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shelrod007
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Concentration: Technology, Other
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GMAT Date: 01-14-2015
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How many different prime numbers are factors of the positive integer Updated on: 22 Jul 2023, 03:48
Originally posted by shelrod007 on 31 May 2014, 10:33.
Last edited by Bunuel on 22 Jul 2023, 03:48, edited 2 times in total.
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C
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75% (hard)

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43% (01:26) correct 57% (01:25) wrong based on 260 sessions

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How many different prime numbers are factors of the positive integer \(n\) ?


(1) \(2n\) has one prime factor.

(2) \(3n\) has one prime factor.


M18-37

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Bunuel
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How many different prime numbers are factors of the positive integer 31 May 2014, 15:54
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shelrod007
How many distinct prime divisors does a positive integer \(n\) have?

(1) \(2n\) has one distinct prime divisor.

(2) \(3n\) has one distinct prime divisor.

M18-37
Show more

How many different prime numbers are factors of the positive integer \(n\) ?

(1) \(2n\) has one prime factor.

Clearly, the sole prime factor of \(2n\) is 2. Thus, possible values for \(2n\) include 2, 4, 8, etc., implying \(n\) could be 1, 2, 4, and so forth. If \(n=1\), it doesn't have any prime factor, but if \(n\) takes any other value (2, 4, ...), it has one prime factor: 2. Not sufficient.

(2) \(3n\) has one prime factor.

The situation here mirrors the first: the only prime factor of \(3n\) is 3. Hence, \(3n\) could be 3, 9, 27, etc., which implies \(n\) could be 1, 3, 9, and so on. If \(n=1\), then it doesn't have a prime factor, but if \(n\) takes any other value (3, 9, ...), it has one prime factor: 3. Not sufficient.

(1)+(2) From above, the only possible value of \(n\) is 1, and 1 does not have any prime factors. Sufficient.


Answer: C
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SomeOneUnique
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How many different prime numbers are factors of the positive integer 21 Jan 2024, 10:49
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Bunuel
shelrod007
How many distinct prime divisors does a positive integer \(n\) have?

(1) \(2n\) has one distinct prime divisor.

(2) \(3n\) has one distinct prime divisor.

M18-37

How many different prime numbers are factors of the positive integer \(n\) ?

(1) \(2n\) has one prime factor.

Clearly, the sole prime factor of \(2n\) is 2. Thus, possible values for \(2n\) include 2, 4, 8, etc., implying \(n\) could be 1, 2, 4, and so forth. If \(n=1\), it doesn't have any prime factor, but if \(n\) takes any other value (2, 4, ...), it has one prime factor: 2. Not sufficient.

(2) \(3n\) has one prime factor.

The situation here mirrors the first: the only prime factor of \(3n\) is 3. Hence, \(3n\) could be 3, 9, 27, etc., which implies \(n\) could be 1, 3, 9, and so on. If \(n=1\), then it doesn't have a prime factor, but if \(n\) takes any other value (3, 9, ...), it has one prime factor: 3. Not sufficient.

(1)+(2) From above, the only possible value of \(n\) is 1, and 1 does not have any prime factors. Sufficient.


Answer: C
Show more



Hello,
I understand that n=1 is common case for both statements.
However, if we combine the 2 statements, we get 2n and 3n have 1 distinct prime divisor.
Isn't this ambiguous ?
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How many different prime numbers are factors of the positive integer 21 Jan 2024, 11:59
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SomeOneUnique
Bunuel
shelrod007
How many distinct prime divisors does a positive integer \(n\) have?

(1) \(2n\) has one distinct prime divisor.

(2) \(3n\) has one distinct prime divisor.

M18-37

How many different prime numbers are factors of the positive integer \(n\) ?

(1) \(2n\) has one prime factor.

Clearly, the sole prime factor of \(2n\) is 2. Thus, possible values for \(2n\) include 2, 4, 8, etc., implying \(n\) could be 1, 2, 4, and so forth. If \(n=1\), it doesn't have any prime factor, but if \(n\) takes any other value (2, 4, ...), it has one prime factor: 2. Not sufficient.

(2) \(3n\) has one prime factor.

The situation here mirrors the first: the only prime factor of \(3n\) is 3. Hence, \(3n\) could be 3, 9, 27, etc., which implies \(n\) could be 1, 3, 9, and so on. If \(n=1\), then it doesn't have a prime factor, but if \(n\) takes any other value (3, 9, ...), it has one prime factor: 3. Not sufficient.

(1)+(2) From above, the only possible value of \(n\) is 1, and 1 does not have any prime factors. Sufficient.


Answer: C



Hello,
I understand that n=1 is common case for both statements.
However, if we combine the 2 statements, we get 2n and 3n have 1 distinct prime divisor.
Isn't this ambiguous ?
Show more

When we combine the statements, we conclude that n = 1. Therefore, (1) indicates that 2n = 2 has one prime factor, which is accurate: 2 has one prime factor, 2 itself. Similarly, (2) implies that 3n = 3 has one prime factor, which is correct: 3 has one prime factor, 3 itself.
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