A science teacher is preparing the 5 stations of a science laboratory. Each station will have either Experiment A materials...
GMAT Algebra : (Alg) Questions
A science teacher is preparing the 5 stations of a science laboratory. Each station will have either Experiment A materials or Experiment B materials, but not both. Experiment A requires 6 teaspoons of salt, and Experiment B requires 4 teaspoons of salt. If \(\mathrm{x}\) is the number of stations that will be set up for Experiment A and the remaining stations will be set up for Experiment B, which of the following expressions represents the total number of teaspoons of salt required?
1. TRANSLATE the problem information
- Given information:
- Total stations: 5
- Each station gets either Experiment A OR Experiment B materials (not both)
- Experiment A needs 6 teaspoons salt per station
- Experiment B needs 4 teaspoons salt per station
- x = number of stations with Experiment A
2. INFER the complementary relationship
- If x stations have Experiment A, then the remaining stations must have Experiment B
- Since there are 5 stations total: stations with Experiment B = \(5 - \mathrm{x}\)
3. TRANSLATE into mathematical expressions
- Salt needed for Experiment A stations: \(6\mathrm{x}\) teaspoons
- Salt needed for Experiment B stations: \(4(5 - \mathrm{x})\) teaspoons
- Total salt needed: \(6\mathrm{x} + 4(5 - \mathrm{x})\)
4. SIMPLIFY the expression
\(6\mathrm{x} + 4(5 - \mathrm{x})\)
\(6\mathrm{x} + 20 - 4\mathrm{x}\)
\(2\mathrm{x} + 20\)
Answer: C. \(2\mathrm{x} + 20\)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Not recognizing the complementary relationship between the two types of stations.
Students may think they need more information to solve this, not realizing that if x stations have Experiment A, then automatically \((5-\mathrm{x})\) stations must have Experiment B. They might try to introduce another variable or feel stuck because they think the problem is incomplete.
This leads to confusion and guessing among the answer choices.
Second Most Common Error:
Poor TRANSLATE reasoning: Misinterpreting what x represents or setting up incorrect expressions.
Some students might think x represents the total salt needed, or they might set up expressions like \(5\mathrm{x}\) (thinking each station needs the same amount) or \(10\mathrm{x}\) (somehow adding the salt requirements). They miss that different station types need different amounts of salt.
This may lead them to select Choice A (\(5\mathrm{x}\)) or Choice B (\(10\mathrm{x}\)).
The Bottom Line:
This problem tests your ability to work with complementary quantities and set up expressions involving two different categories that together make up a fixed total. The key insight is recognizing that in an either/or situation with a fixed total, one category determines the other.