Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 22 Jan 2012
Posts: 17

If 6^y is a factor of (10!)^2, What is the greatest possible
[#permalink]
Show Tags
19 Mar 2012, 23:15
Question Stats:
65% (01:23) correct 35% (01:23) wrong based on 707 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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 59075

Re: If 6^y is a factor of (10!)^2, What is the greatest possible
[#permalink]
Show Tags
19 Mar 2012, 23:47
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: everythingaboutfactorialsonthegmat85592.html (explanation of this concept in details). Similar questions to practice: pandqareintegersifpisdivisibleby10qandcannot109038.htmlquestionaboutpprimeintonfactorial108086.htmlhowmanyzerosdoes100endwith100599.htmlifnistheproductofintegersfrom1to20inclusive106289.htmlwhatisthegreatestvalueofmsuchthat4misafactorof105746.htmlfindthenumberoftrailingzerosintheproductof108248.htmlfindthenumberoftrailingzerosintheexpansionof108249.htmlifdisapositiveintegerandfistheproductofthefirst126692.htmlifmistheproductofallintegersfrom1to40inclusive108971.htmlif10252isdivisibleby10nwhatisthegreatest106060.htmlHope it helps.
_________________




Intern
Joined: 25 Aug 2010
Posts: 16

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
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 59075

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."
_________________



Intern
Joined: 22 Jan 2012
Posts: 17

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



Intern
Joined: 14 Feb 2012
Posts: 35
Location: Germany
Concentration: Technology, Strategy
GMAT Date: 06132012

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



Manager
Joined: 13 Feb 2012
Posts: 126
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....



Current Student
Joined: 03 Sep 2012
Posts: 372
Location: United States
Concentration: Healthcare, Strategy
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 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: 372
Location: United States
Concentration: Healthcare, Strategy
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



Intern
Joined: 23 May 2012
Posts: 28

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?



Math Expert
Joined: 02 Sep 2009
Posts: 59075

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.
_________________



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1729
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
\((10!)^2 = 10^2 * 9^2 * 8^2 * 7^2 * 6^2 * 5^2 * 4^2 * 3^2 * 2^2\) 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 \(3^2\) = 3^2Total powers of 3 = 8 Answer = 8
_________________
Kindly press "+1 Kudos" to appreciate



Intern
Joined: 27 Feb 2015
Posts: 2

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.



Math Expert
Joined: 02 Sep 2009
Posts: 59075

Re: If 6^y is a factor of (10!)^2, What is the greatest possible
[#permalink]
Show Tags
15 Apr 2015, 06:41
harrisadiq wrote: 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...
_________________



Intern
Joined: 27 Feb 2015
Posts: 2

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



Math Expert
Joined: 02 Sep 2009
Posts: 59075

Re: If 6^y is a factor of (10!)^2, What is the greatest possible
[#permalink]
Show Tags
15 Apr 2015, 07:04
harrisadiq wrote: 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.
_________________



Senior Manager
Joined: 23 Sep 2015
Posts: 371
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? \(\frac{100}{6}+ \frac{100}{36}= 6 + 2\)
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 59075

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 \(\frac{100}{6}= 6\)?
_________________



Senior Manager
Joined: 23 Sep 2015
Posts: 371
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
_________________



Current Student
Joined: 20 Jan 2017
Posts: 51
Location: United States (NY)
GMAT 1: 750 Q48 V44 GMAT 2: 610 Q34 V41
GPA: 3.92

Re: If 6^y is a factor of (10!)^2, What is the greatest possible
[#permalink]
Show Tags
24 Jan 2017, 20:18
1) The problem is asking us to find the number of 2*3 prime factors in the sequence of consecutive integers 2) 10/3=3; 10/9=1; 3+1=4 3) Since the sequence is squared 4*2=8
The greatest possible value of y is 8




Re: If 6^y is a factor of (10!)^2, What is the greatest possible
[#permalink]
24 Jan 2017, 20:18



Go to page
1 2
Next
[ 25 posts ]



