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 1,000,figurines,per,hour Machine B at 1:15 p.m., producing 500,figurines,per,hour Machine C at 1:45 p.m., producing 1,500,figurines,per,hour Machine D at 2:00 p.m., producing 400,figurines,per,hour Machine E at 2:45 p.m., producing 900,figurines,per,hour

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

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Two Part Analysis

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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.

1750

4300

7525

2800

6250

Solution

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

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