Sample Question 19:

Bridget, Cassie, and Hannah are discussing the results of their last math test. Hannah shows Bridget and Cassie her test, but Bridget and Cassie don't show theirs to anyone. Cassie says, 'I didn't get the lowest score in our class,' and Bridget adds, 'I didn't get the highest score.' What is the ranking of the three girls from the highest score to the lowest score?

\(\textbf{(A)}\ \text{Hannah, Cassie, Bridget} \qquad \textbf{(B)}\ \text{Hannah, Bridget, Cassie} \\ \qquad \textbf{(C)}\ \text{Cassie, Bridget, Hannah} \qquad \textbf{(D)}\ \text{Cassie, Hannah, Bridget} \\ \qquad \textbf{(E)}\ \text{Bridget, Cassie, Hannah}\)

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Answer Keys

Question 19: D

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Solutions

Question 19
Step 1: Analyze the statement given by Cassie, 'I didn't get the lowest score in our class'. In order for her to know she did not get the lowest score, she must have seen a lower score, which could only be Hannah's for she did not see Bridget's. So, Hannah's score is lower than Cassie's.

Step 2: Consider the statement made by Bridget, 'I didn't get the highest score.' For Bridget to know she did not get the highest score, she must have seen a higher score, again this could only be Hannah's as she did not see Cassie's. This indicates that Hannah's score is higher than Bridget's.

Step 3: Based on these deductions, we can conclude that Hannah’s score is lower than Cassie’s and higher than Bridget's. This corresponds to ranking option \(\textbf{(D)}\ \text{Cassie, Hannah, Bridget}\).