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.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
To determine who earned the most total credits in Science and Math among Zara, Bryan, Charlie, and Diana, we must analyze the information provided in both statements. While each statement has valuable information, neither one alone gives a complete picture; combined, they provide the necessary context to assess the total credits for each individual.
Statement (1) provides comparisons between Zara, Bryan, Charlie, and Diana, but it lacks specific numerical values to definitively determine who has the most credits. Therefore, while it contains useful information, it does not provide a complete answer on its own.
Statement (2) suggests that Diana has higher credits in Science than both Bryan's and Charlie's combined totals, but it doesn't specify how many credits each individual has. As such, this statement alone does not allow us to conclusively determine who has the most credits.
When combined, the information from both statements enables us to compare the credits of all four friends. Statement (1) establishes relative differences, while statement (2) provides crucial insights into Diana's performance relative to others, allowing for a complete assessment.
Neither statement provides enough information independently to ascertain who has the most credits. Each lacks critical data that the other supplies.
To conclude, both statements must be utilized together to evaluate the performance of Zara, Bryan, Charlie, and Diana effectively. Each statement offers distinct insights that, while incomplete in isolation, collectively enable us to ascertain who earned the most total credits in Science and Math. Hence, the answer lies in the combined analysis of both statements.
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