An e-commerce fulfillment center uses two automated sorting machines, Machine X and Machin… — GMAT

An e-commerce fulfillment center uses two automated sorting machines, Machine X and Machine Y, to sort packages. Machine X processes packages at a constant rate of $150$ packages per hour, with an error rate of $4\%$ . Machine Y processes packages at a constant rate of $200$ packages per hour, with an error rate of $1.5\%$ . If both machines operate simultaneously and continuously to process a total batch of $2,100$ packages, what is the total number of incorrectly processed packages in this batch?

Answer: 54 packages

Answer

54 packages

Working together at a combined rate of

350

packages per hour, the machines take

6

hours to complete

2,100

packages. Machine X processes

900

packages with

36

errors (

4\%

), while Machine Y processes

1,200

packages with

18

errors (

1.5\%

). Adding these yields

54

total errors.

Step-by-Step Solution

Determine the combined processing rate of the two machines

350

packages per hour

Machine X and Machine Y work concurrently, so their rates add up (

150 + 200 = 350

Determine total operating time needed for the batch

6

hours

Dividing total packages (

2,100

) by the combined rate (

350

) gives the total operating duration.

Calculate individual volume handled by each machine

Machine X:

900

packages; Machine Y:

1,200

packages

Multiplying the duration (

6

hours) by each machine's hourly rate yields their individual output.

Calculate the error quantity for each machine and total errors

36 + 18 = 54

packages

4\%

900 = 36

, and

1.5\%

1,200 = 18

. The sum of errors is

54

Key Concept

Combined Rates and Weighted Percentage Errors

Question

Answer

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Key Concept

Common Mistakes

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