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Researchers for a textile company carried out an experiment comparing the longevity of two new fabric blends. They conducted a series of usage tests, known as double rubs, on 100 pieces of each type of material. The following scales are used for this type of testing:

\begin{tabular}{|l|c|}
\hline \multicolumn{1}{|c|}{ Fabric Grade } & \begin{tabular}{c}
Number of Double Rubs \\
(in thousands)
\end{tabular} \\
\hline Heavy duty & [tex]$15+$[/tex] \\
\hline Medium duty & [tex]$9-15$[/tex] \\
\hline Light duty & [tex]$3-9$[/tex] \\
\hline Delicate duty & [tex]$\ \textless \ 3$[/tex] \\
\hline
\end{tabular}

After performing the tests on each fabric, researchers found that on average, fabric A lasted through 7,900 double rubs and fabric B lasted through 9,200 double rubs. The marketing department wants to advertise that both fabrics are tested and approved for medium-duty use.

Which statements are true about this situation?

A. Fabric A is a more durable fabric because it has a lower double rub rating than fabric B.

B. Neither fabric meets the requirements of a medium-duty fabric.

C. Fabric B is a more durable fabric because it has a higher double rub rating than fabric A.

D. The sales department can refer to fabric A as a medium-duty fabric.

E. The sales department can refer to fabric B as a medium-duty fabric.



Answer :

GinnyAnswer
Let's analyze each statement step-by-step and compare it to the given conditions and results.

1. Fabric A is a more durable fabric because it has a lower double rub rating than fabric B.
- Durability Consideration: A lower double rub rating implies less durability. Given that fabric A has 7,900 double rubs and fabric B has 9,200 double rubs on average, fabric A is not more durable than fabric B.
- Conclusion: This statement is false.

2. Neither fabric meets the requirements of a medium-duty fabric.
- Medium-Duty Requirement: Medium-duty fabric should have 9,000 to 15,000 double rubs. Fabric A has 7,900 double rubs which makes it a light-duty fabric, and fabric B has 9,200 double rubs which falls within the medium-duty range.
- Conclusion: This statement is false because fabric B does meet the requirements of a medium-duty fabric.

3. Fabric B is a more durable fabric because it has a higher double rub rating than fabric A.
- Durability Consideration: Since fabric B has a higher double rub rating of 9,200 compared to fabric A's 7,900, fabric B is indeed more durable.
- Conclusion: This statement is true.

4. The sales department can refer to fabric A as a medium-duty fabric.
- Fabric A's Rating: Fabric A has 7,900 double rubs, which fits within the light-duty category (3,000 to 9,000 double rubs).
- Conclusion: This statement is false because fabric A is a light-duty fabric, not a medium-duty fabric.

5. The sales department can refer to fabric B as a medium-duty fabric.
- Fabric B's Rating: Fabric B has 9,200 double rubs, which fits within the medium-duty category (9,000 to 15,000 double rubs).
- Conclusion: This statement is true.

To summarize, the true statements about this situation are:
- Fabric B is a more durable fabric because it has a higher double rub rating than fabric A.
- The sales department can refer to fabric B as a medium-duty fabric.

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