(1) Since 2N has only one prime divisor, so 2N = 2, 4, 8, 16, 32.... This means N can take the values 1, 2, 4, 8, 16....
When N = 1, 2N = 2, which will have one prime divisor, 2 but N will not have any prime divisor.
When N = 2, 2N = 4, which again has 1 prime divisor 2, but in this case N will also have 1 prime divisor.
We don't get a unique answer.
So, (1) is NOT SUFFICIENT to answer the question.
(2) Since 3N has only one prime divisor, so 3N = 3, 9, 27, 81.... This means N can take the values 1, 3, 9, 27....
When N = 1, 3N = 3, which will have one prime divisor, 3 but N will not have any prime divisor.
When N = 3, 3N = 9, which again has 1 prime divisor 3, but in this case N will also have 1 prime divisor.
We don't get a unique answer.
So, (2) is NOT SUFFICIENT to answer the question.
Combining (1) and (2), we get that N = 1 is the only possible value, and 1 does not have any distinct prime divisor. Hence, N does not have any distinct prime divisors.
So, the correct answer is (C).
Distinct prime factors
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Just wondering, why doesn't 1. or 2. contain the word 'only'getso wrote:How many distinct prime divisors does a positive integer N have?
1. 2N has one prime divisor
2. 3N has one prime divisor
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