BTGModeratorVI wrote: ↑

Sat Apr 18, 2020 9:25 am

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 number
(2) n and 20 are each divisible by the same number of positive integers

Answer: B
Source: Veritas Prep

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

Cheers,
Brent