A warehouse uses two types of storage containers for inventory. Type X containers each hold 6 cubic meters, and Type...
GMAT Algebra : (Alg) Questions
A warehouse uses two types of storage containers for inventory. Type X containers each hold \(6\) cubic meters, and Type Y containers each hold \(2\) cubic meters. If the warehouse has \(\mathrm{a}\) containers of Type X and \(\mathrm{b}\) containers of Type Y, and the Type X containers hold \(48\) cubic meters more storage capacity than the Type Y containers, which equation represents this situation?
- \(6\mathrm{a} - 2\mathrm{b} = 48\)
- \(6\mathrm{a} + 2\mathrm{b} = 48\)
- \(\mathrm{a} - \mathrm{b} = 48\)
- \(6\mathrm{a} - \mathrm{b} = 48\)
- \(2\mathrm{b} - 6\mathrm{a} = 48\)
1. TRANSLATE the problem information
- Given information:
- Type X containers: 6 cubic meters each, with 'a' containers total
- Type Y containers: 2 cubic meters each, with 'b' containers total
- Type X holds 48 cubic meters MORE than Type Y
2. INFER what we need to calculate
- To compare storage capacities, we need total capacity for each type
- Total capacity = (number of containers) × (capacity per container)
3. Calculate total capacities
- Type X total capacity = \(\mathrm{6a}\) cubic meters
- Type Y total capacity = \(\mathrm{2b}\) cubic meters
4. TRANSLATE the "more than" relationship
- "Type X holds 48 cubic meters more than Type Y" means:
- (Type X capacity) - (Type Y capacity) = 48
- Therefore: \(\mathrm{6a - 2b = 48}\)
Answer: A
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret "more than" and set up the equation as addition instead of subtraction.
They think "Type X holds 48 more" means the total of both types equals 48, leading to \(\mathrm{6a + 2b = 48}\). This fundamental misunderstanding of comparative language in word problems causes them to miss the subtraction relationship entirely.
This may lead them to select Choice B (\(\mathrm{6a + 2b = 48}\)).
Second Most Common Error:
Incomplete INFER reasoning: Students correctly understand "more than" but forget to multiply by the capacity per container.
They set up the relationship as just \(\mathrm{a - b = 48}\), thinking only about the difference in number of containers rather than the difference in total storage capacity. This overlooks that different container types have different capacities.
This may lead them to select Choice C (\(\mathrm{a - b = 48}\)).
The Bottom Line:
This problem tests whether students can accurately translate comparative language ("more than") into mathematical equations while remembering to account for the capacity differences between container types. The key insight is recognizing that "more storage capacity" requires comparing total capacities (\(\mathrm{6a}\) vs \(\mathrm{2b}\)), not just container counts.