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n is on odd positive integer 700<n<800

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n is on odd positive integer 700<n<800 [#permalink] New post 19 May 2017, 01:15
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58% (00:47) correct 41% (00:37) wrong based on 24 sessions


n is an odd positive integer, and 700 < n < 800

Quantity A
Quantity B
The number of the prime factors of n
The number of the prime factors of 2n


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: n is on odd positive integer 700<n<800 [#permalink] New post 26 May 2017, 12:33
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Carcass wrote:


n is an odd positive integer, and 700 < n < 800

Quantity A
Quantity B
The number of the prime factors of n
The number of the prime factors of 2n


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


KEY CONCEPT #1: Every factor of n is also a factor of 2n
So, EITHER n and 2n have the same number of prime factors OR 2n has more prime factors than n has.
In other words, the correct answer is either C or B

KEY CONCEPT #1: Since n is ODD, we can conclude that 2 (a prime number) is NOT a factor of n
Since 2n is EVEN, we can conclude that 2 IS a factor of 2n

Since 2 (a prime number) IS a factor of 2n but NOT a factor of n, we can see that 2n must have MORE prime factors than n has.

Answer:
[Reveal] Spoiler:
B


Cheers,
Brent
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Re: n is on odd positive integer 700<n<800   [#permalink] 26 May 2017, 12:33
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