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# M31-32

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Math Expert
Joined: 02 Sep 2009
Posts: 42618

Kudos [?]: 135771 [0], given: 12708

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26 Jul 2017, 08:52
dhruv solanki wrote:
Bunuel wrote:
Official Solution:

How many different prime factors does positive integer $$n$$ have?

(1) $$44 < n^2 < 99$$. This implies that $$n$$ can be 7, 8, or 9. Each of these numbers has 1 prime: 7, 2, and 3, respectively. Sufficient.

(2) $$8n^2$$ has twelve factors. For $$8n^2=2^3n^2$$ to have twelve factors $$n$$ must be a prime: $$2^3*(prime)^2$$ --> number of factors $$= (3+1)(2+1)=12$$. Sufficient.

hi,
the question ask for prime factors so for 7 it will be 1 for 8 it will be 3 as in (2^3) and 9 it will be (3^2).
i am not able to comprehend properly as the question asks number of prime factors and not the prime numbers it is constituted of..please explain..

7 has only one prime factor, which is 7.
8 has only one prime factor, which is 2.
9 has only one prime factor, which is 3.

But for example, 36 has two primes: 2, and 3.
_________________

Kudos [?]: 135771 [0], given: 12708

Intern
Joined: 11 Dec 2013
Posts: 9

Kudos [?]: 5 [0], given: 14

Location: India
Concentration: Operations, Strategy
GPA: 4

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26 Jul 2017, 08:55
Bunuel wrote:
dhruv solanki wrote:
Bunuel wrote:
Official Solution:

How many different prime factors does positive integer $$n$$ have?

(1) $$44 < n^2 < 99$$. This implies that $$n$$ can be 7, 8, or 9. Each of these numbers has 1 prime: 7, 2, and 3, respectively. Sufficient.

(2) $$8n^2$$ has twelve factors. For $$8n^2=2^3n^2$$ to have twelve factors $$n$$ must be a prime: $$2^3*(prime)^2$$ --> number of factors $$= (3+1)(2+1)=12$$. Sufficient.

hi,
the question ask for prime factors so for 7 it will be 1 for 8 it will be 3 as in (2^3) and 9 it will be (3^2).
i am not able to comprehend properly as the question asks number of prime factors and not the prime numbers it is constituted of..please explain..

7 has only one prime factor, which is 7.
8 has only one prime factor, which is 2.
9 has only one prime factor, which is 3.

But for example, 36 has two primes: 2, and 3.

but doesnt 8 constitute of 3 2's if we consider prime factor it would be 3 right??

Kudos [?]: 5 [0], given: 14

Intern
Joined: 15 Sep 2017
Posts: 5

Kudos [?]: 0 [0], given: 9

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28 Nov 2017, 14:24
Beautiful Question!

Kudos [?]: 0 [0], given: 9

Re: M31-32   [#permalink] 28 Nov 2017, 14:24

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# M31-32

Moderators: chetan2u, Bunuel

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