Aug 24 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Aug 25 09:00 AM PDT  12:00 PM PDT Join a FREE 1day verbal workshop and learn how to ace the Verbal section with the best tips and strategies. Limited for the first 99 registrants. Register today! Aug 25 08:00 PM PDT  11:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE. Aug 28 08:00 AM PDT  09:00 AM PDT Join a FREE live webinar with examPAL and Admissionado and learn how to master GMAT Critical Reasoning questions and the 6pointed star of MBA application essay glory. Save your spot today! Aug 30 08:00 PM PDT  11:00 PM PDT We'll be posting questions in DS/PS/SC/CR in competition mode. Detailed and quickest solution will get kudos. Will be collecting new links to all questions in this topic. Here you can also check links to fresh questions posted.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 01 Jan 2019
Posts: 57
Location: Canada
Concentration: Finance, Economics
GPA: 3.24

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 08:45
Well first we have to find F(12)= 2^2*3
The greatest prime factor of f(12) is 3, now g(3)= 2^3 + 1=9
9=3*3
So smallest prime factor is 3
thus g(f(12))= 3



Manager
Joined: 18 Sep 2018
Posts: 100

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 08:46
IMO B
For every positive integer x, f(x) represents the greatest prime factor of x!, and g(x) represents the smallest prime factor of 2^x+1. What is (g(f(12))?
Given, f(12) represents the greatest prime factor of 12!, which is 11, as we know 12! = 12*11*10*9*8*7*6*5*4*3*2*1
Now g(11) represents the smallest prime factor of 2^11+1 = 2048+1 = 2049, which is 3 (2049=3*683, we do not need to calculate all prime factors as we only need the smallest one which is 3)
So, (g(f(12)) = 3



Director
Joined: 22 Nov 2018
Posts: 534
Location: India
GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33

For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 08:49
Greatest prime factor of 12! will be 11. So f(12)=11 g(11)=smallest prime factor of 2^11+1=Smallest prime factor of 2049 which is 3 (2+0+4+9=15 which is divisible by 3 as per divisibility rules) IMO B
_________________
Give +1 kudos if this answer helps..!!



Manager
Joined: 10 Jan 2017
Posts: 198
Location: India

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 08:51
IMO correct answer is B  3 explanation as attached
Attachments
IMG_20190718_211529.JPG [ 1.14 MiB  Viewed 186 times ]
_________________
Your limitation—it's only your imagination. Please hit +1 Kudos if you like my Post.



Senior Manager
Joined: 13 Feb 2018
Posts: 448

For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 08:53
1) f(12) is the greatest prime factor of 12!, which is 11 2) g(11) is the smallest prime factor of \(2^{11}+1=2049\). not divisible by 2 (the lowest prime) as 2049 is odd, but divisible by 3 (the secondlowest prime) as 2+0+4+9=15, which is divisible by 3
So g(f(12))=3
IMo Ans: B



Manager
Joined: 18 Feb 2017
Posts: 93

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 08:54
IMO B.
f(x) = largest prime factor of x! g(x)= smallest prime factor of \(2^x+1\)
g(f(12)), f(12) > largest prime factor of 12! > 12X11X10X...1 > Highest prime factor would be 11. g(11)= 2^11+1= 2048 + 1 = 2049 . 2049 is not divisible by 2 but is divisble by 3 which is a prime number.
Hence, the answer is 3 which is option B.



Manager
Joined: 17 Jul 2014
Posts: 111

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 08:55
For every positive integer x, f(x) represents the greatest prime factor of x!, and g(x) represents the smallest prime factor of 2x+1. What is (g(f(12))?
Lets find inner equation value first i.e f(12) = 12! > What is the greatest prime factor of 12! > 11 g(11) = \(2^{11}\) + 1 = 2048 +1 = 2049 > What is the smallest prime factor of 2049 2049 is not divisible by 2 Find out if no if divisible by 3  add the digits = sum is divisible by 3, hence 2049 is divisible by 3.. smallest prime factor is 3
B is the answer



Senior Manager
Joined: 24 Nov 2016
Posts: 340
Location: United States

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 08:57
Quote: For every positive integer x, f(x) represents the greatest prime factor of x!, and g(x) represents the smallest prime factor of 2ˆx+1. What is (g(f(12))?
A. 2 B. 3 C. 5 D. 7 E. 11 f(12) is g8primefac of 12!, which is the largest prime from 0 to 12 = 11; g(11) is smallest prime factor of 2ˆ(11)+1=2048+1=2049, notice that 2049 is not divisible by 2, but the sum of its digits is a multiple of 3, so its divisible by 3, which means the smallest pf is 3. Answer (B).



Manager
Joined: 08 Jan 2018
Posts: 145
Location: India
Concentration: Operations, General Management
WE: Project Management (Manufacturing)

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 08:58
IMOB
f(x) = Greatest prime factor of x! g(x) = Smallest prime factor of 2^x + 1
f(12)= Greatest prime factor of 12! = Greatest prime factor ( 12 x 11 x 10 x 9..........x1) = 11 g(11)= Smallest prime factor of 2^11 + 1= Smallest prime factor of 2049 = 3
g(f(12))= g(11)= 3



Manager
Joined: 30 Nov 2017
Posts: 186
WE: Consulting (Consulting)

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 08:59
Given that f(x) represents the greatest prime factor of x! And g(x) represents the smallest prime factor of (2^x) + 1 to find g(f(12)) f(12): since 12! has 11 as the greatest prime factor therefore, f(12) = 11 Also for g(f(12)): we have (2^11) + 1 = 2049 2049/3 = 683 thus, 3 is the smallest prime factor of g(f(12)) Final answer is 3 Hence answer choice B.Thank you for kudos.
_________________
Be Braver, you cannot cross a chasm in two small jumps...



Intern
Joined: 05 May 2013
Posts: 12

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 09:04
(g(f(12)) : F(12)  represent the greatest prime of 12! = 11
g(11) = 2^11+1
The last digit of 2^11 = 4 (based on the pattern of 2,4,8,6) So the smallest prime or the prime that divides g(11) is 5
IMO : C



Manager
Joined: 06 Aug 2018
Posts: 98

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 09:05
First we have 12!
It can be written as
2^10*3^5*5^2*7*11
Greatest prime factor is 11
Then we have 2^11+1
2049 ,this is not divisible by 11 or 7 or 5 or 2
This is divisible by 3
B it is !!
Posted from my mobile device



Manager
Joined: 24 Jun 2019
Posts: 108

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 09:06
For every positive integer x, f(x) represents the greatest prime factor of x!, and g(x) represents the smallest prime factor of \(2^x+1\). What is (g(f(12))?
Start by finding f(12) f(12) = GREATEST prime factor of 12! 12! = 12x11x10x9x8x7x6x5x4x3x2x1
11 is the greatest prime factor
f(12) = 11
g(f(12)) = g(11)
SMALLEST prime factor of \(2^{11} + 1\) = 2048 + 1 = 2049
2049 is not divisible by 2 2049 is divisible by 3.... so 3 is the smallest prime factor of 2049
g(11) = 3 = g(f(12))
Answer: B  3



Manager
Joined: 08 Jan 2018
Posts: 98
Location: India
GPA: 4
WE: Information Technology (Computer Software)

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 09:10
f(x) represents the greatest prime factor of x! f(12) => 12! = 12*11*10*9*8*7*6*5*4*3*2*1 Thus greatest prime factor is 11.
g(x) represents the smallest prime factor of \(2^x\)+1 g(11) => \(2^{11}\) + 1 => 2049 2049 = 3*683 Thus smallest prime factor is 3.
IMO the answer is B.
Please hit kudos if you like the solution.



Manager
Joined: 12 Jul 2017
Posts: 206
GMAT 1: 570 Q43 V26 GMAT 2: 660 Q48 V34

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 09:31
f(12) is highest prime factor of 12! which is 11. so g(11) will be lowest prime factor of (2^11+1) => Plowest ( 2049) => 3
Answer shall be B.
Regards, Rishav



Intern
Joined: 08 Apr 2011
Posts: 12

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 09:42
For every positive integer xx, f(x) represents the greatest prime factor of x! and g(x) represents the smallest prime factor of 2^x+1. What is (g(f(12))?
A. 2 B. 3 C. 5 D. 7 E. 11
Solution f(12) = highest prime factor for 12! and that would be 11 g(11) = 2^11 +1 = odd number option A out 2^11+1 = 2^10 * 2+1 1024*2 +1 = 2049, which is divisible by 3 hence g(11) wud be the smallest prime factor i.e. 3
Answer = B



Manager
Joined: 22 Oct 2018
Posts: 74

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 09:44
For every positive integer x x , f(x) f(x) represents the greatest prime factor of x! x! , and g(x) g(x) represents the smallest prime factor of 2 x +1 2x+1 . What is (g(f(12)) (g(f(12)) ?
A. 2 B. 3 C. 5 D. 7 E. 11 Solution: Its given that for every positive integer x,f(x) represent the greatest prime factor of x!,this implies that from question f(12)=greatest prime factor of 12! factors of 12!=12*11*10*9*8*7*6*5*4*3*2*1=11*7*\(5^(2)\)*\(3^(5)\)*\(2^(10)\)
As the greatest prime factor is 11 ,hence it implies we need to calculate g(11)=2^(11) +1=2048+1=2049 Now factor of 2049=3*683 Hence g(11)=smallest prime factor of\(2^(11)\) +1=smallest prime factor of 3*683=3 Hence B IMO



Manager
Joined: 28 Feb 2014
Posts: 137
Location: India
Concentration: General Management, International Business
GPA: 3.97
WE: Engineering (Education)

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 10:39
We need to find g(f(12))
f(12), the greatest prime of 12! is 11 Now, g(11), smallest prime factor of 2^11 + 1 = 2048+1 = 2049
Smallest prime number by which 2049 is 3 (using divisibility rule for 3)
B is correct.



Intern
Joined: 13 Mar 2019
Posts: 28
Location: India

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 10:43
f(12) greatest prime factor of 12 will be 3. Therefore question becomes g(3) =2^3+1=9 Smallest prime factor of 9 is 3 so the answer option B
Posted from my mobile device



Manager
Joined: 18 Jun 2013
Posts: 141
Location: India
Concentration: Technology, General Management
GPA: 3.2
WE: Information Technology (Consulting)

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 11:07
Given,
1. f(x) => Greatest prime factor of x! 2. g(x) => Smallest prime factor of 2^x + 1
To find,
g(f(12))
Lets do it step by step,
Step 1:
f(12) = Greatest prime factor of 12!
12! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12
=> f(12) = 11
Step 2:
g(x) => Smallest prime factor of 2^x + 1
g(f(12)) = g(11) = Smallest prime factor of 2^11 + 1
=> Smallest prime factor of 2048 + 1 = 2049
Let us check the options which divide 2049
A. 2 > Wrong. Is not a factor of 2049.
B. 3 > Correct. Divides 2049 and is the smallest.
C. 5 > Wrong. Is not a factor of 2049.
D. 7 > Wrong. Is not a factor of 2049.
E. 11 > Wrong. Is not a factor of 2049.




Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
18 Jul 2019, 11:07



Go to page
Previous
1 2 3 4 5
Next
[ 84 posts ]



