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 (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. What is the average of the best and worst score out of 8 tests taken by a student? I. The average of all 8 tests is 84%. II. After dropping the best and worst grade, the average of remaining 6 tests is 86%.

### Concept & Logic The sum of a specific subset of items (the best and worst scores) can be found by subtracting the sum of the remaining items from the total sum of all items. $$ \text{Sum of (Best + Worst)} = \text{Total Sum (8 tests)} - \text{Sum of Remaining (6 tests)} $$ ### Step-by-Step Solution * **From Statement I:** We are given the average of all 8 tests is 84%. Total sum of 8 tests = $8 \times 84 = 672$. We know the grand total, but we do not know any individual scores to isolate the best and worst. Thus, Statement I alone is not sufficient. * **From Statement II:** We are given the average of the middle 6 tests is 86%. Total sum of 6 tests = $6 \times 86 = 516$. We know the subset total, but we don't know the grand total to figure out what is missing. Thus, Statement II alone is not sufficient. * **Combining Statements I and II:** We now have the sum of all 8 tests (672) and the sum of the middle 6 tests (516). The difference between these two sums must equal the sum of the two dropped tests (the best and the worst). Sum of (Best + Worst) = $672 - 516 = 156$. The question specifically asks for the average of these two dropped scores. Average = $\frac{156}{2} = 78\%$. Since we can find a unique numerical answer by relying on both pieces of information, both statements together are required. ### Exam Strategy & Shortcut Visualize the underlying equation conceptually: $(\text{Total Sum}) = (\text{Sum of Middle 6}) + (\text{Best} + \text{Worst})$. You need to find the average of (Best + Worst), which means you inherently need to find their sum. Statement I gives you the Total Sum piece. Statement II gives you the Sum of Middle 6 piece. It is instantly obvious you need both pieces to isolate the final unknown subset. You do not even need to execute the multiplication to confidently mark the answer. ### Common Pitfall Students sometimes overthink this problem and incorrectly believe they need to determine the precise individual values of the "best" score and the "worst" score to calculate their average. You do not need individual values to find an average, only their combined sum and the count of items (which is statically 2). ### Final Answer **Therefore, the correct answer is Data in both Statements I and II together are necessary.**