NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 17:07 It is currently 26 Apr 2024, 17:07
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

For every even positive integer m, f(m) represents

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
B
oss198
Manager
Manager
Joined: 18 Jul 2013
Posts: 69
Own Kudos [?]: 359 [41]
Given Kudos: 120
Location: Italy
Schools: LBS '21 Insead Sept19 Intake (A) IESE '21 (A$)
GMAT 1: 600 Q42 V31
GMAT 2: 700 Q48 V38
GPA: 3.75
Send PM
For every even positive integer m, f(m) represents [#permalink] New post   07 Jan 2014, 15:51
41
Bookmarks
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

80% (01:21) correct 20% (01:39) wrong based on 703 sessions
Hide Show timer Statistics
For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2x4x6x8x10x12. What is the greatest prime factor of f(24)?

A. 23
B. 19
C. 17
D. 13
E. 11
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14831
Own Kudos [?]: 64940 [17]
Given Kudos: 427
Location: Pune, India
Send PM
Re: For every even positive integer m, f(m) represents [#permalink] New post   07 Jan 2014, 20:33
14
Kudos
3
Bookmarks
Expert Reply
oss198 wrote:
For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2x4x6x8x10x12. What is the greatest prime factor of f(24)?

A. 23
B. 19
C. 17
D. 13
E. 11


First let's find out what f(24) is.

f(24) = 2*4*6*8*10*12*14*16*18*20*22*24

The prime factors of 24 are 2 and 3.
The prime factors of 22 are 2 and 11.
11 must be the greatest prime factor you will have in this product. Every term smaller than 22 will certainly have 2 as a factor since they are all even so they cannot have another factor greater than 11.

Answer (E)
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619244 [12]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: For every even positive integer m, f(m) represents [#permalink] New post   08 Jan 2014, 05:11
1
Kudos
11
Bookmarks
Expert Reply
oss198 wrote:
For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2x4x6x8x10x12. What is the greatest prime factor of f(24)?

A. 23
B. 19
C. 17
D. 13
E. 11


Similar questions to practice:
for-every-positive-even-integer-n-the-function-h-n-is-126691.html
for-every-positive-even-integer-n-the-function-h-n-149722.html
for-any-integer-p-p-is-equal-to-the-product-of-all-the-int-112494.html
x-is-the-product-of-all-even-numbers-from-2-to-50-inclusive-156545.html
if-a-and-b-are-odd-integers-a-b-represents-the-product-of-144714.html

Hope this helps.
General Discussion
avatar
B
bharatdivvela
Intern
Intern
Joined: 17 Oct 2013
Posts: 37
Own Kudos [?]: 39 [1]
Given Kudos: 21
Schools: HEC Dec"18
GMAT Date: 02-04-2014
Send PM
Re: For every even positive integer m, f(m) represents [#permalink] New post   08 Jan 2014, 05:39
1
Bookmarks
oss198 wrote:
For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2x4x6x8x10x12. What is the greatest prime factor of f(24)?

A. 23
B. 19
C. 17
D. 13
E. 11



f(24)= 2*4*6*8*10*12*14*16*18*20*22*24
now we need greatest prime factor, so we have to check from right to reach the solution faster
prime factors of 24=2,3
prime factors of 22= 2,11
hence 11 will be the greatest prime factor of f(24)
avatar
S
SeregaP
Manager
Manager
Joined: 03 Jan 2017
Posts: 88
Own Kudos [?]: 83 [0]
Given Kudos: 4
Send PM
Re: For every even positive integer m, f(m) represents [#permalink] New post   22 Mar 2017, 15:37
E, because as we know that the set is made of even integers, we can divide 24 by 2
hence 12, 11 is the closest prime
avatar
B
daviddaviddavid
Manager
Manager
Joined: 26 Mar 2017
Posts: 62
Own Kudos [?]: 221 [0]
Given Kudos: 1
Send PM
Re: For every even positive integer m, f(m) represents [#permalink] New post   13 May 2017, 07:42
I just factored all numbers

after doing this over and over again it just takes you around 20 secs.
User avatar
B
pinkAugust2308
Intern
Intern
Joined: 07 Jun 2017
Posts: 5
Own Kudos [?]: 1 [0]
Given Kudos: 14
GMAT 1: 560 Q42 V25
Send PM
Re: For every even positive integer m, f(m) represents [#permalink] New post   29 Aug 2017, 08:59
F(24)=2×4×6×8×10×12×14×16×18×20×22×24
The prime factors are 2, 3, 5,7,11 so the LCM is 11.
Answer is E.

Posted from my mobile device
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6277 [0]
Given Kudos: 1646
Send PM
Re: For every even positive integer m, f(m) represents [#permalink] New post   01 Sep 2017, 12:01
Expert Reply
oss198 wrote:
For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2x4x6x8x10x12. What is the greatest prime factor of f(24)?

A. 23
B. 19
C. 17
D. 13
E. 11


We are given that for every even positive integer m, f(m) represents the product of all even integers from 2 to m inclusive. We need to determine the greatest prime factor of f(24).

f(24) = 2 x 4 x 6 x … x 20 x 22 x 24

We see from the even numbers from 2 to 24 inclusive that 22 (which is 2 x 11) produces the largest prime factor of 11.

Answer: E
avatar
thang62590
Intern
Intern
Joined: 04 Jun 2017
Posts: 5
Own Kudos [?]: 0 [0]
Given Kudos: 5
Send PM
For every even positive integer m, f(m) represents [#permalink] New post   Updated on: 03 Sep 2017, 11:06
The function given is f(24) = 2*4*6*...*24.

f(24) = (2*1) * (2*2) * (2*4) * ... * (2*12). Note that you can further factor out the 2's. There are twelve 2's.

f(24) = (2^12) * (1*2*3*4* ... * 12)

(1*2*3*4* ... * 12) are all factors of f(24) with 11 being the greatest prime factor. Answer is E.

Originally posted by thang62590 on 02 Sep 2017, 08:18.
Last edited by thang62590 on 03 Sep 2017, 11:06, edited 1 time in total.
User avatar
L
arvind910619
Director
Director
Joined: 20 Dec 2015
Status:Learning
Posts: 876
Own Kudos [?]: 566 [0]
Given Kudos: 755
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
GPA: 3.4
WE:Engineering (Manufacturing)
Send PM
Reviews Badge
Re: For every even positive integer m, f(m) represents [#permalink] New post   02 Sep 2017, 23:25
F(m) =2*4*6......24
=2^12*1*2*3*.....12
=2^12*12!
so we have 11 as the highest prime factor
User avatar
S
Paras96
Director
Director
Joined: 11 Sep 2022
Posts: 501
Own Kudos [?]: 152 [0]
Given Kudos: 2
Location: India
Paras: Bhawsar
GMAT 1: 590 Q47 V24
GMAT 2: 580 Q49 V21
GMAT 3: 700 Q49 V35
GPA: 3.2
WE:Project Management (Other)
Send PM
Re: For every even positive integer m, f(m) represents [#permalink] New post   14 Sep 2023, 10:08
For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2x4x6x8x10x12. What is the greatest prime factor of f(24)?

f(24) = 24x22x20x18x......2
24= 2x2x2x3
22=2x11
18=2x9

As we until 2, we will get the no.s in the form of 2k where k is an integer, since 22 is the no. when broken down yields 2x11 where 11 is the maximum value of prime no., 11 is the answer

Hence E
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6072
Own Kudos [?]: 4690 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
GMAT ToolKit User
Re: For every even positive integer m, f(m) represents [#permalink] New post   14 Sep 2023, 11:12
oss198 wrote:
For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2x4x6x8x10x12. What is the greatest prime factor of f(24)?

A. 23
B. 19
C. 17
D. 13
E. 11

\(f(24) = 2*4*6*8*10*12*14*16*18*20*22*24\)

Here, \(22 = 2*11\), thus Answer must be (E) 11
GMAT Club Bot
gmatclubot
Re: For every even positive integer m, f(m) represents [#permalink]
14 Sep 2023, 11:12
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions