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Re: For every positive integer x, f(x) represents the greatest prime fact
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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.



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 11:22
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))?
Here, the output of f(x) will give the largest prime number less than X or X itself if X is a prime number. (Question uses complex language to confuse people.)
The output of g(x) will be the smallest prime factor. (which will be greater than 2 since the output of g(x) will be odd. )
Now,
f(12) = 11
and g(11) = 3 (2^11 + 1 = 2048 + 1 = 2049 , which is divisible by 3, The smallest possible prime factor.)
ANSWER : B



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 11:28
For every positive integer xx, f(x)f(x) represents the greatest prime factor of x!x!, and g(x)g(x) represents the smallest prime factor of 2x+12x+1. What is (g(f(12))(g(f(12))? A. 2 B. 3 C. 5 D. 7 E. 11 f (12 ) is greatest prime of 12!, which is 11. so g (11) =smallest prime of 2^11 +1 so 2048 + 1 ( infact 2 power odd +1 then 3 will be a divisor)= 2049 is divisible by 3 and not by 2. so 3 is smallest prime so ans is B
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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 11:52
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) = greatest prime factor of (x!) f(12) = greatest prime factor of (12!) > greatest prime factor of (12x11x10x...x2x1) = 11
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 (2049) = smallest prime factor of (3*683) = 3
Therefore g(f(12)) = 3.
A. 2 B. 3 C. 5 D. 7 E. 11
Answer Choice: B



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 12:55
Very nice and typical question for GMAT.
First of all, we need to figure out the greatest prime factor of 12! It's clear, that 11 is the greatest, because 12 = 3*2*2.
The next step is a little bit harder. 2^11 +1 It's clear that this number is not divisible by 2, so A is out. Unfortunately, this information is not enough.
2^11 + 1 = 2^5 * 2^5 * 2 + 1= 32*32*2 + 1= 2049 The sum of the digits of this number (2+4+9 = 15) is divisible by 3. It means that the number itself is divisible by 3.
So the smallest prime factor of 2049 is 3
The answer is B



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 13:36
So f(x) = greatest prime factor of x! g(x)= smallest prime factor of (2^x+1) Now asked g(f(12)) =?
f(12) = 1•2•3•4•5•6•7•8•9•10•11•12 Greatest prime factor =11 .: f(12)=11
g(11) = 2^11 + 1 => 2^5•2^6+1 g(11) = 2049 = 3•683 Smallest prime factor =3 .: g(f(12) =3
Answer B
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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 13:48
Answer B : 3 f(12) : highest prime factor of 12! is 11, so f(12)= 11 G (11) = 2^11+1, which can be written as 32*32*2 +1 : So lowest factor would be 2+1 =3



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 14:33
The largest prime factor for \(12!\) is \(11\), so\(f(12) = 11\) if \(x = 11\), then\(2^{11} + 1 = 2048 + 1 = 2049\), not divisible by 2, but divisible by 3, so \((g(f(12)) = 3\) B
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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 15:27
f(12) = greatest prime of 12! is 11. g(11) = smallest prime of (2^11 + 1)
Since 2^10 = 1024, 2^11 = 2048. Therefore g(11) = 2049.
Since its odd number, check the next smallest prime factor answer choice Now, 2+4+9 = 15, 2049 is divisible by 3.
Therefore, answer is B



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 17:13
f(x) represents the greatest prime factor of x!. 12!=1*2*3*4*5......9*10*11*12 Distinct Prime factors of 12! are 2,3,5,7 and 11. Hence the greatest prime factor of 12! is 11
f(12)=11
g(x) represents the smallest prime factor of \(2^x+1\) g(11) is the smallest prime factor of \(2^{11}+1\)
\(2^{11}\)+1 = 1 (Mod 2). Hence \(2^x+1\) is not divisible by 2.
\(2^{11}\)= \((1)^{11}\) Mod 3 \(2^{11}+1\)= [(1)+1] Mod 3 \(2^{11}\)+1= 0 Mod 3 \(2^{11}+1\) is divisible by 3. Hence the smallest prime factor of \(2^{11}+1\) is 3.
(g(f(12))=3
IMO B



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For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 18:16
\(\) \(f(12) =\) the greatest prime factor of \(12! = 12*11*10*9*...*1\) > \(f(12) = 11\).
\(g(f(12)) = g(11) =\) the smallest prime factor of \((2^{11}+1) =\) the smallest prime factor of \(2049.\)
Since \(2049 = 3 * 683\), where 3 and 683 are both prime factors, then \(g(f(12)) = g(11) = 3.\)
Answer is (B)



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For every positive integer x, f(x) represents the greatest prime fact
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Updated on: 19 Jul 2019, 20:54
For every positive integer xx, f(x)f(x) represents the greatest prime factor of x!x!, and g(x)g(x) represents the smallest prime factor of 2x+12x+1. What is(g(f(12))? solve for (g(f(12)) f(12)= greatest prime factor of 12! ; 11 so g(11) = 2^(x+1) ; 2^11+1 ; 2048+1 ; 2049 so smallest prime factor ; 3 IMO B
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Originally posted by Archit3110 on 18 Jul 2019, 19:00.
Last edited by Archit3110 on 19 Jul 2019, 20:54, edited 1 time in total.



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For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 20:26
f(12) = 12! ==> greatest prime factor of 12! = 11
g(11) = \(2^{11}\)+1 = 2048 + 1 = 2049 ==> 2+0+4+9 = 15, which is divisible by 3 ==> smallest prime factor of \(2^{11}\) + 1 = 3 (choice B)



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 20:32
(g(f(12))) f(12)= greatest prime factor of 12! This means the highest prime number from 1 to 12 which is 7. Hence f(12)=7 Now g(7) is the least prime factor of ((2^7)+1) (2^7)+1 = 128+1= 129. Prime factors of 129 are {3 and13}. Hence g(7)=3. The answer is therefore B.
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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 21:13
f(x) = greatest prime factor of x! and g(x) = smallest prime factor of 2^x+1 What is (g(f(12))?
f(12) = greatest prime factor of 12!, > 12 * 11 *10! Greatest prime factor above is 11
g(11) = smallest prime factor of 2^11 + 1, which is 2
Correct answer A



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 21:14
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))?
A. 2 B. 3 C. 5 D. 7 E. 11
Given (g(f(12)) f(12) = highest prime factor of 12! will be 11 since there will no prime factors greater than 11 now g(11) = smallest prime factor of\(2^{11}\) +1
\(2^{11}\) will be even and +1 will make it odd now \(2^{11}\) +1 = 2048 +1 =2049 this is completely divisble by 3 giving 683 thus smallest is 3 hence B



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 21:22
Given: x is an integer, f(x)=greatest prime factor of x!, g(x)=smallest prime factor of (2^x)+1 To find: g(f(12))=?
Solution: For f(12), x=12 so prime factors for 12! are 2,3,5,7,11 therefore, greatest prime factor=11. Hence f(12)=11 now, g(f(12))=g(11) g(11) is smallest prime factor for (2^x)+1 where x=11 2^11+1=2048+1=2049 Prime factors=3 & 683. Samllest prime factor = 3 Hence, g(11)=3
Answer: B



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For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 21:28
f(x) represents the greatest prime factor of x! g(x) represents the smallest prime factor of \(2^x\)+1
(g(f(12))?
f(12) = 11 (greatest prime factor of 12!)
(g(11)) = 3 (smallest prime factor of 2^11+1 = 2049 = 3*683)
(g(f(12)) = 3
B is the answer



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 21:37
f(x) represents the greatest prime factor of x! g(x) represents the smallest prime factor of \(2^x\)+1 We need to find value of (g(f(12))? Solution: f(12) equals to greatest prime factor of 12!=12*11*10......*1. Greatest prime factor is 11. Now, g(11) equals to 2^(11)+1. 2^(11)+1=2049, and smallest prime factor is 3 (B)



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 21:52
f(12) = greatest prime factor of 12! The greatest prime factor of 12! is 11 f(12) = 11 g(11) = smallest prime factor of 2^11 + 1 = smallest prime factor of 2049 = 3 The answer is (B).
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