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n is on odd positive integer 700<n<800

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Carcass
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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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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.
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B
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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:
Show: ::
B


Cheers,
Brent
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Ashutosh4P
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Re: n is on odd positive integer 700<n<800 [#permalink] New post   10 Jun 2020, 23:23
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r^6=32
A) 32 B)r^5
A greater
B greater
both same
relation cannot be find
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Re: n is on odd positive integer 700<n<800 [#permalink] New post   12 Jun 2020, 01:10
good question
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Re: n is on odd positive integer 700<n<800 [#permalink] New post   18 Aug 2020, 09:48
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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.



Any odd integer is not divisible by 2. So you can pick any odd integer in that range, and when we evaluate \(2n\), and do its prime factorization, it will have a new factor of 2, along with all its factors of \(n\). In other words, in this case, if \(n\) has \(x\) prime factors, \(2n\) has \(x+1\) factors (that +1 being the 2).

So in all cases, Quantity A will be \(x\) and Quantity B will be \(x+1\), where \(x\) is a positive integer. So the answer is B.


Example:

701 is actually prime, so its prime factor is just itself: 701.
2*701 = 1402, which has prime factors of 2 and 701.

735 has a prime factorization of 3*5*29.
2*735 = 1470, which has a prime factorization of 2*3*5*29.
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nishita84
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Re: n is on odd positive integer 700<n<800 [#permalink] New post   18 Aug 2020, 11:44
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Since n is a unique no and 2n will always have one more prime no than n (which is 2). Hence quantity B will be greater
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Re: n is on odd positive integer 700<n<800 [#permalink]
18 Aug 2020, 11:44
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