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.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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