \(\mathrm{900\,figurines\,per\,hour}\)
At 2:45, when Machine E was brought online, the other four machines had produced a total of \(\mathrm{x}\) figurines. After 2:45, the total combined rate of production for all five machines was \(\mathrm{y}\) figurines per hour. Select a value for \(\mathrm{x}\) and a value for \(\mathrm{y}\) so that the above statement accurately reflects the given information. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Visualization Selection
This is a time-based problem with machines starting at different times, so we'll use a timeline.
Timeline Visualization
1:00 PM 1:15 PM 1:45 PM 2:00 PM 2:45 PM → 8:00 PM | | | | | A starts B starts C starts D starts E starts (1000/hr) (500/hr) (1500/hr) (400/hr) (900/hr)
Phase 2: Understanding the Question
We need to find:
- x: Total figurines produced by Machines A, B, C, and D by 2:45 PM
- y: Combined production rate of all five machines after 2:45 PM
Key Insight
After 2:45 PM, all five machines run simultaneously, so y is simply the sum of all production rates.
Phase 3: Finding the Answer
Calculating x (Total production by 2:45 PM)
Let's calculate how long each machine runs until 2:45 PM:
Machine A: 1:00 PM to 2:45 PM = 1 hour 45 minutes = 1.75 hours
- Production: \(1,000 \times 1.75 = 1,750\) figurines
Machine B: 1:15 PM to 2:45 PM = 1 hour 30 minutes = 1.5 hours
- Production: \(500 \times 1.5 = 750\) figurines
Machine C: 1:45 PM to 2:45 PM = 1 hour
- Production: \(1,500 \times 1 = 1,500\) figurines
Machine D: 2:00 PM to 2:45 PM = 45 minutes = 0.75 hours
- Production: \(400 \times 0.75 = 300\) figurines
Total x = \(1,750 + 750 + 1,500 + 300 = 4,300\) figurines
Calculating y (Combined rate after 2:45 PM)
After 2:45 PM, all five machines are running:
- Machine A: 1,000 figurines/hour
- Machine B: 500 figurines/hour
- Machine C: 1,500 figurines/hour
- Machine D: 400 figurines/hour
- Machine E: 900 figurines/hour
Total y = \(1,000 + 500 + 1,500 + 400 + 900 = 4,300\) figurines/hour
Phase 4: Solution
Both x and y equal 4,300, which is available in our answer choices.
Final Answer:
- x = 4,300
- y = 4,300