Sep 23 08:00 AM PDT  09:00 AM PDT Join a free 1hour webinar and learn how to create the ultimate study plan, and be accepted to the upcoming Round 2 deadlines. Save your spot today! Monday, September 23rd at 8 AM PST Sep 26 07:00 AM PDT  08:00 AM PDT a chat session focused on MBA recruitment of international students at US schools. Sep 28 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn two proprietary ways to PreThink assumptions and ace GMAT CR in 10 days. Sep 28 08:00 PM PDT  09:00 PM PDT Round 2 deadlines are just around the corner! Start your GMAT preparation today with a 25% discount. Sale ends on the 28th of September Sep 29 07:00 AM PDT  09:00 AM PDT Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT. Sep 30 10:00 PM PDT  11:00 PM PDT Don't miss Veritas Prep's Fall Kickoff sale  save $100 on GMAT courses from September 2330.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 27 May 2010
Posts: 200

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 22:56
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))? x = 12 f(12) = Greatest prime factor (12!) = 11 g(11) = Smallest prime factor (2^11 + 1) = (2049) = 3 Option B
_________________
Please give Kudos if you like the post



Intern
Joined: 14 Mar 2017
Posts: 40
Location: United States (VA)
GPA: 2.9
WE: Science (Pharmaceuticals and Biotech)

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 23:10
Question: 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 \((g(f(12))\)? \(f(x) =\) The greatest prime factor of \(12!\) \(f(12) =\) The greatest prime factor of \(12!\) \(12! =\text{12 }\times\text{ }\) \(11\) \(\times\text{ 10 }\times\text{9 }\times\text{8 }\times\text{7 }\times\text{6 }\times\text{5 }\times\text{4 }\times\text{3 }\times\text{2 }\times\text{1 }\) \(11\)\(=\) Greatest Prime Factor \(g(x) =\) The smallest prime factor of \(2^x+1\) \(g(\) \(11\)\() =2^{11}+1\) Since \(2^{11}\) is a little much to calculate without a calculator, start small and look for a pattern. \[ \begin{vmatrix*} 2^x & + & 1 & = & # & \to & \div 3?\\ 2^1 & + & 1 & = & 3 & \to & Yes \\ 2^2 & + & 1 & = & 5 & \to & No \\ 2^3 & + & 1 & = & 9 & \to & Yes \\ 2^4 & + & 1 & = & 17 & \to & No \\ 2^5 & + & 1 & = & 33 & \to & Yes \end{vmatrix*} \\ \text{Pattern #1: Every answer is odd and therefore not divisible by 2.}\\ \text{Pattern #2: Every odd exponent of 2 with the addition of 1, equals an answer divisible by 3.}\\ \] \(\text{Since }2^{11} \text{ has an odd exponent, the final answer will be divisible by 3.}\) \(\text{Therefore, 3 is the smallest prime factor of } (2^{11}+1)\). Correct Answer: B. 3
_________________
"What is my purpose?" "You pass butter." "Oh my god..." "Yeah, welcome to the club, pal."



Manager
Joined: 04 Dec 2017
Posts: 93
Location: India
Concentration: Other, Entrepreneurship
GMAT 1: 570 Q36 V33 GMAT 2: 620 Q44 V32 GMAT 3: 720 Q49 V39
GPA: 3
WE: Engineering (Other)

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 23:10
We need to find g(f(12)).
Lets break it down.
First lets find out f(12).
f(12) = greatest prime factor of 12!.
12! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12
Hence, f(12) = 11.
Therefore, g(f(12)) becomes g(11).
g(11) = smallest prime factor of ((2^11)+1) ie, smallest prime factor of 2049.
Using the options we get 3 as the smallest prime factor of 2049.
Answer: B



SVP
Joined: 26 Mar 2013
Posts: 2330

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 23:11
f(12) = greatest prime factor of 12! = 11
g(11) = 2^11 + 1
It is known that 2^10 = 1024
Then 2^11= 2 * 1024 = 2048
g(11) = 2^11 + 1 = 2049
The sum of all digits is divisible by 3
Answer: B



Manager
Joined: 06 Jun 2019
Posts: 118

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 23:27
From the stem we know that: \(f(x)\)  is the greatest prime factor of \(x!\) \(g(y)\)  is the smallest prime factor of \(2^y+1\) Let's figure out step by step what \(g(f(12))\) is. In order to calculate what \(g(y)\) is, we need to first calculate what \(y\) is. Since \(y=f(12)\), we will first calculate what \(f(12)\) is. 1. \(f(12)\) is the greatest prime factor of \(12!\) So \(f(12)=11\) or \(y=11\) 2. \(g(11)\) is the smallest prime factor of \(2^{11}+1\). What is the smallest prime factor of \(2049\) ? \(2049\) is not even, so it can't be \(2\). Is \(2049\) divisible by \(3\) ? \(2+0+4+9=15\) is divisible by \(3\). Thus \(g(11)=3\) Hence B
_________________
Bruce Lee: “I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times.”GMAC: “I fear not the aspirant who has practiced 10,000 questions, but I fear the aspirant who has learnt the most out of every single question.”



Intern
Joined: 01 Jun 2019
Posts: 1

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
19 Jul 2019, 00:03
f(12) = factorial of 12 whose greatest prime factor is 11 as 12! is 1*2*3*4*5*6*7*8*9*10*11*12. Hence, g(f(12)) = g(11) = 2^11 + 1 = 2049 = 3*683. Hence, the smallest prime factor of g(f(12)) is 3.
Correct answer is B.



Manager
Joined: 12 Jan 2018
Posts: 113

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
19 Jul 2019, 00:32
f(12)= greatest prime factor of 12!. That is 11. g(f(12))=g(11)= smallest prime factor of \(2^{11}\)+1=2048+1=2049. Smallest prime number which can divide 2049 is 3. Hence, ans:B
_________________
"Remember that guy that gave up? Neither does anybody else"



Senior Manager
Joined: 18 Jan 2018
Posts: 308
Location: India
Concentration: General Management, Healthcare
GPA: 3.87
WE: Design (Manufacturing)

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
19 Jul 2019, 00:41
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 that f(x) = greatest prime factor of x! g(x) = smallest prime factor of 2^x +1
when x =12 , f(x) = 12! = 12*11*9*8*7*6*5*4*3*2*1 11 is the greatest prime factor g(11) = 2^11 +1 =2048 +1 = 2049 is divisible by 3 ==> 3 is the smallest prime factor
a small Observation here , every odd power of 2 , 2^odd + 1 is a multiple of 3 .
Option B , is the answet



Senior Manager
Joined: 25 Sep 2018
Posts: 413
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)

For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
19 Jul 2019, 02:54
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:The above function is a compound function, in a compound function, the output of one function becomes the input of second function and so on. while solving this, the first function is the inner most function and the last function is the outermost.We'll first solve the innermost function. f(12) = 12! i.e 12 X 11 X 10 X 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1 We observe the the greatest prime is 11. We take 11 as the input for the outer most function, it will be g(11) \(2^{11}\) + 1 = 2048 + 1 =2049. We can try out the options and divide them by 2049, We see that the smallest prime factor is 3. Hence the answer is B.
_________________
Why do we fall?...So we can learn to pick ourselves up again



Intern
Joined: 24 Mar 2018
Posts: 48
Location: India
Concentration: Operations, Strategy
WE: Project Management (Energy and Utilities)

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
19 Jul 2019, 02:56
\(f(12)\) is the greatest prime factor of 12!. \(12!=12*11*10*...1\) The greatest prime factor is 11. So, \(f(12)=11\)
\(g(f(12))=g(11)\) \(g(11)\) is the smallest prime factor of \(2^{11}+1\) (=2048+1=2049) The smallest prime number that can divide 2049 is 3.
Hence, option (B).



Intern
Joined: 08 Jul 2019
Posts: 37

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
19 Jul 2019, 03:47
Greatest factor of 12! is 11. 2^11+1 equals to 2049, which is divisible by 3  smallest prime factor. Answer B



Manager
Joined: 01 Oct 2018
Posts: 112

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
19 Jul 2019, 04:29
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))?
f(12): 12! = 1*2*3...11*12 The greatest prime factor is 11. g(11): 2^11+1 = 2049 2049 / 2 = not int 2049 / 3 = int The smallest prime factor is 3
ANSWER B
A. 2 B. 3 C. 5 D. 7 E. 11



Manager
Joined: 03 Aug 2009
Posts: 58

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
19 Jul 2019, 05:26
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 \((g(f(12))\)?
f(12) = GPF of 12!: GPF of 1*2*3*4*5*6*7*8*9*10*11*12 = 11 \(g(11) = 2^{11}+1 = 2048+1=2049\)
2049 is divisible by 3 as \((2+0+4+9 = 15)\) is divisible by 3. Therefore smallest PF of 2049 is 3
A. 2 B. 3 C. 5 D. 7 E. 11



Manager
Joined: 07 Jul 2019
Posts: 54

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
19 Jul 2019, 05:37
f(12) = highest prime factor of 12 factorial  11 g(11)=2^11+1=2^10=1024*2+1=2049. Smallest prime factor is 2, but 2049 cannot be divided by 2, A will not work B will work 2049 can be evenly divided by 3. B is the answer



Manager
Joined: 25 Jul 2018
Posts: 211

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
19 Jul 2019, 05:41
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))?
If f(x) represents the greatest prime factor of x!, the greatest prime factor of it will be 11. > (g(f(12))=g(11)=2^x+1=2^11+1=2048+1=2049
it says that g(x) represents the smallest prime factor of 2^x+1 (=2049)  > The smallest prime factor of 2049 is 3.
The answer choice is B.



Manager
Joined: 24 Jun 2017
Posts: 71

For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
19 Jul 2019, 05:57
. What is (g(f(12)) (g(f(12))?
f(12) = largest prime factor of 12! which is 11 g(11) = smallest PF of 2^11+1 = 2049 so B. 3 is the answer
Posted from my mobile device



Manager
Joined: 24 Sep 2014
Posts: 50
Concentration: General Management, Technology

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
19 Jul 2019, 06:54
x=12, f(x) is greatest prime factor of x!, so x! = 12! = 12x11x10.....x1, the greatest prime factor is 11 > f(x) = 11 g(x) is smallest prime factor of 2^x+1, since x = f(x) = 11 > g(x) = g(2^11+1) 2^11+1 is odd number (=2049), and the smallest odd prime number is 3, so g(2^11+1) = 3 Answer is (B)



Intern
Joined: 23 Jul 2017
Posts: 20
Location: India
Concentration: Technology, Entrepreneurship
GPA: 2.16
WE: Other (Other)

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
19 Jul 2019, 07:53
f(12) = Greatest Prime Factor of 12!, that is 11.
g(11)= Smallest Prime Factor of 2^11 + 1 2^11+1=32x32x2+1=2049, which is divisible by 3, so the smallest prime factor is 3.
There might be a better solution to avoid the calculation but this is the best I got.



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: 12 Apr 2017
Posts: 134
Location: United States
Concentration: Finance, Operations
GPA: 3.1

Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
Show Tags
18 Jul 2019, 11:12
f(12) = 12!, 11 is the highest prime factor
G(11) = 2^11 + 1, and 2 becomes the lowest prime factor.




Re: For every positive integer x, f(x) represents the greatest prime fact
[#permalink]
18 Jul 2019, 11:12



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



