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M18-37

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M18-37  [#permalink]

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New post 16 Sep 2014, 01:05
2
12
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

45% (01:28) correct 55% (01:19) wrong based on 192 sessions

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Re M18-37  [#permalink]

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New post 16 Sep 2014, 01:05
Official Solution:


(1) \(2n\) has one distinct prime divisor. Obviously that only prime divisor of \(2n\) is 2. So, \(2n\) can be 2, 4, 8, ... Which means that \(n\) can be 1, 2, 4, ... If \(n=1\) then it has no prime divisor but if \(n\) is any other value (2, 4, ...) then it has one prime divisor: 2 itself. Not sufficient.

(2) \(3n\) has one distinct prime divisor. Basically the same here: the only prime divisor of \(3n\) must be 3. So, \(3n\) can be 3, 9, 27, ... Which means that \(n\) can be 1, 3, 9, ... If \(n=1\) then it has no prime divisor but if \(n\) is any other value (3, 9, ...) then it has one prime divisor: 3 itself. Not sufficient.

(1)+(2) From above the only possible value of \(n\) is 1, and 1 has no prime divisor. Sufficient.


Answer: C
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M18-37  [#permalink]

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New post 19 Aug 2015, 15:16
We need to find PRIME divisor. Which means only prime number. If 2n has 1 prime divisor, thus n doesn't have any prime divisor. The same goes for 3n.
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Re: M18-37  [#permalink]

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New post 09 Oct 2016, 11:16
Bunuel wrote:
Official Solution:


(1) \(2n\) has one distinct prime divisor. Obviously that only prime divisor of \(2n\) is 2. So, \(2n\) can be 2, 4, 8, ... Which means that \(n\) can be 1, 2, 4, ... If \(n=1\) then it has no prime divisor but if \(n\) is any other value (2, 4, ...) then it has one prime divisor: 2 itself. Not sufficient.

(2) \(3n\) has one distinct prime divisor. Basically the same here: the only prime divisor of \(3n\) must be 3. So, \(3n\) can be 3, 9, 27, ... Which means that \(n\) can be 1, 3, 9, ... If \(n=1\) then it has no prime divisor but if \(n\) is any other value (3, 9, ...) then it has one prime divisor: 3 itself. Not sufficient.

(1)+(2) From above the only possible value of \(n\) is 1, and 1 has no prime divisor. Sufficient.


Answer: C


my doubt: we could interpret this from each statement alone that only 1 has no prime divisors & no other number satisfies this condition, then why go further?
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Re: M18-37  [#permalink]

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New post 10 Oct 2016, 00:06
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yashrakhiani wrote:
Bunuel wrote:
Official Solution:


(1) \(2n\) has one distinct prime divisor. Obviously that only prime divisor of \(2n\) is 2. So, \(2n\) can be 2, 4, 8, ... Which means that \(n\) can be 1, 2, 4, ... If \(n=1\) then it has no prime divisor but if \(n\) is any other value (2, 4, ...) then it has one prime divisor: 2 itself. Not sufficient.

(2) \(3n\) has one distinct prime divisor. Basically the same here: the only prime divisor of \(3n\) must be 3. So, \(3n\) can be 3, 9, 27, ... Which means that \(n\) can be 1, 3, 9, ... If \(n=1\) then it has no prime divisor but if \(n\) is any other value (3, 9, ...) then it has one prime divisor: 3 itself. Not sufficient.

(1)+(2) From above the only possible value of \(n\) is 1, and 1 has no prime divisor. Sufficient.


Answer: C


my doubt: we could interpret this from each statement alone that only 1 has no prime divisors & no other number satisfies this condition, then why go further?


From each statement n can take more than one value. For example, for (1) n can be can be 1, 2, 4, ... For all these cases 2n has one distinct prime divisor, namely 2.
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Re: M18-37  [#permalink]

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New post 11 Jul 2019, 14:30
Is this the same as saying
Statement 1: \(2n=2^n\)
Statement 2: \(3n=3^n\)?
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Re: M18-37   [#permalink] 11 Jul 2019, 14:30
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