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

 It is currently 01 Sep 2015, 12:20

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Intern
Joined: 22 Jan 2012
Posts: 22
Followers: 0

Kudos [?]: 18 [0], given: 11

If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  19 Mar 2012, 22:15
1
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

61% (02:01) correct 39% (00:52) wrong based on 280 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
Math Expert
Joined: 02 Sep 2009
Posts: 29173
Followers: 4736

Kudos [?]: 50033 [3] , given: 7519

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

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
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.
_________________
Intern
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]  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

Math Expert
Joined: 02 Sep 2009
Posts: 29173
Followers: 4736

Kudos [?]: 50033 [0], given: 7519

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  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."
_________________
Manager
Joined: 07 Dec 2011
Posts: 174
Location: India
Followers: 1

Kudos [?]: 34 [0], given: 24

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  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
Joined: 22 Jan 2012
Posts: 22
Followers: 0

Kudos [?]: 18 [0], given: 11

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  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
Joined: 14 Feb 2012
Posts: 40
Location: Germany
Concentration: Technology, Strategy
GMAT Date: 06-13-2012
Followers: 0

Kudos [?]: 28 [0], given: 13

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  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
Joined: 13 Feb 2012
Posts: 142
GMAT 1: 720 Q49 V38
GPA: 3.67
Followers: 0

Kudos [?]: 4 [0], given: 103

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

Current Student
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: 12

Kudos [?]: 118 [0], given: 31

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  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
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: 12

Kudos [?]: 118 [0], given: 31

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  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
Joined: 23 May 2012
Posts: 31
Followers: 0

Kudos [?]: 20 [0], given: 11

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  15 Oct 2012, 07:21
The tricky thing is limiting factor : 3...
Bunuel you made it look simple..
But is it really sub 600?
Math Expert
Joined: 02 Sep 2009
Posts: 29173
Followers: 4736

Kudos [?]: 50033 [0], given: 7519

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  15 Oct 2012, 07:24
Expert's post
mindmind wrote:
The tricky thing is limiting factor : 3...
Bunuel you made it look simple..
But is it really sub 600?

It's ~700 level question. Tag changed.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 6162
Followers: 344

Kudos [?]: 70 [0], given: 0

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  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.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1859
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 26

Kudos [?]: 1069 [0], given: 193

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  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

_________________

Kindly press "+1 Kudos" to appreciate

Intern
Joined: 27 Feb 2015
Posts: 3
Followers: 0

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

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  15 Apr 2015, 05:33
H:

I was doing trailing zero questions and I got the concept but I have some difficulty in understanding a concept in which sometimes we factorize the denominator but sometimes we don't factorize. For example

If 6^y is a factor of (10!)^2, What is the greatest possible value of y ?. We are not factorizing 6 as 2 and 3 because higher power of 3 is sufficient
but in this question... If N is the product of all positive integers less than 31, than what is the greatest integer k for which N/18^k is an integer? we are factoring 18 as 2^2 and 3.

Could you please help me to understand when we have to factorize and when we do not.

Math Expert
Joined: 02 Sep 2009
Posts: 29173
Followers: 4736

Kudos [?]: 50033 [0], given: 7519

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  15 Apr 2015, 05:41
Expert's post
H:

I was doing trailing zero questions and I got the concept but I have some difficulty in understanding a concept in which sometimes we factorize the denominator but sometimes we don't factorize. For example

If 6^y is a factor of (10!)^2, What is the greatest possible value of y ?. We are not factorizing 6 as 2 and 3 because higher power of 3 is sufficient
but in this question... If N is the product of all positive integers less than 31, than what is the greatest integer k for which N/18^k is an integer? we are factoring 18 as 2^2 and 3.

Could you please help me to understand when we have to factorize and when we do not.

Aren't we make prime factorization in both cases? 6=2*3 and 18=2*3^2. Sorry, but your question is not very clear...
_________________
Intern
Joined: 27 Feb 2015
Posts: 3
Followers: 0

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

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  15 Apr 2015, 05:45
in question number 1, we are not considering the power of 2's but in q2 we are considering the power of 2 and 3 both. I am unable to understand when we consider all the bases as we did in q2 but not in q1
Math Expert
Joined: 02 Sep 2009
Posts: 29173
Followers: 4736

Kudos [?]: 50033 [0], given: 7519

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  15 Apr 2015, 06:04
Expert's post
in question number 1, we are not considering the power of 2's but in q2 we are considering the power of 2 and 3 both. I am unable to understand when we consider all the bases as we did in q2 but not in q1

Yes, we could count only 3's in the second question too and then divide that by 2 (because of 3^2) to get the power of 18.
_________________
Intern
Joined: 27 Feb 2015
Posts: 3
Followers: 0

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

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]  15 Apr 2015, 06:08
Sorry bro . could you explain it with an example. I didnt get it (
Re: If 6^y is a factor of (10!)^2, What is the greatest possible   [#permalink] 15 Apr 2015, 06:08
Similar topics Replies Last post
Similar
Topics:
11 What is the greatest possible common divisor of two differen 10 22 Nov 2012, 09:22
5 What is the greatest possible area of a square that is 7 14 Feb 2012, 05:41
10 If 6^k is a factor of (40!), what is the greatest possible value of k? 7 10 Aug 2011, 08:00
31 What is the greatest possible area of a triangular region 21 01 Nov 2009, 21:12
2 What is the greatest possible area of a triangular region with one 8 13 Jun 2009, 14:18
Display posts from previous: Sort by