The product of two negative integers, a and b, is a prime number p GMAT Problem-Solving

This is a GMAT Problem solving question. Here, the data given in the questions has to be analyzed to answer the question. Several areas of mathematics can be involved in the process. The way options are given is very close to the correct answer, and normal guessing can lead to mistakes. Students need to understand the question properly and use proper methods to approach the answer.
Begin with n: We are informed that n NOT an exact square.

All other positive integers have an even number of factors, however the perfect square has an odd number of factors. Thus, since p is the quantity of n's factors.
then p has to be even. We also understand that p is a prime, and as 2 is the only even prime,
p=2.

Keep in mind that this implies that n must be prime.
Because only primes contain two factors—1 and itself—it must also be a prime.
Secondly, ab = p = 2
suggests that a = -1 and b = −2 or the opposite.
The median is (-1 + 2)/2 = 1/2 since the set is (-2, -1, 2, some prime).
B is the correct answer.

This is a GMAT Problem solving question. Here, the data given in the questions has to be analyzed to answer the question. Several areas of mathematics can be involved in the process. The way options are given is very close to correct answer, and normal guessing can lead to mistakes. Students need to understand the question properly and use proper methods to approach the answer.
given: 1. prime number equals a*b
           2. The numbers a and b are -ve

Therefore, let's claim that one of them is -1.

Given that p is the number of factors of n, where n is not a perfect square, the probable ascending sequence is: {b, a, p, n}. Since only the perfect square has an odd number of elements, p cannot be odd.

Since p is even, the median of b, a, p, and n is equal to (even - 1)/2 =odd / 2.

Only choices B and D remain.
Since D is invalid if the median were 3/2 and p = 4, which is not a prime,
B is the correct answer.

This is a GMAT Problem solving question. Here, the data given in the questions has to be analyzed to answer the question. Several areas of mathematics can be involved in the process. The way options are given is very close to correct answer, and normal guessing can lead to mistakes. Students need to understand the question properly and
Use proper methods to approach the answer.

Prime number a*b.

Since there are only two prime numbers, P and 1, each of their components must include a component that leads to P.
One prime number (the same number) and one are required for the product to be prime. both negative in this instance.
Therefore, a = -1 and B = -P (or the opposite).

The number of factors must be even because N is not a perfect square at this time. Only when p is 2 can it be both even and prime.

A = -1, B = -2, and p = so.

I kind of got stuck here and couldn't figure out n. But we are fairly certain that it is -2 or 2.

If it is 2, the set is -2, -1, 2, 2, and so on. Half is the median. If it is -2, then the set is -2, -2, -1,2 and the median is -3/2. not a viable choice.
The appropriate answer is B.