In a school hallway, there are 18 lockers. Exactly 5 lockers are assigned to seniors, and 2 lockers are out...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
In a school hallway, there are 18 lockers. Exactly 5 lockers are assigned to seniors, and 2 lockers are out of order. If one locker is selected at random from the 18, what is the probability that the locker selected is available for general student use (that is, neither assigned to seniors nor out of order)?
- \(\frac{1}{9}\)
- \(\frac{5}{18}\)
- \(\frac{7}{18}\)
- \(\frac{11}{18}\)
- \(\frac{13}{18}\)
1. TRANSLATE the problem information
- Given information:
- Total lockers: 18
- Lockers assigned to seniors: 5
- Lockers out of order: 2
- Want: Probability that a randomly selected locker is 'available for general student use'
- What 'available for general student use' means:
- NOT assigned to seniors AND NOT out of order
- These are the lockers that are unrestricted
2. INFER the solution approach
- To find available lockers, we need to remove all restricted lockers from the total
- Restricted lockers = seniors' lockers + out-of-order lockers
- Strategy: Find available lockers first, then calculate probability
3. SIMPLIFY to find the answer
- Total restricted lockers = \(5 + 2 = 7\)
- Available lockers = \(18 - 7 = 11\)
- Probability = Available/Total = \(\frac{11}{18}\)
Answer: (D) \(\frac{11}{18}\)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret what 'available for general student use' means and only subtract one type of restricted locker.
For example, they might think: 'Available means not assigned to seniors' and calculate \(18 - 5 = 13\) available lockers, giving probability \(\frac{13}{18}\).
This may lead them to select Choice (E) \(\frac{13}{18}\)
Second Most Common Error:
Poor INFER reasoning: Students correctly identify both types of restricted lockers but use the restricted count as the favorable outcome instead of the available count.
They calculate \(\frac{7}{18}\) thinking this represents the probability of getting an available locker.
This may lead them to select Choice (C) \(\frac{7}{18}\)
The Bottom Line:
This problem tests whether students can properly interpret 'neither A nor B' language and recognize that they must account for ALL restrictions when finding the complement of an event.