It is currently 23 Oct 2017, 10:40

### 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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 22 Jan 2012
Posts: 22

Kudos [?]: 51 [2], given: 11

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

### Show Tags

19 Mar 2012, 23:15
2
KUDOS
15
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

64% (00:52) correct 36% (00:54) wrong based on 616 sessions

### HideShow 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
[Reveal] Spoiler: OA

Kudos [?]: 51 [2], given: 11

Math Expert
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129475 [6], given: 12201

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

### Show Tags

19 Mar 2012, 23:47
6
KUDOS
Expert's post
17
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.
_________________

Kudos [?]: 129475 [6], given: 12201

Intern
Joined: 25 Aug 2010
Posts: 17

Kudos [?]: 1 [0], given: 11

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

### Show Tags

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
_________________

regards
eshwar

Kudos [?]: 1 [0], given: 11

Math Expert
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129475 [0], given: 12201

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

### Show Tags

23 Mar 2012, 02:49
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."
_________________

Kudos [?]: 129475 [0], given: 12201

Manager
Joined: 07 Dec 2011
Posts: 151

Kudos [?]: 41 [0], given: 31

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

### Show Tags

23 Mar 2012, 03:34
If we write down 10! in expanded form we can see that 4 pairs of 2x3. 10!^2 will thus have 8.

Kudos [?]: 41 [0], given: 31

Intern
Joined: 22 Jan 2012
Posts: 22

Kudos [?]: 51 [0], given: 11

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

### Show Tags

23 Mar 2012, 22:44
wow, that link really helped thanks soooo much; it's so much simpler now that I understand the concept

Kudos [?]: 51 [0], given: 11

Intern
Joined: 14 Feb 2012
Posts: 40

Kudos [?]: 42 [0], given: 13

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

### Show Tags

11 Apr 2012, 02:19
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

Kudos [?]: 42 [0], given: 13

Manager
Joined: 13 Feb 2012
Posts: 143

Kudos [?]: 17 [0], given: 107

GMAT 1: 720 Q49 V38
GPA: 3.67
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]

### Show Tags

11 Apr 2012, 02:22
Thank Bunuel for very clear and concise answer.
_________________

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

Kudos [?]: 17 [0], given: 107

Senior Manager
Joined: 03 Sep 2012
Posts: 352

Kudos [?]: 232 [3], given: 35

Location: United States
Concentration: Healthcare, Strategy
GMAT 1: 730 Q48 V42
GPA: 3.88
WE: Medicine and Health (Health Care)
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]

### Show Tags

01 Oct 2012, 06:13
3
KUDOS
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

Kudos [?]: 232 [3], given: 35

Senior Manager
Joined: 03 Sep 2012
Posts: 352

Kudos [?]: 232 [0], given: 35

Location: United States
Concentration: Healthcare, Strategy
GMAT 1: 730 Q48 V42
GPA: 3.88
WE: Medicine and Health (Health Care)
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]

### Show Tags

01 Oct 2012, 06:13
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

Kudos [?]: 232 [0], given: 35

Intern
Joined: 23 May 2012
Posts: 31

Kudos [?]: 43 [0], given: 11

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

### Show Tags

15 Oct 2012, 08:21
The tricky thing is limiting factor : 3...
Bunuel you made it look simple..
But is it really sub 600?

Kudos [?]: 43 [0], given: 11

Math Expert
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129475 [0], given: 12201

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

### Show Tags

15 Oct 2012, 08:24
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.
_________________

Kudos [?]: 129475 [0], given: 12201

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1853

Kudos [?]: 2633 [1], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]

### Show Tags

10 Jul 2014, 01:06
1
KUDOS
$$(10!)^2 = 10^2 * 9^2 * 8^2 * 7^2 * 6^2 * 5^2 * 4^2 * 3^2 * 2^2$$

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

Kudos [?]: 2633 [1], given: 193

Intern
Joined: 27 Feb 2015
Posts: 2

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

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

### Show Tags

15 Apr 2015, 06:33
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.

I shall be looking for your reply.

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

Math Expert
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129475 [0], given: 12201

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

### Show Tags

15 Apr 2015, 06:41
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.

I shall be looking for your reply.

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...
_________________

Kudos [?]: 129475 [0], given: 12201

Intern
Joined: 27 Feb 2015
Posts: 2

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

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

### Show Tags

15 Apr 2015, 06:45
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

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

Math Expert
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129475 [0], given: 12201

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

### Show Tags

15 Apr 2015, 07:04
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.
_________________

Kudos [?]: 129475 [0], given: 12201

BSchool Forum Moderator
Joined: 23 Sep 2015
Posts: 405

Kudos [?]: 89 [0], given: 72

Location: France
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]

### Show Tags

17 Jan 2016, 05:42
Hi Bunuel,

Is it ok to square the 10 before computing or did I just get lucky?
$$\frac{100}{6}+ \frac{100}{36}= 6 + 2$$
_________________

New Application Tracker : update your school profiles instantly!

Kudos [?]: 89 [0], given: 72

Math Expert
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129475 [0], given: 12201

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

### Show Tags

17 Jan 2016, 05:48
Icecream87 wrote:
Hi Bunuel,

Is it ok to square the 10 before computing or did I just get lucky?
$$\frac{100}{6}+ \frac{100}{36}= 6 + 2$$

Why do you want to square?
What do you square?
How is 10/3+10/3^2 squared equal to $$\frac{100}{6}+ \frac{100}{36}$$?
How do you get $$\frac{100}{6}= 6$$?
_________________

Kudos [?]: 129475 [0], given: 12201

BSchool Forum Moderator
Joined: 23 Sep 2015
Posts: 405

Kudos [?]: 89 [0], given: 72

Location: France
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)
Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]

### Show Tags

17 Jan 2016, 06:22
Bunuel wrote:
Icecream87 wrote:
Hi Bunuel,

Is it ok to square the 10 before computing or did I just get lucky?
$$\frac{100}{6}+ \frac{100}{36}= 6 + 2$$

Why do you want to square?
What do you square?
How is 10/3+10/3^2 squared equal to $$\frac{100}{6}+ \frac{100}{36}$$?
How do you get $$\frac{100}{6}= 6$$?

Good question. I somehow managed to omit the 1 (from 16) on 100/6 to only maintain 6 to my liking. And I also just squared the 10 initially not the whole fraction and I dind't get why 3 was used instead of 6. Anyway, I am having trouble understanding all the powers.

Does this mean that if we had 15 instead of 6 we would have taken the biggest of the primes of 15 to find the powers: $$\frac{10!^2}{15^x}$$then we would use $$\frac{10}{5}= 2*2$$ so as to get $$15^4$$ ?
Thanks
_________________

New Application Tracker : update your school profiles instantly!

Kudos [?]: 89 [0], given: 72

Re: If 6^y is a factor of (10!)^2, What is the greatest possible   [#permalink] 17 Jan 2016, 06:22

Go to page    1   2    Next  [ 24 posts ]

Display posts from previous: Sort by

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

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

 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®.