Sarah needs to get from the ground floor to the 8th floor of an office building. She can either take...
GMAT Algebra : (Alg) Questions
Sarah needs to get from the ground floor to the 8th floor of an office building. She can either take the elevator, which takes 3 minutes to travel to the 8th floor once it arrives, or she can take the stairs, which takes 13 minutes. The elevator runs continuously, and the number of minutes, \(\mathrm{t}\), that Sarah waits for the elevator varies between 0 and 18. Which of the following inequalities gives the values of \(\mathrm{t}\) for which it would be faster for Sarah to take the stairs?
- \(\mathrm{t - 3 \lt 13}\)
- \(\mathrm{t - 3 \gt 13}\)
- \(\mathrm{t + 3 \lt 13}\)
- \(\mathrm{t + 3 \gt 13}\)
1. TRANSLATE the problem information
- Given information:
- Stairs take 13 minutes total
- Elevator takes t minutes waiting + 3 minutes traveling = (t + 3) minutes total
- We want to find when stairs are faster
2. INFER the mathematical relationship
- 'Faster' means less time
- For stairs to be faster than elevator: Stairs time < Elevator time
- This gives us: \(\mathrm{13 \lt t + 3}\)
3. SIMPLIFY to match answer format
- The inequality \(\mathrm{13 \lt t + 3}\) can be rewritten as \(\mathrm{t + 3 \gt 13}\)
- This matches choice (D)
Answer: D
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students set up the inequality backwards, thinking that for stairs to be faster, we need \(\mathrm{t + 3 \lt 13}\) (elevator time less than stairs time) instead of recognizing that we want stairs time less than elevator time (\(\mathrm{13 \lt t + 3}\)).
This may lead them to select Choice (C) (\(\mathrm{t + 3 \lt 13}\))
Second Most Common Error:
Poor TRANSLATE reasoning: Students might subtract the travel time from the wait time instead of adding them, thinking the elevator time is \(\mathrm{t - 3}\).
This may lead them to select Choice (A) (\(\mathrm{t - 3 \lt 13}\)) or Choice (B) (\(\mathrm{t - 3 \gt 13}\))
The Bottom Line:
This problem requires careful attention to what 'faster' means mathematically - the faster option takes LESS time, so you need to set up the inequality with the faster option on the left side of the < symbol.