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      Question

      Is 'x' an even number?

      Statement I: 'x' is not divisible by 8. Statement II: When 1 is added to three times 'x', the result is an odd number. Statement III: The difference between 29 and 'x' is a prime number. Statement IV: 'x' is a composite number. The question consists of four statements numbered “I, II III and IV” given below it. You have to decide whether the data provided in any of the statements alone is suicient to answer the question.
      A Therefore, data in statement Ill and statement IV alone is sufficient to answer the question while data in statement I alone and II alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      B Therefore, data in statement I and statement II alone is sufficient to answer the question while data in statement Ill alone and statement IV alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      C Therefore, data in statement II alone is sufficient to answer the question while data in statement I alone, statement Ill alone and statement IV alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      D The data in none of the statements alone is sufficient to answer the question Correct Answer Incorrect Answer
      E Therefore, data in statement I alone and statement IV alone is sufficient to answer the question while data in statement II alone and statement Ill alone is not sufficient to answer the question. Correct Answer Incorrect Answer

      Solution

      ATQ, Statement I: ‘x’ is not divisible by 8. Therefore, statement I alone is not suicient to answer the question. Statement II: When 1 is added to thrice of ‘x’, the resultant is an even number. When 3 is multiplied to an even number and then 1 is added to it, the resultant will be an odd number Therefore, statement II alone is sufficient to answer the question. Statement III: Given, the difference between 29 and ‘x’ is a prime number Let x be 27,  so 29 – 27 = 2 (prime number) Let x be 26,  so 29 – 27 = 3 (prime number) Therefore, data in statement III alone is not sufficient to answer the question. Statement IV: ‘x’ is a composite number, i.e. it can be even or odd. Therefore, data in statement IV alone is not sufficient to answer the question. Therefore, data in statement II and III alone is sufficient to answer the question while data in statement I and III alone is not sufficient to answer the question.

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