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.
Suggest answer please
Help with This Question
This topic has expert replies
- MartyMurray
- Legendary Member
- Posts: 2131
- Joined: Mon Feb 03, 2014 9:26 am
- Location: https://martymurraycoaching.com/
- Thanked: 955 times
- Followed by:140 members
- GMAT Score:800
Statement 1: n is the product of a prime number and a non-prime positive integer.
Look at two extreme cases.
n = 3 The factors of n are 3, prime, and 1, non prime. Answer: 2
n = 3000 Two of the factors of n are 3, prime, and 1000, non prime. n has many factors. Answer: Way more than 2.
Two different answers.
Insufficient.
Statement 2: n and 20 are each divisible by the same number of positive integers.
Since you can determine by how many positive integers 20 is divisible, you can determine by how many n is divisible.
Sufficient.
The correct answer is B.
Look at two extreme cases.
n = 3 The factors of n are 3, prime, and 1, non prime. Answer: 2
n = 3000 Two of the factors of n are 3, prime, and 1000, non prime. n has many factors. Answer: Way more than 2.
Two different answers.
Insufficient.
Statement 2: n and 20 are each divisible by the same number of positive integers.
Since you can determine by how many positive integers 20 is divisible, you can determine by how many n is divisible.
Sufficient.
The correct answer is B.
Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
The biggest takeaway here is that you don't even need to bother unpacking S2: since it will give you a unique answer (the number of factors of 20), it's sufficient! (Not a big deal on this problem, since finding the factors of 20 is pretty trivial, but it'd be a big deal if the number were 13,122, or something.)