The following question has three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. Ram appeared in 5 exams. Each exam was of 100 marks. To pass the exams, he should obtain at least 40% marks subject wise and 50% in aggregate. Determine, whether he is pass or fail? I) He secured 255 marks in aggregate II) His aggregate marks in first two exams is 78 III) His marks in last two exams is 2.5 ∶ 1 Correct Answer Any two of them Considering Statement I, He secured 255 marks in aggregate which is more than 50% of 500 This statement clears that Ram is pass But the case may be different. It is also possible that he is not able to get 40% in any one or more subject. Hence, this statement is not sufficient alone Considering Statement II, His aggregate marks in the first two exams are 78. It means that Ram has scored less than 40% marks in any one subject It clears that Ram is fail But there is no such option provided Considering statement III, His marks in last 2 exams are in the ratio of 2.5 ∶ 1 It means that if Ram has scored 100 in 4th exam then he has scored 10/25 of 100 in 5th exam i.e. equal to 40 It states that Ram is pass but the case can be different Hence, this statement is not sufficient alone Considering I and II together, From I, Ram is pass From II, Ram is fail Hence, he is fail Considering II and III together, From II, Ram is fail From III, Ram can pass Hence, he is fail Considering I and III together, From I, Ram scored 255 in aggregate, he is pass From III, Ram can pass only if he has scored 100 in 4th subject ⇒ 255 - 100 = 155 It means that Ram scored in remaining 4 exams 155 in aggregate. If we calculate average, we get ⇒ 155/4 = 38.75 which is less than 40% Hence, Ram is fail ∴ Any two of the given statements are required to answer the question.