GRE Prep 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.
In N is a positive integer less than 200, and 14N/60 is an i
[#permalink]
10 Aug 2020, 11:52
10 Aug 2020, 11:52
Expert Reply
00:00
Question Stats:
65% (01:23) correct
35% (01:43) wrong based on 20 sessions
Hide Show timer Statistics
In N is a positive integer less than 200, and \(\frac{14N}{60}\) is an integer, then N has how many different positive prime factors?
A. 2
B. 3
C. 5
D. 6
E. 8
A. 2
B. 3
C. 5
D. 6
E. 8
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In N is a positive integer less than 200, and 14N/60 is an i
[#permalink]
10 Aug 2020, 11:58
10 Aug 2020, 11:58
2
Carcass wrote:
In N is a positive integer less than 200, and \(\frac{14N}{60}\) is an integer, then N has how many different positive prime factors?
A. 2
B. 3
C. 5
D. 6
E. 8
A. 2
B. 3
C. 5
D. 6
E. 8
Let's choose a nice value of N that satisfies the given information.
GIVEN: 14N/60 is an integer
Prime factorize the numerator and denominator to get: (7)(2)(N)/(2)(2)(3)(5) is an integer
Simplify: (7)(N)/(2)(3)(5) is an integer
Notice that, when N = 30 (aka the product of 2, 3, and 5), then (7)(N)/(2)(3)(5) = (7)(2)(3)(5)/(2)(3)(5) = 7, which IS an integer
So, N = 30 satisfies the given information.
N has how many different positive prime factors?
30 = (2)(3)(5)
So, N has 3 different positive prime factors (2, 3 and 5)
Answer: B
Re: In N is a positive integer less than 200, and 14N/60 is an i
[#permalink]
12 Aug 2020, 08:30
12 Aug 2020, 08:30
1
14N/60 = 7N/30
For 7N/30 to be an integer then N must be a multiple of 30.
Prime factorization of 30 is 3*2*5
Therefore so far N has at least 3 prime factors
Since N is a multiple of 30 we can let N=m*30
The question now is: are there any other prime factors coming from m besides 2,3,5?
Since N<200 and a positive integer
then 0<m*30<200
0<m<200/30
0<m<6.6666...
so m can be 1,2,3,4,5,6
and in prime factor form
m can be 1,2,3,2^2,5,2*3
Notice that all of the prime factors in the list are already factors of 30
So the only prime factors of N=m*30 are the same ones as those from 30,
namely: 2,3,5
Final Answer: B
For 7N/30 to be an integer then N must be a multiple of 30.
Prime factorization of 30 is 3*2*5
Therefore so far N has at least 3 prime factors
Since N is a multiple of 30 we can let N=m*30
The question now is: are there any other prime factors coming from m besides 2,3,5?
Since N<200 and a positive integer
then 0<m*30<200
0<m<200/30
0<m<6.6666...
so m can be 1,2,3,4,5,6
and in prime factor form
m can be 1,2,3,2^2,5,2*3
Notice that all of the prime factors in the list are already factors of 30
So the only prime factors of N=m*30 are the same ones as those from 30,
namely: 2,3,5
Final Answer: B
