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      Question

      The question consists of two

      statements numbered "I and II" given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. A rope of length 48 metres is cut into three unequal pieces. Find the length of the middle-sized piece. Statement I: The sum of the two shorter pieces is 28 metres. Statement II: The sum of the two longer pieces is 37 metres.
      A The data in statement I alone are sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      B The data in statement II alone are sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      C The data either in statement I alone or in statement II alone is sufficient to answer the question. Correct Answer Incorrect Answer
      D The data given in both statements I and II together is not sufficient to answer the question. Correct Answer Incorrect Answer
      E The data in both statements I and II together is necessary to answer the question. Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the pieces be a, b, c with a > b > c. Need b. Total: a + b + c = 48 … (1) Statement I: b + c = 28 … (2) From (1): a = 48 − 28 = 20. b unknown. → I alone: Not sufficient. Statement II: a + b = 37 … (3) From (1): c = 48 − 37 = 11. b unknown. → II alone: Not sufficient. Together: (2) b + c = 28, (3) a + b = 37. Add: a + 2b + c = 65. Subtract (1): (a + 2b + c) − (a + b + c) = 65 − 48 ⇒ b = 17. Together sufficient.  Answer: b = 17 metres. So, data in statement I and II together is sufficient to answer the question

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