Last visit was: 24 Jul 2024, 15:33 It is currently 24 Jul 2024, 15:33
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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Intern
Intern
Joined: 13 Mar 2020
Posts: 8
Own Kudos [?]: 13 [13]
Given Kudos: 24
Send PM
Most Helpful Reply
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4127
Own Kudos [?]: 9465 [10]
Given Kudos: 91
 Q51  V47
Send PM
General Discussion
Senior Manager
Senior Manager
Joined: 18 Sep 2018
Posts: 253
Own Kudos [?]: 204 [3]
Given Kudos: 322
Location: India
Concentration: Finance, International Business
GMAT 1: 690 Q49 V36
GPA: 3.72
WE:Investment Banking (Investment Banking)
Send PM
Senior Manager
Senior Manager
Joined: 18 Sep 2018
Posts: 253
Own Kudos [?]: 204 [0]
Given Kudos: 322
Location: India
Concentration: Finance, International Business
GMAT 1: 690 Q49 V36
GPA: 3.72
WE:Investment Banking (Investment Banking)
Send PM
Re: Which of the following could be a value of k if 10^k and 12^k are fact [#permalink]
IanStewart. Dyamnn..

Didn't think that way.??

Posted from my mobile device
Manager
Manager
Joined: 05 Jan 2020
Posts: 108
Own Kudos [?]: 52 [0]
Given Kudos: 353
Send PM
Re: Which of the following could be a value of k if 10^k and 12^k are fact [#permalink]
IanStewart wrote:
If you knew, say, that 10^13 was a factor of some number n, then certainly 10^12 would also be a factor of n. So if any answer from B through E were correct here, A would automatically also be correct. Since a GMAT question can only have one right answer, logically A is the only possible answer, so there's no reason to do any work.

You don't see questions set up like this on the actual test.


Hi,

I didn't understand what you meant by that. It will be really helpful if you can explain it in details.

Thank you :)

Posted from my mobile device
Manager
Manager
Joined: 05 Jan 2020
Posts: 108
Own Kudos [?]: 52 [0]
Given Kudos: 353
Send PM
Re: Which of the following could be a value of k if 10^k and 12^k are fact [#permalink]
Harsh9676 wrote:
IMO A

we need to find the value of K for which 10^K and 12^K become factors of 50!

So 10 = 2*5 and 12 = 2^2 * 3

Minimum value of K should have two 2s, one 3s and one 5s.

We can infer that 50! has already two 2s and one 3. We just need to find the max power of 5 in 50!

Quotient of (50/5 )+ Quotient of (50/5^2) = 10 + 2 = 12

Ans. A



Hi,

How did we infer that 50! has two 2s and one 3.? And why is it important to find the max power of 5 of 50!.?

Thank you. :)

Posted from my mobile device
Senior Manager
Senior Manager
Joined: 18 Sep 2018
Posts: 253
Own Kudos [?]: 204 [0]
Given Kudos: 322
Location: India
Concentration: Finance, International Business
GMAT 1: 690 Q49 V36
GPA: 3.72
WE:Investment Banking (Investment Banking)
Send PM
Re: Which of the following could be a value of k if 10^k and 12^k are fact [#permalink]
Nups1324

What he meant was if 10^16 is a factor of 50!, automatically 10^12, 10^13,10^14 and 10^15 would become factors of 50!

And since there can only be one answer straight away you can mark A.

Posted from my mobile device
Manager
Manager
Joined: 05 Jan 2020
Posts: 108
Own Kudos [?]: 52 [0]
Given Kudos: 353
Send PM
Re: Which of the following could be a value of k if 10^k and 12^k are fact [#permalink]
Harsh9676 wrote:
Nups1324

What he meant was if 10^16 is a factor of 50!, automatically 10^12, 10^13,10^14 and 10^15 would become factors of 50!

And since there can only be one answer straight away you can mark A.

Posted from my mobile device



Oh. Damn. I knew this rule but I couldn't see how I can use this.

That was smooth Ian. And thanks to you Harsh, I read it again and it clicked. :lol:

Can you explain me your working in detail? Harsh9676.

I really want to learn how you did it.

Thank you. :)
Senior Manager
Senior Manager
Joined: 18 Sep 2018
Posts: 253
Own Kudos [?]: 204 [1]
Given Kudos: 322
Location: India
Concentration: Finance, International Business
GMAT 1: 690 Q49 V36
GPA: 3.72
WE:Investment Banking (Investment Banking)
Send PM
Which of the following could be a value of k if 10^k and 12^k are fact [#permalink]
1
Kudos
Nups1324 wrote:
Harsh9676 wrote:
IMO A

we need to find the value of K for which 10^K and 12^K become factors of 50!

So 10 = 2*5 and 12 = 2^2 * 3

Minimum value of K should have two 2s, one 3s and one 5s.

We can infer that 50! has already two 2s and one 3. We just need to find the max power of 5 in 50!

Quotient of (50/5 )+ Quotient of (50/5^2) = 10 + 2 = 12

Ans. A


50! = 1*2*3*4*...*50. So 50! Has 2 twos and one 3.

We can also infer that the no of 2 s and no of 3 s in 50! Would be more than the no of 5s. This means that the no of 12s would be higher than no of 10s. So the limiting factor is 5.


So we need to find the no of 5 s in 50!.

Posted from my mobile device
Manager
Manager
Joined: 05 Jan 2020
Posts: 108
Own Kudos [?]: 52 [1]
Given Kudos: 353
Send PM
Re: Which of the following could be a value of k if 10^k and 12^k are fact [#permalink]
1
Bookmarks
Harsh9676 wrote:
Nups1324 wrote:
Harsh9676 wrote:
IMO A

we need to find the value of K for which 10^K and 12^K become factors of 50!

So 10 = 2*5 and 12 = 2^2 * 3

Minimum value of K should have two 2s, one 3s and one 5s.

We can infer that 50! has already two 2s and one 3. We just need to find the max power of 5 in 50!

Quotient of (50/5 )+ Quotient of (50/5^2) = 10 + 2 = 12

Ans. A


50! = 1*2*3*4*...*50. So 50! Has 2 twos and one 3.

We can also infer that the no of 2 s and no of 3 s in 50! Would be more than the no of 5s. This means that the no of 12s would be higher than no of 10s. So the limiting factor is 5.


So we need to find the no of 5 s in 50!.

Posted from my mobile device



I'm really sorry, but how 50! has only two 2s and one 3.

1*2*3*(2*2)*5*(2*3).....*50?

This part I understood, "We can also infer that the no of 2 s and no of 3 s in 50! Would be more than the no of 5s. This means that the no of 12s would be higher than no of 10s. So the limiting factor is 5."



Secondly, what is this formula that you used to find the max power of 5 in 50! in your original answer.?

[ Quotient of (50/5 )+ Quotient of (50/5^2) = 10 + 2 = 12 ]


Thank you.
Senior Manager
Senior Manager
Joined: 18 Sep 2018
Posts: 253
Own Kudos [?]: 204 [1]
Given Kudos: 322
Location: India
Concentration: Finance, International Business
GMAT 1: 690 Q49 V36
GPA: 3.72
WE:Investment Banking (Investment Banking)
Send PM
Which of the following could be a value of k if 10^k and 12^k are fact [#permalink]
1
Kudos
Hi Nups1324

No Problem at all.

50! has obviously more than two 2's and one 3.

Two 2's and one 3 is the bare minimum (for 12 to be a factor of 50!).

Basically K should be equal to a number that satisfies the condition that 12^K and 10^K are factors of 50!. Since the the no of 2's and 3's (12 = 2^2 * 3) would be more than no of 5's (10 = 5 *2), we will have more 12's than 10's. So the limiting factor here is the no of 5's.

Regarding the formula: you can find it in this post.

https://gmatclub.com/forum/math-number- ... 88376.html

-Harsh
GMAT Club Legend
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4915
Own Kudos [?]: 7818 [1]
Given Kudos: 221
Location: India
Send PM
Re: Which of the following could be a value of k if 10^k and 12^k are fact [#permalink]
1
Bookmarks
Top Contributor
The question is asking you to find out the possible value of k such that \(10^k\) and \(12^k\) are factors of 50! or in other words the value of k such that 50! is perfectly divisible by \(10^k \)and \(12^k\).

So we can use the maximum power concept of a factorial to find the value of k.

\(10^k\) can be prime factorized as \(2^k \)* \(5^k\)

\(12^k\) can be prime factorized as \(2^k\) * \(2^k\) * \(3^k\)

Since the prime factors here are 2, 3, and 5, the maximum value of k depends upon the maximum power of the maximum prime (In this case the number of 5s).
So divide 50! by 5 until you cannot divide anymore and add up the quotients

\(\frac{50}{5} +\frac{50}{25^}\)
Adding the two quotients, we get 12. (Perform successive division)

So, the maximum value of k is 12.
(Remember that k = 12 is the maximum value k can take)
* Note : k can also be any value ≤ 12 which will still make \(10^k\) and \(12^k \)factors of 50!.

Option A is the answer.

Thanks,
Clifin J Francis
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34080
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: Which of the following could be a value of k if 10^k and 12^k are fact [#permalink]
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 Club Bot
Re: Which of the following could be a value of k if 10^k and 12^k are fact [#permalink]
Moderator:
Math Expert
94609 posts