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. How many children are there in the group? I. Average age of the children in this group is 15 years. The total age of all the children in this group is 240 years. II. The total age of all the children in the group and the teacher is 264 years. The age of the teacher is 9 years more than the average age of the children.

### Concept & Logic The number of items in a group can be directly calculated if both the sum of the items and the average of the items are known. $$ \text{Number of Items} = \frac{\text{Sum of Items}}{\text{Average of Items}} $$ ### Step-by-Step Solution * **From Statement I:** We are explicitly given the average age ($15$ years) and the total age ($240$ years). $$ \text{Number of children} = \frac{240}{15} = 16 $$ Since we can find the exact number of children, Statement I alone is sufficient. * **From Statement II:** Let the number of children be $n$ and their average age be $A$. Total age of children is $nA$. We are told: $nA + \text{Teacher's Age} = 264$. We are also told: $\text{Teacher's Age} = A + 9$. Substituting this gives: $nA + A + 9 = 264 \implies A(n + 1) = 255$. We have one equation with two unknown variables ($A$ and $n$). We cannot uniquely solve for $n$. Statement II alone is not sufficient. ### Exam Strategy & Shortcut In Data Sufficiency, once you see that Statement I gives a simple solvable formula ($N = \frac{\text{Total}}{\text{Average}}$), evaluate Statement II strictly independently. Don't accidentally carry the $A = 15$ from Statement I into Statement II. Since Statement II introduces an equation with two unknowns ($A$ and $n$), it clearly isn't sufficient on its own. ### Common Pitfall The most common trap is the "carry-over" mistake. A student might read Statement II, mentally plug in the average age of 15 from Statement I, find the teacher's age ($15 + 9 = 24$), subtract it from 264 to get 240, and think Statement II is also sufficient. You must treat the statements as completely isolated universes until you are forced to combine them. ### Final Answer **Therefore, the correct answer is Data in Statement I alone are sufficient.**