If n is an integer, then n is divisible by how many positive

[alanforde800Maximus]

If n is an integer, then n is divisible by how many positive integers?
(1) n is the product of a prime number and a non-prime positive integer.
(2) n and 20 are each divisible by the same number of positive integers.

Please assist with above problem.

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Hi alanforde800Maximus,

This question can be solved by TESTing VALUES and a bit of arithmetic.

We're told that N is an INTEGER. We're asked how many positive factors N has.

1) N is the product of a prime number and a non-prime positive integer.

IF...
N = (2)(4) = 8
Then it's factors are 1, 2, 4 and 8 and the answer to the question is 4

IF...
N = (2)(6) = 12
Then it's factors are 1, 2, 3, 4, 6 and 12 and the answer to the question is 6
Fact 1 is INSUFFICIENT

2) N and 20 are each divisible by the SAME number of positive integers.

The factors of 20 are 1, 2, 4, 5, 10 and 20, so it has a total of 6 factors. We're told that N has the SAME number of factors, so the answer to the question is 6.
Fact 1 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

[fiza gupta]

1) n is a product of prime and non prime number
let n = 3 * 9 = 27 ( 4 factors)
let n = 2 * 6 = 12 ( 6 factors)
INSUFFICIENT

2) n and 20 same factor
20 have 6 factors
so n will also have 6 factors
SUFFICIENT

SO B

[Brent@GMATPrepNow]

If n is an integer, then n is divisible by how many positive integers?

(1) n is the product of a prime number and a non-prime positive integer.
(2) n and 20 are each divisible by the same number of positive integers.

Target question: n is divisible by how many positive integers?

Statement 1: n is the product of a prime number and a non-prime positive integer.
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several scenarios that satisfy statement 1. Here are two:
Case a: n = (3)(1) = 3 [3 is a prime number and 1 is NOT a prime number]. In this case n is divisible by 2 positive integers (1 and 3)
Case b: n = (3)(4) = 12. In this case n is divisible by 6 positive integers (1, 2, 3, 4, 6 and 12)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: n and 20 are each divisible by the same number of positive integers.
20 is divisible by 6 positive integers (1, 2, 4, 5, 10 and 20), so n must be divisible by 6 positive integers
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

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- Introduction to Divisibility: https://www.gmatprepnow.com/module/gmat ... /video/820
- Prime Numbers: https://www.gmatprepnow.com/module/gmat ... /video/824