Direction: Each of the questions below consists of a question-statement and two statements I and II are given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Give answer. Whose body weight is second highest among the five boys Arun, Vinay, Suraj, Raju and Pratap? I. Average weight of Arun, Suraj and Vinay is $68$ kg and average weight of Raju and Pratap is $72$ kg. Also Suraj is $78$ kg, Raju is $68$ kg and Vinay is $46$ kg. II. Average weight of Arun, Suraj, Vinay and Raju is $68$ kg and also Suraj is $78$ kg, Raju is $68$ kg and Vinay is $46$ kg all of them have different weights.

### Concept & Logic To determine whose body weight is the second highest among five people, we must either find the exact weights of all five boys or establish a strict relative order among them. We use the formula for the sum of elements given their average: $$Sum = Average \times Number of Elements$$ ### Step-by-Step Solution **Evaluating Statement I alone:** * Given: Average weight of Arun (A), Suraj (S), and Vinay (V) = $68$ kg. * Sum of A, S, V = $3 \times 68 = 204$ kg. * Given individual weights: S = $78$, R = $68$, V = $46$. * Substitute S and V to find A: A + $78$ + $46$ = $204$ kg $\rightarrow$ A + $124$ = $204$ kg $\rightarrow$ A = $80$ kg. * Given: Average weight of Raju (R) and Pratap (P) = $72$ kg. * Sum of R, P = $2 \times 72 = 144$ kg. * Substitute R to find P: $68$ + P = $144$ kg $\rightarrow$ P = $76$ kg. * Now we have all five weights: A = $80$, S = $78$, P = $76$, R = $68$, V = $46$. * Arranging in descending order: A, S, P, R, V. The second highest is Suraj (S). Statement I is sufficient. **Evaluating Statement II alone:** * Given: Average weight of A, S, V, R = $68$ kg. * Sum of A, S, V, R = $4 \times 68 = 272$ kg. * Given weights: S = $78$, R = $68$, V = $46$. * Find A: A + $78$ + $68$ + $46$ = $272$ kg $\rightarrow$ A + $192$ = $272$ kg $\rightarrow$ A = $80$ kg. * We know four weights: A = $80$, S = $78$, R = $68$, V = $46$. * However, Statement II provides absolutely no information about Pratap (P). Without P's weight, we cannot guarantee who holds the second highest position. Statement II is not sufficient. ### Exam Strategy & Shortcut For data sufficiency questions involving averages, quickly check if the variables match up. In Statement I, you are given the average of 3 boys and the exact weights of 2 of them. This immediately tells you that you can find the 3rd. You are then given the average of the remaining 2 boys and the weight of 1 of them. This means you can find the final boy's weight. Since all 5 weights can be determined, Statement I is definitely sufficient. Statement II lacks Pratap entirely, so it is instantly insufficient. You do not even need to calculate the final values to mark the answer! ### Common Pitfall A major mistake is performing all the arithmetic calculations during a data sufficiency problem. While we solved it above for clarity, calculating $80$ and $76$ consumes precious time. Recognize that having $n$ independent variables and $n$ independent linear equations guarantees a solution. ### Final Answer **Therefore, the correct answer is The data in statement I alone was sufficient to answer the question while II alone are not sufficient to answer the question.**