Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Sep 2014, 11:59

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If 6^y is a factor of (10!)^2, What is the greatest possible

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 22 Jan 2012
Posts: 23
Followers: 0

Kudos [?]: 10 [0], given: 11

If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post 19 Mar 2012, 22:15
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

60% (01:51) correct 40% (00:50) wrong based on 187 sessions
If 6^y is a factor of (10!)^2, What is the greatest possible value of y ?

A. 2
B. 4
C. 6
D. 8
E. 10
[Reveal] Spoiler: OA
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23064
Followers: 3537

Kudos [?]: 27229 [3] , given: 2725

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post 19 Mar 2012, 22:47
3
This post received
KUDOS
Expert's post
essarr wrote:
If 6^y is a factor of (10!)^2, What is the greatest possible value of y ?

A. 2
B. 4
C. 6
D. 8
E. 10

... I was hoping to get a better explanation, as I'm still confused about the explanation provided.
Thanks!


6=2*3. Now, there will be obviously less 3's than 2's in (10!)^2, so maximum power of 3 will be limiting factor for maximum power of 6, which is y.

Finding the maximum powers of a prime number 3, in 10!: \frac{10}{3}+\frac{10}{3^2}=3+1=4 (take only quotients into account). So, we have that the maximum power of 3 in 10! is 4, thus maximum power of 3 in (10!)^2 will be 8: (3^4)^2=3^8. As discussed 8 is the maximum power of 6 as well.

Answer: D.

For more on this subject check: everything-about-factorials-on-the-gmat-85592.html (explanation of this concept in details).

Similar questions to practice:
p-and-q-are-integers-if-p-is-divisible-by-10-q-and-cannot-109038.html
question-about-p-prime-in-to-n-factorial-108086.html
how-many-zeros-does-100-end-with-100599.html
if-n-is-the-product-of-integers-from-1-to-20-inclusive-106289.html
what-is-the-greatest-value-of-m-such-that-4-m-is-a-factor-of-105746.html
find-the-number-of-trailing-zeros-in-the-product-of-108248.html
find-the-number-of-trailing-zeros-in-the-expansion-of-108249.html
if-d-is-a-positive-integer-and-f-is-the-product-of-the-first-126692.html
if-m-is-the-product-of-all-integers-from-1-to-40-inclusive-108971.html
if-10-2-5-2-is-divisible-by-10-n-what-is-the-greatest-106060.html

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 25 Aug 2010
Posts: 17
Followers: 0

Kudos [?]: 0 [0], given: 11

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post 23 Mar 2012, 01:45
hi bunuel,

i did nt understand how did u get 3's more than 2's in 10!.

i am of the view that 10! = 10*9*8*7*6*5*4*3*2*1

if we expand this we get = 2*5 *3*3 *2*2*2 *7 *3*2* 5* 2*2* 3* 2 *1

so there are 8 2's and 4 3's in the expansion above.

so how to interpret this and proceed
_________________

regards
eshwar

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23064
Followers: 3537

Kudos [?]: 27229 [0], given: 2725

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post 23 Mar 2012, 01:49
Expert's post
pappueshwar wrote:
hi bunuel,

i did nt understand how did u get 3's more than 2's in 10!.

i am of the view that 10! = 10*9*8*7*6*5*4*3*2*1

if we expand this we get = 2*5 *3*3 *2*2*2 *7 *3*2* 5* 2*2* 3* 2 *1

so there are 8 2's and 4 3's in the expansion above.

so how to interpret this and proceed


It's: "there will be obviously LESS 3's than 2's in (10!)^2, so maximum power of 3 will be limiting factor for maximum power of 6, which is y."
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 07 Dec 2011
Posts: 174
Location: India
Followers: 1

Kudos [?]: 32 [0], given: 24

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post 23 Mar 2012, 02:34
If we write down 10! in expanded form we can see that 4 pairs of 2x3. 10!^2 will thus have 8.
Intern
Intern
avatar
Joined: 22 Jan 2012
Posts: 23
Followers: 0

Kudos [?]: 10 [0], given: 11

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post 23 Mar 2012, 21:44
wow, that link really helped thanks soooo much; it's so much simpler now that I understand the concept
Intern
Intern
avatar
Joined: 14 Feb 2012
Posts: 40
Location: Germany
Concentration: Technology, Strategy
GMAT Date: 06-13-2012
Followers: 0

Kudos [?]: 16 [0], given: 13

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post 11 Apr 2012, 01:19
essarr wrote:
If 6^y is a factor of (10!)^2, What is the greatest possible value of y ?

A. 2
B. 4
C. 6
D. 8
E. 10


... I was hoping to get a better explanation, as I'm still confused about the explanation provided.
Thanks!


10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7
6= 2*3

Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice D
Manager
Manager
avatar
Joined: 13 Feb 2012
Posts: 137
Followers: 0

Kudos [?]: 21 [0], given: 82

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post 11 Apr 2012, 01:22
Thank Bunuel for very clear and concise answer.
_________________

Kudos!!!... If you think I help you in some ways....

Manager
Manager
User avatar
Joined: 28 Jul 2011
Posts: 213
Followers: 0

Kudos [?]: 29 [0], given: 13

Number properties [#permalink] New post 21 Jul 2012, 17:21
If 6y is a factor of (10!)^2, what is the greatest possible value of y?

A. 2
B. 4
C. 6
D. 8
E. 10
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23064
Followers: 3537

Kudos [?]: 27229 [0], given: 2725

Re: Number properties [#permalink] New post 22 Jul 2012, 02:00
Expert's post
Merging similar topics. Please refer to the solutions above.

kuttingchai wrote:
If 6y is a factor of (10!)^2, what is the greatest possible value of y?

A. 2
B. 4
C. 6
D. 8
E. 10


Notice that it should be 6^y instead of 6y. Please check the questions while posting.

Also, please read and follow: rules-for-posting-please-read-this-before-posting-133935.html (rule #3).
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Current Student
User avatar
Joined: 03 Sep 2012
Posts: 339
Location: United States
Concentration: Healthcare, Strategy
GMAT 1: 730 Q48 V42
GPA: 3.88
WE: Medicine and Health (Health Care)
Followers: 10

Kudos [?]: 76 [0], given: 31

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post 01 Oct 2012, 05:13
Factorial of 10 can be written as 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

or 2 x 5 x 3 x 3 x 2 x 2 x 2 x 7 x 2 x 3 x 5 x 2 x 2 x 3 x 2 x 1

So in 10 factorial we have 08 2's and 4 three's ... Square of 10 factorial will give us 16 2's and 8 three's

to get six we know that we would have to take one 2 and one three ..the maximum number of three's we can take is 8 therefore 8 different 6's can be formed therefore max possible value of y can be 6 ..

2 x 3
2 x 3
2 x 3
2 x 3
2 x 3
2 x 3
2 x 3
2 x 3

D..
_________________

"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas

Current Student
User avatar
Joined: 03 Sep 2012
Posts: 339
Location: United States
Concentration: Healthcare, Strategy
GMAT 1: 730 Q48 V42
GPA: 3.88
WE: Medicine and Health (Health Care)
Followers: 10

Kudos [?]: 76 [0], given: 31

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post 01 Oct 2012, 05:13
Factorial of 10 can be written as 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

or 2 x 5 x 3 x 3 x 2 x 2 x 2 x 7 x 2 x 3 x 5 x 2 x 2 x 3 x 2 x 1

So in 10 factorial we have 08 2's and 4 three's ... Square of 10 factorial will give us 16 2's and 8 three's

to get six we know that we would have to take one 2 and one three ..the maximum number of three's we can take is 8 therefore 8 different 6's can be formed therefore max possible value of y can be 8 ..

2 x 3
2 x 3
2 x 3
2 x 3
2 x 3
2 x 3
2 x 3
2 x 3

D..
_________________

"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas

Intern
Intern
avatar
Joined: 23 May 2012
Posts: 31
Followers: 0

Kudos [?]: 9 [0], given: 11

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post 15 Oct 2012, 07:21
The tricky thing is limiting factor : 3...
Bunuel you made it look simple..
But is it really sub 600?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23064
Followers: 3537

Kudos [?]: 27229 [0], given: 2725

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post 15 Oct 2012, 07:24
Expert's post
CEO
CEO
User avatar
Joined: 09 Sep 2013
Posts: 2550
Followers: 200

Kudos [?]: 40 [0], given: 0

Premium Member
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post 09 Jul 2014, 05:52
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Director
Director
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 976
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 6

Kudos [?]: 248 [0], given: 167

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post 10 Jul 2014, 00:06
(10!)^2 = 10^2 * 9^2 * 8^2 * 7^2 * 6^2 * 5^2 * 4^2 * 3^2 * 2^2

Just concentrate on the power of 3 (Power of 2's would be more as compared to 3; so it can be ignored)

9^2 = 3^4

6^2 = 3^2 * 2^2

3^2 = 3^2

Total powers of 3 = 8

Answer = 8
_________________

Kindly press "+1 Kudos" to appreciate :)

Re: If 6^y is a factor of (10!)^2, What is the greatest possible   [#permalink] 10 Jul 2014, 00:06
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic What is the greatest possible area of a square that is rxs0005 3 14 Feb 2012, 05:41
What is the greatest possible common divisor of two Riuscita 3 15 Mar 2006, 21:23
1078 is divided by 56^r . What is the greatest possible rlevochkin 3 30 Nov 2005, 07:43
If 15!/3^m is an integer, what is the greatest possible faisalt 5 27 Nov 2005, 18:08
What is the greatest possible common divisor of two cpcalanoc 3 19 Dec 2004, 17:46
Display posts from previous: Sort by

If 6^y is a factor of (10!)^2, What is the greatest possible

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.