Oct 22 08:00 AM PDT  09:00 AM PDT Join to learn strategies for tackling the longest, wordiest examples of Counting, Sets, & Series GMAT questions Oct 22 09:00 AM PDT  10:00 AM PDT Watch & learn the Do's and Don’ts for your upcoming interview Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Oct 27 07:00 AM EDT  09:00 AM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 26 Dec 2018
Posts: 144
Location: India

For any positive integer n, π(n) represents the number of factors of n
[#permalink]
Show Tags
Updated on: 15 Jul 2019, 03:00
Question Stats:
81% (01:11) correct 19% (01:51) wrong based on 37 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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.
Added Source



Manager
Joined: 01 May 2017
Posts: 82
Location: India

Re: For any positive integer n, π(n) represents the number of factors of n
[#permalink]
Show Tags
06 Jan 2019, 07:13
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



Senior Manager
Joined: 12 Sep 2017
Posts: 302

Re: For any positive integer n, π(n) represents the number of factors of n
[#permalink]
Show Tags
21 Jan 2019, 15:14
Hello,
Could anyone please provide an answer?
I am a bit confused



NUS School Moderator
Joined: 18 Jul 2018
Posts: 1021
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)

Re: For any positive integer n, π(n) represents the number of factors of n
[#permalink]
Show Tags
21 Jan 2019, 16:08
jfranciscocuencag wrote: Hello,
Could anyone please provide an answer?
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+24 = 0 Hence C is the answer. Hope it helps. Posted from my mobile device
_________________
Press +1 Kudos If my post helps!



Senior Manager
Joined: 12 Sep 2017
Posts: 302

Re: For any positive integer n, π(n) represents the number of factors of n
[#permalink]
Show Tags
21 Jan 2019, 16:26
Afc0892 wrote: jfranciscocuencag wrote: Hello,
Could anyone please provide an answer?
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+24 = 0 Hence C is the answer. Hope it helps. Posted from my mobile deviceHello Afc0892 ! Why are we taking n=1?



NUS School Moderator
Joined: 18 Jul 2018
Posts: 1021
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)

Re: For any positive integer n, π(n) represents the number of factors of n
[#permalink]
Show Tags
21 Jan 2019, 16:55
jfranciscocuencag wrote: Afc0892 wrote: jfranciscocuencag wrote: Hello,
Could anyone please provide an answer?
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+24 = 0 Hence C is the answer. Hope it helps. Posted from my mobile deviceHello 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.
_________________
Press +1 Kudos If my post helps!




Re: For any positive integer n, π(n) represents the number of factors of n
[#permalink]
21 Jan 2019, 16:55






