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

It is currently 05 Dec 2019, 08:00

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59561
For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 07:59
1
5
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

72% (01:39) correct 28% (01:46) wrong based on 283 sessions

HideShow timer Statistics

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


 

This question was provided by Veritas Prep
for the Game of Timers Competition

 


_________________
Manager
Manager
User avatar
G
Joined: 08 Jan 2018
Posts: 129
CAT Tests
For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post Updated on: 21 Jul 2019, 21:22
1
Given:
f(x): greatest prime factor of x!
g(x): smallest prime factor of \(2^x + 1\)

f(12): greatest prime factor of 12! = 12*11*10*9*8*7*6*5*4*3*2*1 -> 11
g(11): smallest prime factor of \(2^{11} + 1\)= 2049 = 3 * 683 -> 3

Therefore, (g(f(23)) = 3

Answer B

Originally posted by Sayon on 18 Jul 2019, 08:08.
Last edited by Sayon on 21 Jul 2019, 21:22, edited 2 times in total.
Director
Director
User avatar
P
Joined: 16 Jan 2019
Posts: 507
Location: India
Concentration: General Management
WE: Sales (Other)
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 08:10
1
\(f(12)\) is the greatest prime factor of \(12!\) which is \(11\)

\(g(11)\) is the smallest prime factorial of \(2^11+1\)

\(2^11+1 = 2049\)

\(2049\) is an odd number and the sum of digits of \(2049\) is \(15\) which is a multiple of \(3\). So \(2049\) is divisible by \(3\) and so \(3\) is the smallest prime factor of \(2049\)

\(g(f(12)) = 3\)

Answer is (B)
SVP
SVP
User avatar
D
Joined: 03 Jun 2019
Posts: 1874
Location: India
Premium Member Reviews Badge CAT Tests
For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post Updated on: 19 Jul 2019, 03:22
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: 1. For every positive integer x, f(x) represents the greatest prime factor of x!
2. For every positive integer x,g(x) represents the smallest prime factor of 2^x+1
Asked: What is (g(f(12))?

12!=1*2*3*4*5*6*7*8*9*10*11*12=> Prime factors = 2,3,5,7 and 11 => Greatest prime factor = 11
f(12) = greatest prime factor of 12! = 11
g(f(12)) = g(11) = smallest prime factor of (2^11+1 = 2048+1= 2049)
Since 2049 is odd, 2 is not a factor
2049/3 = 643, 3 is a factor of 2049
g(11) = 3 = g(f(12))

IMO B
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com

Originally posted by Kinshook on 18 Jul 2019, 08:10.
Last edited by Kinshook on 19 Jul 2019, 03:22, edited 2 times in total.
ISB School Moderator
User avatar
G
Joined: 08 Dec 2013
Posts: 615
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '21
GMAT 1: 630 Q47 V30
WE: Operations (Non-Profit and Government)
Reviews Badge CAT Tests
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 08:12
1
f(12) gives 12! so greatest prime factor is 11
g(11) gives us (2^11 + 1), i.e. 2049, smallest prime factor of which is 3.
_________________
Kindly drop a '+1 Kudos' if you find this post helpful.

GMAT Math Book


-I never wanted what I gave up
I never gave up what I wanted-
Manager
Manager
avatar
G
Joined: 26 Jan 2016
Posts: 181
CAT Tests
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 08:14
2
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))?

Largest prime factor of f(12)=11
Now g(11)=2^11+1

Now, we know with power of 2...units digit can be 2,4,8,6
For 2^11, units digit would be 8.
2^3=8 and 8+1=9 which is divisible by 3
Similarly, 2^7=128 & 128+1=129 (again divisible by 3)

Hence based on pattern 2^11 +1 would be divisible by 3

Hence B
_________________
Your Kudos can boost my morale..!!

I am on a journey. Gradually I'll there..!!
Senior Manager
Senior Manager
avatar
P
Joined: 27 Aug 2014
Posts: 368
Location: Netherlands
Concentration: Finance, Strategy
Schools: LBS '22, ISB '21
GPA: 3.9
WE: Analyst (Energy and Utilities)
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 08:22
1
IMO answer is B

largest prime factor of f(12)= 12! is 11
and g(11) = 2048 = 683*3
as 683 is odd, smaller prime number than 3, which is 2 is not possible, so answer is 3, B
Manager
Manager
avatar
G
Joined: 30 May 2018
Posts: 157
Location: Canada
GMAT 1: 710 Q49 V36
GPA: 3.8
Premium Member Reviews Badge
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 08:28
1
B

First off, we need to find the greatest prime factor of 12!. So, 12! = 12*11*10 ....*1

Clearly, 12 is not prime, so greatest prime factor is 11. So f(12) = 11

Now, g(f(12)) = g(11) = 2^11 + 1 = 2049

Factorize 2049, we get 2049 = 3*683

We dont have to try to factorize 683 further since 3 is the smallest prime factor possible.
Manager
Manager
avatar
S
Joined: 17 Apr 2018
Posts: 107
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 08:29
1
f(12) = largest prime divisor of 12! ==> 11

Now g(11) = smallest prime factor of 2^11 +1
2 cannot be the factor.

Try with 3
Remainder
(-1)^11 +1
-1+1=0
3 is smallest prime factor.

Hence, B is the answer.
Manager
Manager
User avatar
G
Joined: 28 Jan 2019
Posts: 127
Location: Peru
Premium Member
For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post Updated on: 18 Jul 2019, 19:34
1
First, we have to find f(12), which is greatest factor of 12!, so we have 11 from this one.

Then, we have to find out g(11) = 2^11 +1, which is 2048 + 1 = 2049, factorizing, we have that it has only two factors 3 and 683.

g(f(12))= 3, so (B) is our answer

Originally posted by Mizar18 on 18 Jul 2019, 08:31.
Last edited by Mizar18 on 18 Jul 2019, 19:34, edited 2 times in total.
Manager
Manager
avatar
S
Joined: 21 Jan 2019
Posts: 100
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 08:35
1
Quote:
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)= greatest prime factor of 12 !
As 12! = 12 *11* 10!
therefore f(12) = 11
Now g(11)= smallest prime factor of \(2^(11)\) +1

\(2^(10)\) = 1024
\(2^(11)\) = 2048
therefore \(2^(11)\) +1 = 2049
divisible by 3
Hence option B is the answer
Senior Manager
Senior Manager
User avatar
G
Joined: 05 Mar 2017
Posts: 261
Location: India
Concentration: General Management, Marketing
GPA: 3.6
WE: Marketing (Hospitality and Tourism)
Reviews Badge CAT Tests
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 08:38
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))?

This is an easy question.
F(12) = 12! so the greatest prime factor is going to be 11.
g(11) = 2^11 +1 = 2048+1 = 2049. (Trick for divisibility the total is divisible by 3 and not be 2)
so the smallest prime factor of G(11) is going to be 3.


A. 2
B. 3
C. 5
D. 7
E. 11

Hence the answer is B. (3).
BSchool Moderator
User avatar
G
Joined: 07 Dec 2018
Posts: 146
Location: India
CAT Tests
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 08:40
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

f(12) = greatest prime factor of x! = 11 (Because 12! = 12*11*10*9*...*1)
g(11) = smallest prime factor of \(2^{11}\)+1
\(2^{11}\)= 2048

So, we need to find the smallest prime factor of 2049.
Can't be divided by 2. But the sum of digits is divided by 3 so, Ans should be (B)
Manager
Manager
User avatar
G
Joined: 10 Mar 2019
Posts: 75
Location: Russian Federation
Schools: Booth '22, Haas '22
GMAT 1: 730 Q50 V39
GPA: 3.95
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 08:40
1
The greatest prime factor of 12! is 11.
Ok, the next step is 2^(11)+1=2049
2049 is not divisible by 2 because it is odd
But it is divisible by 3
And thus 3 is the answer

IMO B
Director
Director
User avatar
P
Joined: 04 Sep 2015
Posts: 664
Location: India
WE: Information Technology (Computer Software)
Premium Member Reviews Badge
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 08:40
1
IMO :B

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

Sol:

greatest prime factor of 12! is 11, because rest of the number will be smaller than 11 and the numbers greater than this number will not be prime numbers.
then g((2^11)+1)=2048+1=2049

2049 is divisible by 1,3... 2049 so 3 is the smallest prime factor for g(x)

B is the correct answer.
Manager
Manager
avatar
S
Joined: 26 Mar 2019
Posts: 105
Concentration: Finance, Strategy
For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post Updated on: 18 Jul 2019, 08:43
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 \(2^x+1\). What is \((g(f(12))\)?


The task tells us that \(f(x)\) represents greatest prime factor of \(x!\). Prime factor is a positive integer which is not equal to \(1\) and has two factors: itself and \(1\). Let us find \(f(x)\) first, and then find \(g(f(x))\).
\(f(12)\) = greatest prime factor of \(12!\)
Let us find out what greatest prime factor of \(12!\) is: \(12! = 1 * 2* 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12\).
As we can see from above, the greatest of the numbers is \(11\) which is the greatest prime factor for \(12!\)
\(12!\) cannot have higher prime factor since \(12\) itself is equal to \(2*2*3\), and any product of its numbers will have more factors than \(2\) and will not be prime.
Hence, \(f(12) = 11\)

Now, let us find what \(g(f(12))\) is.
\(g(f(12)) = g(11)\) and is the smallest prime factor of \(2^1+1\)
\(2^1+1=2048+1=2049\)
Let us find what are the factors for \(2049\). As \(2+0+4+9=15\) and is divisible by \(3\), \(3\) is one of prime factors for \(2049\). Also, we can notice that \(2049\) is odd, and hence not dividable by \(2\).
Because of this, the smallest prime factor of \(2049\) is \(3\).
\(g(11) = 3\).

Answer: B

Originally posted by RusskiyLev on 18 Jul 2019, 08:41.
Last edited by RusskiyLev on 18 Jul 2019, 08:43, edited 1 time in total.
Manager
Manager
avatar
S
Joined: 11 Feb 2018
Posts: 80
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 08:41
1
Lets break down the simplification of g(f(12)) in to two steps.

1. f(12) - f(12) will be the largest prime factor of 12! (as stated in the question). \(12!=12*11*10*9*8*7*...*2*1\). It is obvious that the largest prime factor here will be 11. Lets move to the next step now.

2. \(g(f(12))\) - \(f(12)=11\), so expression becomes, \(g(11)\), \(g(11)\) is defined as the smallest prime factor of 2^(11)+1, now as 1 is being added to a power of 2 the resulting value shall be odd, so 2 can't be the smallest prime factor. 2^(11)=2048+1=2049. The next smallest prime factor after 2 is 3, we apply the divisibility by 3 rule to see if 3 is a factor of 2049. Divisibility rule of 3 states that if the sum of the digits of any number is divisible by 3 then that number is also divisible by 3. \(2+0+4+9=15\) and 15 is divisible by 3 so 2049 is thus also divisible by 3. You can also obviously do the division directly without knowing the divisibility rule to see if \(\frac{2049}{3}\) is an integer and you will see that it is and that \(\frac{2049}{3}=683\) but knowing the rule saves us the extra step and speeds things up.

\(g(f(12))=g(11)=3\). Answer is B.
Senior Manager
Senior Manager
User avatar
P
Joined: 12 Dec 2015
Posts: 444
CAT Tests
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 08:42
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))?
Solution:
f(12) = greatest prime factor of 12! = greatest prime factor of (12*11*10!) = 11
g(f(12) = g(11) = smallest prime factor of \(2^11+1\) = smallest prime factor of 2049 = smallest prime factor of (3* 683) = 3. (2^11 = 1024*2=2048)

A. 2
B. 3 --> correct
C. 5
D. 7
E. 11
Manager
Manager
avatar
S
Joined: 30 Aug 2018
Posts: 104
Location: India
Concentration: Finance, Accounting
GMAT 1: 600 Q49 V23
GPA: 3.36
WE: Consulting (Computer Software)
Premium Member
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 08:44
1
f(12) => 12*11*10....1
greatest prime=11
g(11)= 2^11+1=2049
Smallest prime factor of 2049
checked from options Answer=3.
Manager
Manager
User avatar
S
Joined: 27 Mar 2018
Posts: 79
Location: India
GMAT ToolKit User
Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

Show Tags

New post 18 Jul 2019, 08:45
1
f(x)= greatest prime factor of x!
=> f(12)= greatest prime factor of 12! = 12*11*10*...
f(12)=11

g(11)=smallest prime factor of 2^11+1
=> smallest prime factor of 2049
Start checking from smallest prime number we get 3 which is a factor of 2049.
Hence, g(f(12))=3. Option B
_________________
Thank you for the kudos. You are awesome! :)
GMAT Club Bot
Re: For every positive integer x, f(x) represents the greatest prime fact   [#permalink] 18 Jul 2019, 08:45

Go to page    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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne