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But I want to clarify one point which was not clarified by the discussion run on the link referred above ( at least it is not clear to me)

The problem is:

How many divisors does positive integer N have? 1) The difference between the largest and the smallest divisor of N is 21 2) N+1 has 2 divisors

Here is a point which is not clear to me: whether negative integers can, from the official GMAT tests' point, be considered divisors of a positive integer? Regarding of the problem given here, whether -20 can be taken as a divisor of N? If "yes", then the condition (1) must also not be sufficient. Insofar as I know the problem does not specify that a divisor of N must be a positive integer. Taking this into account one may on the basis of the problem assume that except zero any integer, regardless -ve or +ve one, can be a divisor of N provided the result must be a whole number.

Thanks for your help and + 1 kudos for any clarification.

But I want to clarify one point which was not clarified by the discussion run on the link referred above ( at least it is not clear to me)

The problem is:

How many divisors does positive integer N have? 1) The difference between the largest and the smallest divisor of N is 21 2) N+1 has 2 divisors

Here is a point which is not clear to me: whether negative integers can, from the official GMAT tests' point, be considered divisors of a positive integer? Regarding of the problem given here, whether -20 can be taken as a divisor of N? If "yes", then the condition (1) must also not be sufficient. Insofar as I know the problem does not specify that a divisor of N must be a positive integer. Taking this into account one may on the basis of the problem assume that except zero any integer, regardless -ve or +ve one, can be a divisor of N provided the result must be a whole number.

Thanks for your help and + 1 kudos for any clarification.

ALL GMAT divisibility questions are limited to positive integers only. For example, every GMAT divisibility question will tell you in advance that any unknowns represent positive integers.
_________________

But I want to clarify one point which was not clarified by the discussion run on the link referred above ( at least it is not clear to me)

The problem is:

How many divisors does positive integer N have? 1) The difference between the largest and the smallest divisor of N is 21 2) N+1 has 2 divisors

Here is a point which is not clear to me: whether negative integers can, from the official GMAT tests' point, be considered divisors of a positive integer? Regarding of the problem given here, whether -20 can be taken as a divisor of N? If "yes", then the condition (1) must also not be sufficient. Insofar as I know the problem does not specify that a divisor of N must be a positive integer. Taking this into account one may on the basis of the problem assume that except zero any integer, regardless -ve or +ve one, can be a divisor of N provided the result must be a whole number.

Thanks for your help and + 1 kudos for any clarification.

ALL GMAT divisibility questions are limited to positive integers only. For example, every GMAT divisibility question will tell you in advance that any unknowns represent positive integers.

Many thanks to you, Bunuel. I highly appreciate your help.