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. What is the average weight of the three new members who are recently included into the team? I. The average weight of the team increases by 20 kg. II. The three new men substitute earlier members whose weights are 64 kg, 75 kg and 66 kg.

### Concept & Strategy In replacement problems involving averages, the change in the total sum depends heavily on the initial size of the group. $$New \ Sum = Old \ Sum - Sum \ of \ Leaving + Sum \ of \ Joining$$ An increase in the overall average by a specific amount means the total weight increased by $N \times Increase$, where $N$ is the total number of members. ### Step-by-Step Solution Let the original number of team members be $n$. Let the original average be $A$. Total original weight = $nA$. **Evaluating Statement I:** * The new average becomes $A + 20$. * This tells us the total weight increased, but without knowing how many people are in the team ($n$) or who left/joined, we cannot find the weight of the new members. * Statement I alone is not sufficient. **Evaluating Statement II:** * The three leaving members have a total weight of $64 + 75 + 66 = 205$ kg. * We do not know how this affects the overall average or the total sum, as we have no information about the new members. * Statement II alone is not sufficient. **Evaluating Statements I and II Together:** * From Statement I, the total weight increase of the entire team is $n \times 20$ kg. * The difference between the incoming group and the outgoing group causes this total increase. $$Sum \ of \ New - Sum \ of \ Old = Total \ Increase$$ $$Sum \ of \ New - 205 = 20n$$ $$Sum \ of \ New = 205 + 20n$$ * We need to find the average of the 3 new members: $$New \ Average = \frac{Sum \ of \ New}{3} = \frac{205 + 20n}{3}$$ * The formula still contains the unknown variable $n$ (the total number of team members). Because $n$ is never provided in either statement or the question prompt, we cannot calculate a unique numerical answer. ### Exam Strategy & Shortcut Look for missing foundational variables. Whenever a question involves a shift in an average across a group, you must know the size of the group ($n$). Scan the prompt and both statements—if $n$ is nowhere to be found, you can confidently immediately mark "not sufficient" even when combining everything. ### Common Pitfall A classic mistake is assuming the team size $n$ is simply the 3 people mentioned. The text says "three new members who are recently included into the team," implying a larger pre-existing team. Never assume a variable's value if it is not explicitly stated. ### Final Answer **Therefore, the correct answer is If the data even in both Statements I and II together are not sufficient to answer the question.**