Given below is a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Two natural numbers, P and Q, are taken. What will be their HCF I. Their LCM is a three digit number. II. P and Q are consecutive.?

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  1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
  2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
  3. The data in statement I alone or in statement II alone is sufficient to answer the question.
  4. The data in both the statements I and II is not sufficient to answer the question.

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Option 2 : The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

From statement I:

Their LCM is a three digit number. Knowing that LCM has three digits, HCF cannot be found.

If numbers are 16 and 9, LCM is 144, and HCF is 1.

If numbers are 120 and 60, LCM is 120, and HCF is 60.

∴ Statement I alone is not sufficient to answer the question.

From statement II:

P and Q are consecutive. We know that consecutive numbers are always relatively prime. Hence, their HCF will be 1.

∴ Statement II alone is sufficient to answer the question.

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