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Re: n is on odd positive integer 700<n<800 [#permalink]
good question
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Re: n is on odd positive integer 700<n<800 [#permalink]
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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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Re: n is on odd positive integer 700<n<800 [#permalink]
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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]
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