GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 09 Dec 2019, 12:27 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # For every positive integer x, f(x) represents the greatest prime fact

Author Message
TAGS:

### Hide Tags

Manager  B
Joined: 01 Jan 2019
Posts: 80
Concentration: Finance, Entrepreneurship
GPA: 3.24
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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  S
Joined: 18 Sep 2018
Posts: 100
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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  P
Joined: 22 Nov 2018
Posts: 562
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

1
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
Senior Manager  P
Joined: 10 Jan 2017
Posts: 330
Location: India
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
IMO correct answer is B - 3
explanation as attached
Attachments IMG_20190718_211529.JPG [ 1.14 MiB | Viewed 226 times ]

Senior Manager  P
Joined: 13 Feb 2018
Posts: 488
GMAT 1: 640 Q48 V28 For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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 second-lowest prime) as 2+0+4+9=15, which is divisible by 3

So g(f(12))=3

IMo
Ans: B
Manager  S
Joined: 18 Feb 2017
Posts: 93
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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  G
Joined: 17 Jul 2014
Posts: 177
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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

Director  P
Joined: 24 Nov 2016
Posts: 935
Location: United States
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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.

Manager  G
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

1
IMO-B

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  G
Joined: 30 Nov 2017
Posts: 194
WE: Consulting (Consulting)
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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))

Thank you for kudos.
_________________
Be Braver, you cannot cross a chasm in two small jumps...
Intern  B
Joined: 05 May 2013
Posts: 12
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

(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  S
Joined: 06 Aug 2018
Posts: 97
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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  B
Joined: 24 Jun 2019
Posts: 113
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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))

Manager  S
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

1
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.

Please hit kudos if you like the solution.
Manager  G
Joined: 12 Jul 2017
Posts: 216
Schools: NUS '22 (S)
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

1
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

Regards,
Rishav
Intern  B
Joined: 08 Apr 2011
Posts: 12
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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

Manager  S
Joined: 22 Oct 2018
Posts: 73
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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  G
Joined: 28 Feb 2014
Posts: 209
Location: India
GPA: 3.97
WE: Engineering (Education)
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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  B
Joined: 13 Mar 2019
Posts: 28
Location: India
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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  G
Joined: 18 Jun 2013
Posts: 139
Location: India
Concentration: Technology, General Management
GMAT 1: 690 Q50 V35 GPA: 3.2
WE: Information Technology (Consulting)
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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 ]

Display posts from previous: Sort by

# For every positive integer x, f(x) represents the greatest prime fact  