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Question

# If m and n are both positive integers, then how less is n than m? I. m + n =20 II. m = n2

A

If 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

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B

If 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

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C

If the data either in statement I alone or in statement II alone are sufficient to answer the question

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D

If the data in both statements I and II together are necessary to answer the question.

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Solution

## The correct option is C If the data either in statement I alone or in statement II alone are sufficient to answer the question From Statement I, m + n = 20 From Statement II, m = n2 On putting m = n2 in Statement I, we get n2 + n = 20 ⟹ n2 + n - 20 = 0 ⟹ n2 + 5n - 4n - 20 = 0 ⟹ n(n + 5) - 4 (n + 5) = 0 ⟹ (n - 4) (n + 5) = 0 ∴n = 4, - 5 (since, m and n are the positive integers, so we cannot take n = - 5 ) Taking n = 4 and putting in Statement I, m+ 4 = 20 ∴m = 20 - 4 = 16 Now, m - n = 16 - 4 = 12 Hence, m is greater than n by 12. So, both statements are required to answer the question.

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