Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
02 Mar 2022, 08:30
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
48% (01:40) correct
52%
(01:45)
wrong
based on 227
sessions
History
Date
Time
Result
Not Attempted Yet
If n is a positive integer, does n have four or more distinct factors?
(1) n is not prime
(2) 900 ≤ n < 1100
Are You Up For the Challenge: 700 Level Questions
(1) n is not prime
(2) 900 ≤ n < 1100
Are You Up For the Challenge: 700 Level Questions
02 Mar 2022, 11:14
Kudos
Bookmarks
Bunuel
Given: n is a positive integer
Target question: Does n have four or more distinct factors?
Key property: If p is a prime number, then p² will have exactly 3 distinct factors: 1, p and p²
For example, 5 is prime. 5² = 25, and 25 has exactly three distinct factors: 1, 5 and 25
NOTE: In general, if p is prime, and n is a positive integer, then p^n will have exactly n+1 distinct factors.
Given this, we can head straight to....
Statements 1 and 2 combined
Statement 1 tells us that n is not prime
Statement 2 tells us that 900 ≤ n < 1100
There are several values of n that satisfy BOTH statements. Here are two:
Case a: If n = 1000 then the answer to the target question is YES, n has four or more distinct factors
Case b: If n = 31² (note that 31 is prime AND 900 ≤ 31² < 1100) then n has exactly 3 distinct factors (1, 31 and 31²). So, the answer to the target question is NO, n does not have four or more distinct factors
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
General Discussion
PyjamaScientist
Admitted - Which School Forum Moderator
Joined: 25 Oct 2020
Last visit: 04 Apr 2026
Posts: 1,125
Own Kudos:
Given Kudos: 633
Schools: Ross '25 (M$)
GMAT 1: 740 Q49 V42 (Online)
Products:
02 Mar 2022, 08:37
Kudos
Bookmarks
(C) in my opinion.
Statement (1): n can be 4 (3 factors: 1,2,4) or n can be 10 (4 factors: 1,2,5,10).
Insufficient alone.
Statement (2): n can be any prime no. between 900 to 1100 and have only two factors, 1 and itself. Or it can be a non-prime and have more than 4 or 4 factors.
Insufficient alone.
Both together, if n is prime and between 900 - 1100, it will only have two factors, 1 and itself. Thus it is sufficient to answer the question. (C)
Statement (1): n can be 4 (3 factors: 1,2,4) or n can be 10 (4 factors: 1,2,5,10).
Insufficient alone.
Statement (2): n can be any prime no. between 900 to 1100 and have only two factors, 1 and itself. Or it can be a non-prime and have more than 4 or 4 factors.
Insufficient alone.
Both together, if n is prime and between 900 - 1100, it will only have two factors, 1 and itself. Thus it is sufficient to answer the question. (C)
