Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read both the statements and give answer. During a five day period, Monday through Friday, the average high temperature was 86 degrees Fahrenheit. What was the high temperature on Friday? I. The average high temperature for Monday through Thursday was 87 degrees Fahrenheit. II. The high temperature on Friday reduced the average high temperature by 1 degree Fahrenheit.

### Concept & Formula When an additional item changes an average, you can find the value of that specific item using the total sums. $$Value \ of \ New \ Item = (New \ Total \ Sum) - (Old \ Total \ Sum)$$ ### Step-by-Step Solution **Given:** * 5-day Average (Mon-Fri) = 86°F. * Total sum for 5 days = $86 \times 5 = 430°F$. **Evaluating Statement I:** * 4-day Average (Mon-Thu) = 87°F. * Total sum for 4 days = $87 \times 4 = 348°F$. * Friday's temperature = (Sum of 5 days) - (Sum of 4 days) * Friday = $430 - 348 = 82°F$. * We have a unique answer. Statement I alone is sufficient. **Evaluating Statement II:** * It states Friday *reduced* the overall average by 1 degree. * Since the final 5-day average is 86°F (given in the prompt), this implies the average *before* Friday (i.e., Mon-Thu) must have been $86 + 1 = 87°F$. * This means the 4-day average for Mon-Thu was 87°F. * This is exactly the same information provided in Statement I! * Since it mathematically translates to the exact same premise as Statement I, it allows us to do the exact same calculation ($430 - 348 = 82$). * We have a unique answer. Statement II alone is sufficient. ### Exam Strategy & Shortcut Read carefully for rephrased statements. Statement II is just Statement I dressed in different vocabulary. "The first four days averaged 87" is mathematically identical to saying "Adding the fifth day to reach 86 dropped the average by 1." If you determine Statement I is sufficient, and Statement II is logically identical, immediately select "Either Statement alone is sufficient." ### Common Pitfall Students often misinterpret Statement II as meaning "Friday's temperature was $86 - 1 = 85$." This is incorrect. The statement says Friday reduced the *average* by 1 degree, not that Friday's temperature was 1 degree less than the average. Always distinguish between a data point and the average itself. ### Final Answer **Therefore, the correct answer is If the data either in Statement I or in Statement II alone are sufficient to answer the question.**