What marks did Abhijit score in English? I. Marks in Mathematics exceed marks in Science by 20. II. Total marks in Mathematics, Science, English = 197. III. Marks in Science exceed marks in English by 12.
Verbal Reasoning
Data Sufficiency
Difficulty: Medium
Choose an option
Answer
Correct Answer: I, II and III
Explanation
Introduction / Context:We must uniquely determine the English score using linear relations among three subjects.
Step-by-Step Solution:
- Let E = English, S = Science, M = Math.
- I: M = S + 20.
- II: M + S + E = 197.
- III: S = E + 12.
Substitute III into I ⇒ M = (E + 12) + 20 = E + 32.Use II: (E + 32) + (E + 12) + E = 197 ⇒ 3E + 44 = 197 ⇒ E = 51.
Sufficiency Check:Any two statements leave one degree of freedom; all three are needed for a unique E.
Final Answer:I, II and III.