Let n(1) be a composite integer such that n is not an integer. Consider the following statements: A: n has a perfect integer - valued divisor which is greater than 1 and less than n . B: n has a perfect integer- valued divisor which is greater than n but less than n. Then,

Question

Let n(>1) be a composite integer such that $\sqrt{n}$ is not an integer.

Consider the following statements:

A: n has a perfect integer - valued divisor which is greater than 1 and less than $\sqrt{n}$ .

B: n has a perfect integer- valued divisor which is greater than $\sqrt{n}$ but less than n.

Then,

Accepted Answer

Both A and B are true — Consider a number n = 10, then n &#8776; 36 . A: We have a divisor 2 which is greater than 1 and less than 3.16. B: We have a divisor 5 which is greater than 3.16 but less than 10. &there4; Both statements A and B are true. Also, as a rule, any composite number which is not a perfect square has at least one factor less than n and another factor more than n, such that their product is n. &there4; Both statements are true. Hence, option (d).

CAT 2003 Slot 2 — QA Question 11

Answer & solution