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 was the combined average attendance per game at the Jawaharlal Nehru stadium for the months of June and July? I. The total attendance for the month of June was 23100 and the total attendance for the month of July was 25200. II. There were 20 games played in June and 22 games played in July.

### Concept & Logic To find the combined average (or overall mean) across multiple sets of data, you must have the total sum of all values divided by the total number of items across all sets. $$ \text{Combined Average} = \frac{\text{Total Attendance in June} + \text{Total Attendance in July}}{\text{Total Games in June} + \text{Total Games in July}} $$ ### Step-by-Step Solution * **From Statement I:** We are given the total attendance for June ($23100$) and July ($25200$). This gives us the numerator of our combined average formula. However, without the number of games played, we cannot find the average per game. Thus, Statement I alone is not sufficient. * **From Statement II:** We are given the number of games played in June ($20$) and July ($22$). This gives us the denominator. Without the attendance figures, we cannot calculate the average. Thus, Statement II alone is not sufficient. * **Combining Statements I and II:** Now we have both the numerators and denominators. $$ \text{Combined Average} = \frac{23100 + 25200}{20 + 22} = \frac{48300}{42} $$ Since we possess all the necessary components to calculate a definitive numerical value, both statements together are required. ### Exam Strategy & Shortcut Identify the formula required: $\text{Average} = \frac{\text{Sum}}{\text{Count}}$. Notice that the prompt asks for a "combined" average, which means you need the combined Sum and combined Count. Scan Statement I—it only provides the Sums. Scan Statement II—it only provides the Counts. It is instantly apparent that you must marry the two statements to complete the formula. Do not waste time calculating $48300 / 42$; simply confirming you have all the variables is enough. ### Common Pitfall A common error is to assume the number of games per month is a constant or easily derivable (like 1 game per day, so 30 games in June, 31 in July). Never introduce outside assumptions into Data Sufficiency problems. Unless stated, you cannot infer the "Count" variable, making Statement II strictly necessary. ### Final Answer **Therefore, the correct answer is Data in both Statements I and II together are necessary.**