A food scientist tested five meal prep techniques: T 1, T 2, T 3, T 4, and T 5.
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A food scientist tested five meal prep techniques: $T_1, T_2, T_3, T_4$, and $T_5$. The following observations were recorded:
- $T_1$ is twice as effective as $T_4$, but less effective than $T_5$ ($T_4 < T_1 < T_5$).
- $T_2$ is thrice as effective as $T_5$ ($T_2 = 3 T_5$).
- $T_3$ is equally effective as $T_4$ ($T_3 = T_4$).
Which of the following choices is TRUE regarding the conclusions drawn below?
Conclusions:
- $T_5$ is more effective than $T_1$.
- $T_2$ is more effective than $T_5$.
- $T_2$ is more effective than $T_1$.
- $T_4$ is more effective than $T_1$.
Show answer & explanation
Based on the given inequalities and equalities, the effectiveness order is T2 > T5 > T1 > T4 = T3. Conclusions 1, 2, and 3 align with this order, while Conclusion 4 contradicts it.
Step-by-step Derivation:
Step 1: Analyze the given observations to establish relationships between the techniques.
- Observation 1: $T_4 < T_1 < T_5$ (T1 is more effective than T4, and T5 is more effective than T1).
- Observation 2: $T_2 = 3 T_5$. Since effectiveness is a positive measure, $T_2 > T_5$.
- Observation 3: $T_3 = T_4$.
Step 2: Combine these into a single chain of effectiveness:
$T_2 > T_5 > T_1 > T_4 = T_3$.
Step 3: Evaluate the conclusions based on the chain:
- Conclusion 1: '$T_5$ is more effective than $T_1$'. From the chain $T_5 > T_1$, this is TRUE.
- Conclusion 2: '$T_2$ is more effective than $T_5$'. From the chain $T_2 > T_5$, this is TRUE.
- Conclusion 3: '$T_2$ is more effective than $T_1$'. Since $T_2 > T_5$ and $T_5 > T_1$, by transitivity $T_2 > T_1$. This is TRUE.
- Conclusion 4: '$T_4$ is more effective than $T_1$'. From the chain $T_1 > T_4$, this is FALSE.
Step 4: Identify the correct option. Conclusions 1, 2, and 3 are true. This matches Option A.