1. Four school friends, Zara, Bryan, Charlie, and Diana, are competing to see who will earn the most credits in Science and Math. Who earned the most total credits in Science and Math? (1) Zara earned 15% more credits in Science than Bryan, and 10% fewer credits in Math than Charlie, while Diana earned 20% more total credits in Science and Math than Zara. (2) Bryan's total credits in Science and Math are fewer than Charlie's, and Diana's credits in Science are higher than both Bryan's and Charlie's combined total credits in Science and Math.
Answer: C
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
To determine who earned the most total credits in Science and Math, both statements must be considered together, as neither statement alone provides enough information to reach a conclusion.
A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (1) provides information about the relationships between Zara, Bryan, Charlie, and Diana's credits, but it does not give the precise credit amounts necessary to determine who earned the most. Therefore, statement (1) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Statement (2 indicates that Bryan has fewer total credits than Charlie and that Diana's Science credits exceed both Bryan's and Charlie's combined credits. However, it does not specify the actual credit amounts for any of the friends, making it insufficient on its own to determine the highest total credits.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
When combined, statements (1) and (2) provide a complete picture of the relationships among the friends' credits. Statement (1) establishes how Zara compares to Bryan and Charlie, while statement (2) provides context on Diana's credits relative to the others. Together, they allow us to conclude that Diana earned the most total credits.
D) EACH statement ALONE is sufficient.
This option is incorrect because neither statement provides enough standalone information to determine the total credits earned by each friend. Both statements are necessary to derive a conclusion.
Conclusion
The correct answer is C because it reflects that both statements are required to ascertain who earned the most credits. Statement (1) outlines the relationships among the friends' credits, while statement (2) clarifies Diana's position, allowing us to ultimately identify her as the one with the highest total credits.