A portable hard drive has a total storage capacity of 1,800 gigabytes (GB). The drive's file system reserves 12 GB...
GMAT Algebra : (Alg) Questions
A portable hard drive has a total storage capacity of 1,800 gigabytes (GB). The drive's file system reserves 12 GB of space for system files, and this space cannot be used for user storage. The owner plans to use the remaining space to store project folders, each averaging 4 GB in size, and media files, each averaging 15 GB in size. Which inequality represents the possible number of project folders, \(\mathrm{p}\), and media files, \(\mathrm{m}\), the owner can store on the drive?
1. TRANSLATE the storage information
- Given information:
- Total drive capacity: 1,800 GB
- System files reserve: 12 GB (unavailable for user storage)
- Project folders: 4 GB each, p folders total
- Media files: 15 GB each, m files total
2. TRANSLATE to find available space
- Available space = Total capacity - Reserved space
- Available space = \(\mathrm{1,800 - 12 = 1,788}\) GB
3. TRANSLATE file storage into mathematical expressions
- Space used by project folders: \(\mathrm{4p}\) GB
- Space used by media files: \(\mathrm{15m}\) GB
- Total space used by all files: \(\mathrm{4p + 15m}\) GB
4. INFER the relationship constraint
- The total space used cannot exceed available space
- This means: Total space used ≤ Available space
- Therefore: \(\mathrm{4p + 15m \leq 1,788}\)
5. Match with answer choices
- The inequality \(\mathrm{4p + 15m \leq 1,788}\) matches choice (A)
Answer: A
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students mix up which coefficient belongs to which variable. They might see "project folders, each averaging 4 GB" and "media files, each averaging 15 GB" but accidentally write \(\mathrm{15p + 4m}\) instead of \(\mathrm{4p + 15m}\).
This reversal error leads them to select Choice (C) (\(\mathrm{15p + 4m \leq 1,800}\)) - which also happens to use the wrong total (1,800 instead of 1,788), making it seem more plausible.
Second Most Common Error:
Poor INFER reasoning about inequality direction: Students correctly set up \(\mathrm{4p + 15m}\) but choose the wrong inequality symbol. They might think "we want at least this much space" and use ≥ instead of recognizing that storage used cannot exceed available space.
This leads them to select Choice (B) (\(\mathrm{4p + 15m \geq 1,788}\)).
The Bottom Line:
This problem tests careful attention to detail in translation - students must track which numbers go with which variables AND remember to subtract the reserved space from the total capacity. The multiple similar-looking choices are designed to catch common translation mistakes.