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 will be the average weight of the remaining class? I. Average weight of 30 children out of total 46 in the class is 22.5 kg and that of the remaining children is 29.125 kg. A child having weight more than 40 kg is excluded. II. Average weight of a class of 46 children is 23.5 kg. A child weighing 46 kg is dropped out.

## Concept & Logic To find the average weight of the remaining class, you need exactly three pieces of information: the total initial weight of the class, the exact weight of the excluded child, and the new number of children in the class. $$ \text{New Average} = \frac{\text{Initial Total Weight} - \text{Weight of Excluded Child}}{\text{Total Children} - 1} $$ ## Step-by-Step Solution * **Evaluating Statement I:** * Total children = $46$. * Total weight can be found using the two groups given: $30 \times 22.5 + 16 \times 29.125 = 1141$ kg. * However, the statement says, "A child having weight *more than* $40$ kg is excluded." * Because the exact weight of the excluded child is unknown (it could be $41$ kg, $45$ kg, etc.), we cannot determine the exact new total weight. * Therefore, Statement I alone is **not sufficient**. * **Evaluating Statement II:** * Initial total weight = $46 \times 23.5 = 1081$ kg. * Weight of dropped child = $46$ kg. * Remaining total weight = $1081 - 46 = 1035$ kg. * Remaining children = $46 - 1 = 45$. * New average = $1035 / 45 = 23$ kg. * Therefore, Statement II alone provides exactly what is needed and is **sufficient**. ## Exam Strategy & Shortcut In Data Sufficiency, do not waste time calculating the exact final answer unless required. Scan the statements for "exactness". Statement I gives a range ("more than $40$ kg"), which immediately flags it as insufficient for an exact average calculation. Statement II provides concrete numbers for all required variables, making it sufficient at a glance. ## Common Pitfall A major pitfall is spending precious exam time calculating the total weight in Statement I ($675 + 466 = 1141$), only to realize at the very end that the subtracted weight is an inequality. Always read the complete statement before doing arithmetic. ## Final Answer **Therefore, the correct answer is 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.**