GMAT Changed on April 16th - Read about the latest changes here
close

It is currently 24 May 2018, 18:35
Search
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
Unanswered

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 Workbook Learn more
Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar
CLICK HERE TO HIDE/SHOW EVENTS

6- If f(n) is the product of n consecutive

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
  Sort by Date Sort by Kudos  
Search for:
 
Print view
First unread post
Author Message
TAGS:

Hide Tags
Expert Post
1 KUDOS received
e-GMAT Representative
User avatar
G
Joined: 04 Jan 2015
Posts: 1238
6- If f(n) is the product of n consecutive [#permalink]

Show Tags

New post Updated on: 07 Mar 2018, 06:07
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (01:47) correct 36% (03:17) wrong based on 99 sessions

HideShow timer Statistics

e-GMAT Question:



If \(f(n)\) is the product of \(n\) consecutive integers from \(1\) to \(N\), then what is the number of odd factors of\(f(10)\).
A) 30
B) 60
C) 120
D) 256
E) 512

This is

Question 11 of The e-GMAT Number Properties Marathon




Go to

the next level of the Marathon

Spoiler: OA

_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com


Originally posted by EgmatQuantExpert on 28 Feb 2018, 03:11.
Last edited by EgmatQuantExpert on 07 Mar 2018, 06:07, edited 2 times in total.
BSchool Forum Moderator
User avatar
G
Joined: 07 Jan 2016
Posts: 723
Location: India
GMAT 1: 710 Q49 V36
Reviews Badge
Re: 6- If f(n) is the product of n consecutive [#permalink]

Show Tags

New post 28 Feb 2018, 03:46
EgmatQuantExpert wrote:

Question:



If \(f(n)\) is the product of \(n\) consecutive integers from \(1\) to \(N\), then what is the number of odd factors of\(f(10)\).
A) 30
B) 60
C) 120
D) 256
E) 512


10! = 1 x 2 x 3 x 2^2 x 5 x 2 x 3 x 7 x 2^3 x 3^2 x 2 x 5
10! = 2^8 x 3^4 x 5^2 x 7

factors = 9 x 5 x 3 x 2


odd factors = 5x3x2

(A) 30 imo
Expert Post
e-GMAT Representative
User avatar
G
Joined: 04 Jan 2015
Posts: 1238
Re: 6- If f(n) is the product of n consecutive [#permalink]

Show Tags

New post 28 Feb 2018, 11:44
Expert's post
1
This post was
BOOKMARKED

Solution:



We are given:
\(F(n)= 1×2×3×4×5×……….×n\)
We need to find the number of odd factors of \(f(10)\).
Thus, we need to find the value of \(f(10).\) Then, we need to write \(f(10)\) in its prime factorized form. After which we can calculate the value of odd factors of\(f(10)\).
Number of Odd factors \(f(10)\)
    \(f(10)= 1×2×3×4×5×6×7×8×9×10\)
    \(f(10)= 1×2×3×(2×2)×5×(2*3)×7×(2*2*2)×(3*3)×(2*5)\)
    \(f(10)= 2^8 * 3^4 * 5^2 *7\)
Odd factors of \(f(10)\)= (power of 3+1)*(power of 5+1)* (power of 7+1)
Odd factors of \(f(10)=5*3*2\)
Odd factors of \(f(10)=30\)
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com
Expert Post
e-GMAT Representative
User avatar
G
Joined: 04 Jan 2015
Posts: 1238
Re: 6- If f(n) is the product of n consecutive [#permalink]

Show Tags

New post 28 Feb 2018, 11:55
Expert's post

Solution:



We are given:
\(f(n)= n!\)
Thus we can write:
    \(f(10)= 10!\)
    \(10! = 1×2×3×4×5×6×7×8×9×10\)
    \(10!= 2^8 * 3^4 * 5^2 *7\)
Total factors of \(10!= 9*5*3*2=270\)
Total factors = Even factors + Odd factors
Odd factors= Total factors – Even factors
Thus, if we can find the even factors of \(10!\) then we can find the odd factors of \(10!\).
\(10!= 2*(2^7 * 3^4 * 5^2 *7)\)
We can say that all the factors of \(2^7 * 3^4 * 5^2 *7\) after multiplying by \(2\) becomes a factor of \(10!\).
We also know that any number, which is multiple of \(2\), is an even number.
Thus,
    Total number of factors of\(2^7 * 3^4 * 5^2 *7\) = Even number of factors of \(10!.\)
    Even factors of \(10!\)= Total factors of \(2^7 * 3^4 * 5^2 *7\)
    Even factors of \(10!\)= \(8*5*3*2\)
    Even factors of \(10!\)=\(240\)
Therefore, Odd factors= Total factors – Even factors
Odd factors= \(270-240\)
Odd factors=\(30\)
Answer: Option \(A\)
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com
Intern
Intern
User avatar
B
Status: Studying Quant
Joined: 04 Sep 2017
Posts: 29
GPA: 3.6
WE: Sales (Computer Software)
6- If f(n) is the product of n consecutive [#permalink]

Show Tags

New post 08 May 2018, 05:01
1
This post was
BOOKMARKED
EgmatQuantExpert wrote:

e-GMAT Question:



If \(f(n)\) is the product of \(n\) consecutive integers from \(1\) to \(N\), then what is the number of odd factors of\(f(10)\).
A) 30
B) 60
C) 120
D) 256
E) 512

This is

Question 11 of The e-GMAT Number Properties Marathon




Go to

the next level of the Marathon



The principle this question is testing is Finding the Number of Factors of an Integer

Number of odd factors of 10!

10!=1x2x3x4x5x6x7x8x9x10.
10!=2x3x(\(2^{2}\))x5x(2x3)x7x(\(2^{3}\))x(\(3^{2}\))x(5x2)
10!=\(2^{8}\)\(3^{4}\)\(5^{2}\)7

Take the exponents of the odd factors. Add 1 to each of them and multiply them by each other.
(4+1)(2+1)(1+1)=30

Answer = A
Attachments

Prime factors.PNG
Prime factors.PNG [ 29.38 KiB | Viewed 279 times ]

DS Forum Moderator
User avatar
P
Joined: 27 Oct 2017
Posts: 463
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
6- If f(n) is the product of n consecutive [#permalink]

Show Tags

New post 13 May 2018, 08:43
HI
I feel question would have been more interesting if there is an option 270 in the answer choices.
If someone fail to read odd factors (as I did ;) ), one would mark 270 as answer.
Fortunately, answer choices saved me.

Regards

EgmatQuantExpert wrote:

Solution:



We are given:
\(F(n)= 1×2×3×4×5×……….×n\)
We need to find the number of odd factors of \(f(10)\).
Thus, we need to find the value of \(f(10).\) Then, we need to write \(f(10)\) in its prime factorized form. After which we can calculate the value of odd factors of\(f(10)\).
Number of Odd factors \(f(10)\)
    \(f(10)= 1×2×3×4×5×6×7×8×9×10\)
    \(f(10)= 1×2×3×(2×2)×5×(2*3)×7×(2*2*2)×(3*3)×(2*5)\)
    \(f(10)= 2^8 * 3^4 * 5^2 *7\)
Odd factors of \(f(10)\)= (power of 3+1)*(power of 5+1)* (power of 7+1)
Odd factors of \(f(10)=5*3*2\)
Odd factors of \(f(10)=30\)

_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups

6- If f(n) is the product of n consecutive   [#permalink] 13 May 2018, 08:43
Print view
First unread post
Display posts from previous: Sort by

6- If f(n) is the product of n consecutive

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

Moderators: chetan2u, VeritasPrepKarishma, niks18, Bunuel, mikemcgarry, generis

Search for:


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions