Question

If m and n are both positive integers, then how less is n than m?

I. m + n =20

II. m = n${}^2$

• 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
• 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
• C. If the data either in statement I alone or in statement II alone are sufficient to answer the question
• D. If the data in both statements I and II together are necessary to answer the question.

Answer 1

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 = n${}^2$

On putting m = n${}^2$ in Statement I, we get n${}^2$ + n = 20

$⟹$ n${}^2$ + n - 20 = 0

$⟹$ n${}^2$ + 5n - 4n - 20 = 0

$⟹$ n(n + 5) - 4 (n + 5) = 0

$⟹$ (n - 4) (n + 5) = 0

$\therefore$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

$\therefore$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.