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

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Manager
Joined: 26 Dec 2018
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For any positive integer n, π(n) represents the number of factors of n  [#permalink]

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Updated on: 15 Jul 2019, 03:00
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Difficulty:

15% (low)

Question Stats:

81% (01:11) correct 19% (01:51) wrong based on 37 sessions

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For any positive integer n, π(n) represents the number of factors of n, inclusive of 1 and itself. If a and
b are prime numbers, then π(a) + π(b) – π(a b) =

(A) –4
(B) –2
(C) 0
(D) –2
(E) 4

Source: Nova GMAT
Difficulty Level: 550

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Originally posted by UB001 on 06 Jan 2019, 03:41.
Last edited by SajjadAhmad on 15 Jul 2019, 03:00, edited 1 time in total.
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Re: For any positive integer n, π(n) represents the number of factors of n  [#permalink]

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06 Jan 2019, 07:13
1
For any positive integer n, π(n) represents the number of factors of n, inclusive of 1 and itself. If a and
b are prime numbers, then π(a) + π(b) – π(a b) =

π(a) = 2 (1, a since prime)
π(b) = 2 (1, b since prime)
π(a b) = 4 ( 1,a,b,ab since a,b are prime we can't factorize them furture)

π(a) + π(b) – π(a b) = 2+2 - 4 =0
Option C is correct
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Re: For any positive integer n, π(n) represents the number of factors of n  [#permalink]

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21 Jan 2019, 15:14
Hello,

I am a bit confused
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Joined: 18 Jul 2018
Posts: 1021
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Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: For any positive integer n, π(n) represents the number of factors of n  [#permalink]

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21 Jan 2019, 16:08
jfranciscocuencag wrote:
Hello,

I am a bit confused

Hey jfranciscocuencag,

Let's consider examples to understand.

As a and b are prime numbers, let's take a as 2 and b as 3.
Note that the factors of 2 are only 1 and 2 itself.
Similarly for 3, it's 1 and 3.
Now ab = 2*3 = 6. The factors of 6 are 1,2,3,6.

As the theory part goes, Factors are Numbers we can multiply together to get another number.

Example 2 = 1*2. So 1 and 2 are factors of 2.
Similarly for 3 = 1*3. So 1 and 3 are factors of 3.
Now, 6 = 1*6 or 2*3.
Hence 6 has 4 factors 1,2,3,6.

Coming to the question.
π(a)+π(b)-π(ab) = 2+2-4 = 0

Hope it helps.

Posted from my mobile device
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Posts: 302
Re: For any positive integer n, π(n) represents the number of factors of n  [#permalink]

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21 Jan 2019, 16:26
Afc0892 wrote:
jfranciscocuencag wrote:
Hello,

I am a bit confused

Hey jfranciscocuencag,

Let's consider examples to understand.

As a and b are prime numbers, let's take a as 2 and b as 3.
Note that the factors of 2 are only 1 and 2 itself.
Similarly for 3, it's 1 and 3.
Now ab = 2*3 = 6. The factors of 6 are 1,2,3,6.

As the theory part goes, Factors are Numbers we can multiply together to get another number.

Example 2 = 1*2. So 1 and 2 are factors of 2.
Similarly for 3 = 1*3. So 1 and 3 are factors of 3.
Now, 6 = 1*6 or 2*3.
Hence 6 has 4 factors 1,2,3,6.

Coming to the question.
π(a)+π(b)-π(ab) = 2+2-4 = 0

Hope it helps.

Posted from my mobile device

Hello Afc0892 !

Why are we taking n=1?
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Posts: 1021
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Re: For any positive integer n, π(n) represents the number of factors of n  [#permalink]

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21 Jan 2019, 16:55
jfranciscocuencag wrote:
Afc0892 wrote:
jfranciscocuencag wrote:
Hello,

I am a bit confused

Hey jfranciscocuencag,

Let's consider examples to understand.

As a and b are prime numbers, let's take a as 2 and b as 3.
Note that the factors of 2 are only 1 and 2 itself.
Similarly for 3, it's 1 and 3.
Now ab = 2*3 = 6. The factors of 6 are 1,2,3,6.

As the theory part goes, Factors are Numbers we can multiply together to get another number.

Example 2 = 1*2. So 1 and 2 are factors of 2.
Similarly for 3 = 1*3. So 1 and 3 are factors of 3.
Now, 6 = 1*6 or 2*3.
Hence 6 has 4 factors 1,2,3,6.

Coming to the question.
π(a)+π(b)-π(ab) = 2+2-4 = 0

Hope it helps.

Posted from my mobile device

Hello Afc0892 !

Why are we taking n=1?

1 is a factor of any number.
Example : 20 = 1*20 or 4*5 or 10*2.
So factors of 20 are 1,2,4,5,10 and 20.
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Re: For any positive integer n, π(n) represents the number of factors of n   [#permalink] 21 Jan 2019, 16:55
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