A laboratory incubator is set to 37 degrees Celsius (°C). A safety protocol requires that the actual internal temperature must...
GMAT Algebra : (Alg) Questions
A laboratory incubator is set to 37 degrees Celsius (°C). A safety protocol requires that the actual internal temperature must remain within 1.5°C of the setpoint at all times during a 24-hour test. Which inequality describes all possible actual temperatures \(\mathrm{T}\), in °C, during the test?
- \(\mathrm{T \leq 35.5}\)
- \(\mathrm{35.5 \leq T \leq 38.5}\)
- \(\mathrm{T \geq 37}\)
- \(\mathrm{|T - 37| \geq 1.5}\)
1. TRANSLATE the problem information
- Given information:
- Incubator set to \(\mathrm{37°C}\)
- Temperature must remain within \(\mathrm{1.5°C}\) of setpoint
- Need to find inequality for all possible temperatures T
- What "within \(\mathrm{1.5°C}\) of \(\mathrm{37°C}\)" means: The actual temperature can be at most \(\mathrm{1.5°C}\) away from \(\mathrm{37°C}\) in either direction
2. TRANSLATE to mathematical inequality
- "Within \(\mathrm{1.5°C}\) of \(\mathrm{37°C}\)" becomes: \(\mathrm{|T - 37| \leq 1.5}\)
- The absolute value captures deviation in both directions
- The ≤ symbol indicates "at most" \(\mathrm{1.5°C}\) away
3. SIMPLIFY the absolute value inequality
- Convert \(\mathrm{|T - 37| \leq 1.5}\) to compound inequality:
\(\mathrm{-1.5 \leq T - 37 \leq 1.5}\)
- Add 37 to all three parts:
\(\mathrm{37 - 1.5 \leq T \leq 37 + 1.5}\)
\(\mathrm{35.5 \leq T \leq 38.5}\)
Answer: B. \(\mathrm{35.5 \leq T \leq 38.5}\)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret "within \(\mathrm{1.5°C}\)" as meaning "at least \(\mathrm{1.5°C}\) away from" instead of "at most \(\mathrm{1.5°C}\) away from."
They incorrectly set up \(\mathrm{|T - 37| \geq 1.5}\), thinking the safety protocol requires the temperature to be significantly different from the setpoint. This completely reverses the intended meaning of the safety constraint.
This leads them to select Choice D (\(\mathrm{|T - 37| \geq 1.5}\)).
Second Most Common Error:
Incomplete TRANSLATE reasoning: Students understand that there are bounds but only consider one direction, thinking either "no more than \(\mathrm{1.5°C}\) above" or "no more than \(\mathrm{1.5°C}\) below" rather than considering both directions simultaneously.
This partial understanding may lead them to select Choice A (\(\mathrm{T \leq 35.5}\)) if they only consider the lower bound, or Choice C (\(\mathrm{T \geq 37}\)) if they focus only on staying at or above the setpoint.
The Bottom Line:
The key challenge is correctly interpreting "within X units" as creating a two-sided constraint (absolute value ≤), not a one-sided constraint or a "separation" requirement (absolute value ≥).