Based on the following, which of the following statements is true? A CD…
2024
Based on the following, which of the following statements is true?
A CD contains 12 music tracks which are of lengths (in minutes):
3, 7, 4, 3, 5, 6, 4, 5, 4, 7, 8, 8 and each minute of music requires 12 MB of storage.
Answer: C. 768 MB of memory is used for the 12 music tracks. — Concept: For uncompressed audio the storage needed is directly proportional to the playing time — total storage = (total playing time) × (storage required per…
- A.
512 MB of memory is used for the 12 music tracks.
- B.
1 GB of memory is used for the 12 music tracks.
- C.
768 MB of memory is used for the 12 music tracks.
- D.
If the tracks are to be stored in MP3 format, then each music track will be reduced in size by 90%. The storage that the 12 tracks would require is 69.12 MB.
Attempted by 4 students.
Show answer & explanation
Correct answer: C
Concept: For uncompressed audio the storage needed is directly proportional to the playing time — total storage = (total playing time) × (storage required per minute). Reducing a file's size by r% leaves (100 − r)% of the original size. Also, in storage units, 1 GB = 1024 MB.
Application:
Total playing time = 3 + 7 + 4 + 3 + 5 + 6 + 4 + 5 + 4 + 7 + 8 + 8 minutes.
Grouping the numbers to add quickly: (3 + 7) + (4 + 3 + 5 + 6) + (4 + 5 + 4) + (7 + 8 + 8) = 10 + 18 + 13 + 23 = 64 minutes.
Total storage = 64 minutes × 12 MB per minute = 768 MB.
Cross-check and contrast:
Re-doing the product a different way confirms it: 64 × 12 = (64 × 10) + (64 × 2) = 640 + 128 = 768 MB.
512 MB would account for only 512 ÷ 12 ≈ 42.67 minutes of music, which is less than the 64 minutes actually listed.
1 GB is 1024 MB, which would account for 1024 ÷ 12 ≈ 85.33 minutes of music, far more than the 64 minutes actually listed.
For the MP3 claim, a 90% reduction leaves 10% of the size, so the tracks would need 10% of 768 MB = 76.8 MB, not 69.12 MB (69.12 MB would correspond to keeping 9%, that is a 91% reduction).
So, of the four statements, the one that holds is that the 12 music tracks occupy 768 MB of memory.