A data center began processing a large file of 874{,500} megabytes (MB) at the start of a workday. After 14...

1. TRANSLATE the problem information

• Given information:
  • Initial file size: 874,500 MB
  • Processing time: 14 minutes (continuous)
  • Remaining file size: 660,300 MB
  • Need to find: average megabytes processed per second

2. INFER the solution approach

• To find processing rate, we need: Rate = Amount Processed ÷ Time
• We don't have "amount processed" directly - we need to calculate it first
• The time is in minutes, but we need rate per second - unit conversion required
• Strategy: Find processed amount → Convert time → Calculate rate

3. Calculate the amount of data processed

SIMPLIFY the subtraction:

\(\mathrm{Amount\ processed = Initial\ size - Remaining\ size}\)

\(\mathrm{Amount\ processed = 874,500\ MB - 660,300\ MB = 214,200\ MB}\)

4. TRANSLATE time units for the rate calculation

Since we need rate per second:

\(\mathrm{Time\ in\ seconds = 14\ minutes × 60\ seconds/minute = 840\ seconds}\)

5. SIMPLIFY to find the processing rate

\(\mathrm{Rate = Amount\ processed ÷ Time\ in\ seconds}\)

\(\mathrm{Rate = 214,200\ MB ÷ 840\ seconds}\) (use calculator)

\(\mathrm{Rate = 255\ MB\ per\ second}\)

Answer: B. 255

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students try to use the remaining amount (660,300 MB) instead of calculating the processed amount first.

They might divide \(\mathrm{660,300 ÷ 840 = 786}\), leading them to select Choice C (786). This happens because they misinterpret "remaining to be processed" as "already processed."

Second Most Common Error:

Poor TRANSLATE reasoning: Students forget to convert minutes to seconds and calculate rate per minute instead of per second.

They correctly find 214,200 MB processed in 14 minutes, then calculate \(\mathrm{214,200 ÷ 14 = 15,300}\) MB per minute. This leads them to select Choice D (15,300), not realizing the question asks for rate per second.

The Bottom Line:

This problem tests whether students can work backwards from "what's left" to find "what was processed," while also managing unit conversions. The multi-step nature means one wrong turn early leads to completely wrong final answers.