Directions: Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. How many marks did Tarun secure in English? I. The average marks obtained by Tarun in four subjects including English is 60. II. The total marks obtained by him in English and Mathematics together is 170. III. The total marks obtained by him in Mathematics and Science together is 180.

## Concept & Logic To find a specific variable in a system of linear equations, you must have enough distinct equations that cover all the unknown variables. The number of distinct equations must equal or exceed the number of variables to find a unique solution. $$ \text{Total Marks} = \text{Average Marks} \times \text{Number of Subjects} $$ ## Step-by-Step Solution * **Evaluate Statement I:** Let the four subjects be English ($E$), Mathematics ($M$), Science ($S$), and a fourth unknown subject ($X$). Total marks in $4$ subjects = $4 \times 60 = 240$. Equation 1: $E + M + S + X = 240$ * **Evaluate Statement II:** Equation 2: $E + M = 170$ * **Evaluate Statement III:** Equation 3: $M + S = 180$ * **Attempting to Combine:** From Equation 2, we know $M = 170 - E$. Substitute this into Equation 3: $(170 - E) + S = 180 \implies S = 10 + E$. Now, substitute $M$ and $S$ into Equation 1: $E + (170 - E) + (10 + E) + X = 240$ $180 + E + X = 240$ $E + X = 60$ Because we have no information about the marks in the fourth subject ($X$), we cannot isolate and determine the value of $E$. Therefore, even combining all three statements, the data is insufficient. ## Exam Strategy & Shortcut Count the variables and equations. We have $4$ variables ($E, M, S, X$) but only $3$ equations. Without a fourth piece of information (specifically about the fourth subject), it is mathematically impossible to solve for all individual variables. You can confidently mark it as insufficient without doing the algebraic substitutions. ## Common Pitfall A common mistake is assuming the "four subjects" must strictly be limited to English, Math, and Science, mistakenly creating a 3-variable system when 4 actually exist. Always account for undefined variables mentioned in the text. ## Final Answer **Therefore, the correct answer is None of these.**