NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 16:56 It is currently 26 Apr 2024, 16:56
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

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
essarr
Intern
Intern
Joined: 22 Jan 2012
Posts: 12
Own Kudos [?]: 195 [94]
Given Kudos: 11
Send PM
If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post   19 Mar 2012, 23:15
11
Kudos
83
Bookmarks
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

68% (01:20) correct 32% (01:26) wrong based on 1575 sessions
Hide Show timer Statistics
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
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619243 [56]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post   19 Mar 2012, 23:47
20
Kudos
36
Bookmarks
Expert Reply
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.
User avatar
B
vomhorizon
Senior Manager
Senior Manager
Joined: 03 Sep 2012
Posts: 356
Own Kudos [?]: 929 [8]
Given Kudos: 47
Location: United States
Concentration: Healthcare, Strategy
Schools: Duke '16 (A) McCombs '20 (A) Foster '20 (A)
GMAT 1: 730 Q48 V42
GPA: 3.88
WE:Medicine and Health (Health Care)
Send PM
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post   01 Oct 2012, 06:13
6
Kudos
2
Bookmarks
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..
General Discussion
avatar
pappueshwar
Intern
Intern
Joined: 25 Aug 2010
Posts: 16
Own Kudos [?]: 4 [0]
Given Kudos: 11
Send PM
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post   23 Mar 2012, 02:45
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
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619243 [1]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post   23 Mar 2012, 02:49
1
Kudos
Expert Reply
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."
avatar
essarr
Intern
Intern
Joined: 22 Jan 2012
Posts: 12
Own Kudos [?]: 195 [0]
Given Kudos: 11
Send PM
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post   23 Mar 2012, 22:44
wow, that link really helped thanks soooo much; it's so much simpler now that I understand the concept
avatar
B
hellscream
Manager
Manager
Joined: 13 Feb 2012
Posts: 121
Own Kudos [?]: 80 [0]
Given Kudos: 109
GMAT 1: 720 Q49 V38
GPA: 3.67
Send PM
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post   11 Apr 2012, 02:22
Thank Bunuel for very clear and concise answer.
avatar
PareshGmat
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1562
Own Kudos [?]: 7208 [2]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post   10 Jul 2014, 01:06
1
Kudos
1
Bookmarks
\((10!)^2 = 10^2 * 9^2 * 8^2 * 7^2 * 6^2 * 5^2 * 4^2 * 3^2 * 2^2\)

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
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11181
Own Kudos [?]: 31969 [2]
Given Kudos: 291
Send PM
Reviews Badge
Re: If 6y is a factor of (10!)2 , what is the greatest possible value o [#permalink] New post   12 Feb 2017, 05:25
2
Kudos
Expert Reply
gupta87 wrote:
If
6^y is a factor of (10!)^2, what is the greatest possible value of y?

Ans is 8......kindly explain.........i understood there are 8 3s but there are 14 2s


Hi,

Since you already know there are 8 3s and 14 2s, I'll start from thereon...
Each 6 is composed of 3 and 2...
So it requires equal number of 3 and 2..

But (14-8) that is 6 of 2s do not have a 3 to make a 6..
Therefore the number of 6s will depend on the integer (3or2) with lowest value thus answer is 8..
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16845 [0]
Given Kudos: 165
Send PM
If 6y is a factor of (10!)2 , what is the greatest possible value o [#permalink] New post   12 Feb 2017, 05:33
Expert Reply
gupta87 wrote:
If
6^y is a factor of (10!)^2, what is the greatest possible value of y?

Ans is 8......kindly explain.........i understood there are 8 3s but there are 14 2s



Hey,

PFB the solution.

    • \(6^y\) can be written as \(2^y * 3^y\)

    • To find the greatest possible value of y, we need to find out how many \(3\)'s are there in \((10!)^2\)

    • Now \(10! = 1 * 2 *3 * 4 * 5 * 6 * 7 * 8 * 9 * 10\)
    • Which can be written as -
      o \(10! = 2^8 * 3^4 * 5^2 * 7^1\)

    • Therefore \((10!)^2 = 2^{16} * 3^8 * 5^4 * 7^2\)
    • As we can see there are 16 2's but only 8 3's

    • But to make a \(6\) we need both one \(2\) and one \(3\).

    • Therefore, the maximum number of \(6\)'s that we can make is \(8\).

    • Please note: that out of the 16 2's we can use only 8 of them and the rest 8 cannot be clubbed with any 3's, as there aren't any left.

    • Hence, the value of y = \(8\).


Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

User avatar
B
Akriti_Khetawat
Intern
Intern
Joined: 21 Jul 2023
Posts: 12
Own Kudos [?]: 0 [0]
Given Kudos: 7
Send PM
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post   17 Mar 2024, 04:12
Bunuel wrote:
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: https://gmatclub.com/forum/everything-a ... 85592.html (explanation of this concept in details).

Similar questions to practice:
https://gmatclub.com/forum/p-and-q-are- ... 09038.html
https://gmatclub.com/forum/question-abo ... 08086.html
https://gmatclub.com/forum/how-many-zer ... 00599.html
https://gmatclub.com/forum/if-n-is-the- ... 06289.html
https://gmatclub.com/forum/what-is-the- ... 05746.html
https://gmatclub.com/forum/find-the-num ... 08248.html
https://gmatclub.com/forum/find-the-num ... 08249.html
https://gmatclub.com/forum/if-d-is-a-po ... 26692.html
https://gmatclub.com/forum/if-m-is-the- ... 08971.html
https://gmatclub.com/forum/if-10-2-5-2- ... 06060.html

Hope it helps.

­Hey what's a limiting factor and why are we considering only that number to find the answer? 
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619243 [1]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink] New post   17 Mar 2024, 05:08
1
Kudos
Expert Reply
Akriti_Khetawat wrote:
Bunuel wrote:
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: https://gmatclub.com/forum/everything-a ... 85592.html (explanation of this concept in details).

Similar questions to practice:
https://gmatclub.com/forum/p-and-q-are- ... 09038.html
https://gmatclub.com/forum/question-abo ... 08086.html
https://gmatclub.com/forum/how-many-zer ... 00599.html
https://gmatclub.com/forum/if-n-is-the- ... 06289.html
https://gmatclub.com/forum/what-is-the- ... 05746.html
https://gmatclub.com/forum/find-the-num ... 08248.html
https://gmatclub.com/forum/find-the-num ... 08249.html
https://gmatclub.com/forum/if-d-is-a-po ... 26692.html
https://gmatclub.com/forum/if-m-is-the- ... 08971.html
https://gmatclub.com/forum/if-10-2-5-2- ... 06060.html

Hope it helps.

­Hey what's a limiting factor and why are we considering only that number to find the answer? 

­
There will be obviously less 3's than 2's in (10!)^2, so the power of 3 in (10!)^2 will determine the power of 6 in (10!)^2. Please follow the links given in that post for more.
GMAT Club Bot
gmatclubot
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]
17 Mar 2024, 05:08
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