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

 It is currently 08 Dec 2019, 03:37 ### 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  S
Joined: 12 Apr 2017
Posts: 142
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

f(12) = 12!, 11 is the highest prime factor

G(11) = 2^11 + 1, and 2 becomes the lowest prime factor.
Manager  S
Joined: 24 Jan 2019
Posts: 107
Location: India
Concentration: Strategy, Finance
GMAT 1: 730 Q51 V38 GPA: 4
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))?

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.)

Manager  G
Joined: 15 Jun 2019
Posts: 216
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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
Manager  S
Joined: 10 Aug 2016
Posts: 68
Location: India
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 $$(g(f(12))$$?

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

Manager  G
Joined: 06 Feb 2019
Posts: 110
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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

Senior Manager  P
Joined: 20 Mar 2018
Posts: 407
Location: Ghana
Concentration: Finance, Real Estate
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
So f(x) = greatest prime factor of x!
g(x)= smallest prime factor of (2^x+1)

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

Posted from my mobile device
Manager  S
Joined: 12 Mar 2019
Posts: 158
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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
Director  V
Status: Manager
Joined: 27 Oct 2018
Posts: 746
Location: Egypt
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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
Intern  B
Joined: 08 Jan 2018
Posts: 38
GMAT 1: 730 Q51 V38 Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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.

VP  V
Joined: 19 Oct 2018
Posts: 1157
Location: India
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!.
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
Senior Manager  D
Joined: 30 Sep 2017
Posts: 451
GMAT 1: 720 Q49 V40 GPA: 3.8
For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1

$$f(12) =$$ 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 $$g(f(12)) = g(11) = 3.$$

GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5446
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

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

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.
Rice (Jones) School Moderator P
Joined: 18 Jun 2018
Posts: 315
Location: United States (AZ)
Concentration: Finance, Healthcare
GMAT 1: 600 Q44 V28 GPA: 3.36
For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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)
Director  P
Joined: 18 May 2019
Posts: 529
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
(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.

Posted from my mobile device
Manager  S
Joined: 12 Mar 2018
Posts: 83
Location: United States
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

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

Director  V
Joined: 28 Jul 2016
Posts: 670
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
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))?

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
Manager  S
Joined: 29 Apr 2017
Posts: 56
Location: India
Concentration: Operations, Other
GMAT 1: 660 Q43 V38 GPA: 4
WE: Operations (Transportation)
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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

Senior Manager  P
Joined: 31 May 2018
Posts: 457
Location: United States
Concentration: Finance, Marketing
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!
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

Manager  G
Joined: 30 May 2019
Posts: 109
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!
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)
Manager  G
Status: Not Applying
Joined: 27 Apr 2009
Posts: 178
Location: India
Schools: HBS '14 (A)
GMAT 1: 730 Q51 V36 Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

### Show Tags

1
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

_________________
http://www.wizius.in
Better Prep. Better Scores. Better Schools

Guaranteed Admission to Top-50 MBA Programs
You either get-in or get your money-back. Re: For every positive integer x, f(x) represents the greatest prime fact   [#permalink] 18 Jul 2019, 21:52

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  