If N is a positive integer and 14N/60 is an integer. What is the smallest value of N for which N has exactly four different prime factors?
A)30
B)60
C)180
D)210
E)cannot be determined
The OA is D.
Why D is the correct answer? Can any expert explain this PS question please?. Thanks.
If N is a positive integer...
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Hello.
If you see carefully the options on the list you can determine which is the correct answer.
Let's see option by option.
- Option A: 30
30=2*3*5, so 30 has 3 different prime factors. OUT
- Option B: 60
60=2*2*3*5, so 60 has 3 different prime factors. OUT.
- Option C: 180
180=2*2*3*3*5, so 180 has 3 different prime factors, OUT.
- Option D: 210
210=2*3*5*7, so 210 has exactly 4 different prime factors. In addition, 14*210/60=49, so 14N/60 is an integer. CORRECT.
We don't need to analyze the last option.
So, the answer is D.
I hope this answer could help you.
I'm available if youd like any follow up.
If you see carefully the options on the list you can determine which is the correct answer.
Let's see option by option.
- Option A: 30
30=2*3*5, so 30 has 3 different prime factors. OUT
- Option B: 60
60=2*2*3*5, so 60 has 3 different prime factors. OUT.
- Option C: 180
180=2*2*3*3*5, so 180 has 3 different prime factors, OUT.
- Option D: 210
210=2*3*5*7, so 210 has exactly 4 different prime factors. In addition, 14*210/60=49, so 14N/60 is an integer. CORRECT.
We don't need to analyze the last option.
So, the answer is D.
I hope this answer could help you.
I'm available if youd like any follow up.
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14N/60 = 7N/30.LUANDATO wrote:If N is a positive integer and 14N/60 is an integer. What is the smallest value of N for which N has exactly four different prime factors?
A)30
B)60
C)180
D)210
E)cannot be determined
The smallest prime numbers are 2, 3, 5 and 7.
Thus, the smallest integer with 4 different prime factors = 2*3*5*7 = 210.
Test whether N=210 yields an integer value for 7N/30:
(7*210)/30= 7*7 = 49.
Success!
Thus, the least possible value for N = 210.
The correct answer is D.
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We are given that 14N/60 is an integer, and we need to determine the smallest value of N for which N has exactly four different prime factors.LUANDATO wrote:If N is a positive integer and 14N/60 is an integer. What is the smallest value of N for which N has exactly four different prime factors?
A)30
B)60
C)180
D)210
E)cannot be determined .
14N/60 = 7N/30
In order for 7N/30 to be an integer, N must be divisible by 30. In other words, N must be a multiple of 30.
However, since 30 = 2 x 3 x 5, which are 3 different primes, the smallest value of n with 4 different primes is 2 x 3 x 5 x 7 = 210.
Answer: D
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