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# For any positive integer n, π(n) represents the number of fa

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For any positive integer n, π(n) represents the number of fa [#permalink]  04 Apr 2018, 12:33
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55% (00:45) correct 44% (00:57) wrong based on 43 sessions

For any positive integer n, $$\pi(n)$$ represents the number of factors of n, inclusive of 1 and itself. a and b are prime numbers

 Quantity A Quantity B $$\pi(a) + \pi(b)$$ $$\pi(a * b)$$

A. The quantity in Column A is greater
B. The quantity in Column 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: For any positive integer n, π(n) represents the number of fa [#permalink]  04 Apr 2018, 15:43
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A: P(a) + P(b)
The only factors of a prime number are 1 and the number itself.
So P(a) + P(b) always equals 2+2 = 4

B: P(a*b)
The factors of a*b are 1, a, b, a*b. Why not more than 4? Because no new divider is produced with multiplying a to b. If there were any it was a factor of a or b (a factor other than a and b themselves and a) and thus a or b couldn’t be prime. So factors of a*b are 4 numbers.
For example if a = 3 and b = 11 then P(a*b) = P(33) = 4 (1, 3, 11, 33)

A and B are both 4 and equal. The answer is C.

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Re: For any positive integer n, π(n) represents the number of fa [#permalink]  06 May 2018, 18:29
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I have reservation on the ans
because it could be a case of $$a = b$$
and hence qty B can have 3 factors
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

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Re: For any positive integer n, π(n) represents the number of fa [#permalink]  06 May 2018, 18:39
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amorphous wrote:
I have reservation on the ans
because it could be a case of $$a = b$$
and hence qty B can have 3 factors

I second that thought if a = b then $$\pi(a*b)$$ will have 3 factors 1, a , b and a*b.
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Re: For any positive integer n, π(n) represents the number of fa [#permalink]  27 Feb 2019, 10:47
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Hi if a=b at this style the quantity of B has just 3 factor, am i right? for example put a and b equal to 2 now we see that it has just 3 factor
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Re: For any positive integer n, π(n) represents the number of fa [#permalink]  09 Mar 2019, 11:41
Expert's post
shahab1987 wrote:
Hi if a=b at this style the quantity of B has just 3 factor, am i right? for example put a and b equal to 2 now we see that it has just 3 factor

Yes, it seems that if a = b, then quantity B could be 3. This isn't an official question, so it should say "a and b are different prime numbers," or have D as the answer.
Re: For any positive integer n, π(n) represents the number of fa   [#permalink] 09 Mar 2019, 11:41
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