Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 20 Jul 2019, 01:03

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

What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?

  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: 56300
What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?  [#permalink]

Show Tags

New post 05 Apr 2016, 07:43
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:40) correct 39% (02:03) wrong based on 268 sessions

HideShow timer Statistics


Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7764
Re: What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?  [#permalink]

Show Tags

New post 05 Apr 2016, 19:28
1
2
Bunuel wrote:
What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?

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



Hello,
\(\frac{(11! × 10!  + 10! × 9!)}{111}\)...
In numerator take out 10!*9! as common term

\(\frac{10!*9!(11 × 10  + 1 )}{111}\)
\(\frac{10!*9!*111}{111}\)
\(10!*9!\)
10! has 7 as the greatest prime factor, so ans is 7
D
_________________
Senior Manager
Senior Manager
avatar
P
Joined: 27 Dec 2016
Posts: 332
CAT Tests
Re: What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?  [#permalink]

Show Tags

New post 31 Oct 2017, 06:55
Hi, could anyone please explain to me how 10!*9! has 7 as its highest prime factor? I was able to get to 10!*9! but didn't know how to proceed further.

Thank You!
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7764
Re: What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?  [#permalink]

Show Tags

New post 31 Oct 2017, 07:01
1
csaluja wrote:
Hi, could anyone please explain to me how 10!*9! has 7 as its highest prime factor? I was able to get to 10!*9! but didn't know how to proceed further.

Thank You!


hi..
ill help you..
10! means product of first 10 numbers or 1*2*3*4*5*6*7*8*9*10 so this has 7 as the greatest prime factor
similarly 10!*9! = 1*2*3...10*1*2*3...*9... again &7 is the biggest prime factor
_________________
Senior Manager
Senior Manager
avatar
P
Joined: 27 Dec 2016
Posts: 332
CAT Tests
Re: What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?  [#permalink]

Show Tags

New post 31 Oct 2017, 12:18
chetan2u wrote:
csaluja wrote:
Hi, could anyone please explain to me how 10!*9! has 7 as its highest prime factor? I was able to get to 10!*9! but didn't know how to proceed further.

Thank You!


hi..
ill help you..
10! means product of first 10 numbers or 1*2*3*4*5*6*7*8*9*10 so this has 7 as the greatest prime factor
similarly 10!*9! = 1*2*3...10*1*2*3...*9... again &7 is the biggest prime factor



This was very helpful! Thank You & Kudos given!!
Intern
Intern
User avatar
B
Joined: 22 Jun 2017
Posts: 17
Location: Italy
GPA: 3.64
GMAT ToolKit User
What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?  [#permalink]

Show Tags

New post 02 Nov 2017, 08:00
Can someone link similar exercises? thanks
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3852
Location: Canada
What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?  [#permalink]

Show Tags

New post Updated on: 02 Apr 2018, 16:18
1
Top Contributor
Bunuel wrote:
What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?

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


We are trying to find the greatest prime factor of the given value.
Since we can only find the greatest prime factor of an INTEGER, we can conclude that the numerator must be divisible by 111, so that it cancels out with the denominator.
How does this happen?

First notice that we can factor 10! out of the given numerator
That is, 11! × 10!  + 10! × 9! = 10!(11! + 9!)

Next we should recognize that there's also a 9! "hiding" within 11!
11! = (11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)
= (11)(10)(9!)
This means (11! + 9!) = 9![(11)(10) + 1]

So, 11! × 10!  + 10! × 9! = 10!(11! + 9!)
= (10!)(9!)[(11)(10) + 1]
= (10!)(9!)[110 + 1]
= (10!)(9!)[111]

So, (11! × 10!  + 10! × 9!)/111 = (10!)(9!)[111]/111
= (10!)(9!)
= [(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)][(9)(8)(7)(6)(5)(4)(3)(2)(1)]
= [(2)(5)(3)(3)(2)(2)(2)(7)(3)(2)(5)(2)(2)(3)(2)(1)][(3)(3)(2)(2)(2)(7)(3)(2)(5)(2)(2)(3)(2)(1)]

The greatest prime factor is 7
Answer: D

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image

Originally posted by GMATPrepNow on 02 Nov 2017, 11:09.
Last edited by GMATPrepNow on 02 Apr 2018, 16:18, edited 1 time in total.
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6968
Location: United States (CA)
Re: What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?  [#permalink]

Show Tags

New post 02 Nov 2017, 17:03
Bunuel wrote:
What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?

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


We can simplify the given expression:

(11! x 10! + 10! x 9!)/111

(11 x 10 x 9! x 10! + 10! x 9!)/111

Let’s pull out the common factor of 9! x 10! from the two terms in the expression:

9! x 10! x (11 x 10 + 1)/111

9! x 10! x 111/111

9! x 10!

We see that the largest prime factor of 9! x 10! is 7 (since 11 won’t divide into either 9! or 10!).

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56300
What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?  [#permalink]

Show Tags

New post 02 Nov 2017, 22:49
1
Giampa wrote:
Can someone link similar exercises? thanks


Similar questions:
https://gmatclub.com/forum/what-is-the- ... 90090.html
https://gmatclub.com/forum/what-is-the- ... 91913.html
http://gmatclub.com/forum/what-is-the-g ... 58991.html
http://gmatclub.com/forum/what-is-the-g ... 04757.html
http://gmatclub.com/forum/what-is-the-g ... 70126.html
http://gmatclub.com/forum/what-is-the-g ... 90425.html
https://gmatclub.com/forum/what-is-the- ... 94487.html
https://gmatclub.com/forum/what-is-the- ... 40381.html
https://gmatclub.com/forum/what-is-the- ... 19097.html
https://gmatclub.com/forum/what-is-the- ... 30937.html
http://gmatclub.com/forum/what-is-the-g ... 13300.html
https://gmatclub.com/forum/what-is-the- ... 31625.html


Hope it helps.
_________________
Intern
Intern
User avatar
B
Joined: 22 Jun 2017
Posts: 17
Location: Italy
GPA: 3.64
GMAT ToolKit User
Re: What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?  [#permalink]

Show Tags

New post 03 Nov 2017, 00:33
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11712
Re: What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?  [#permalink]

Show Tags

New post 12 Jan 2019, 07:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?   [#permalink] 12 Jan 2019, 07:25
Display posts from previous: Sort by

What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?

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





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