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If 5^a is a factor of n!, and the greatest integer value of a is 6, wh
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Updated on: 14 Sep 2018, 09:50
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If 5^a is a factor of n!, and the greatest integer value of a is 6, what is the largest possible value of b so that 7^b is a factor of n!? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6
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Originally posted by patnaiksonal on 14 Sep 2018, 09:15.
Last edited by patnaiksonal on 14 Sep 2018, 09:50, edited 1 time in total.




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If 5^a is a factor of n!, and the greatest integer value of a is 6, wh
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14 Sep 2018, 09:56
patnaiksonal wrote: If 5^a is a factor of n!, and the greatest integer value of a is 6, what is the largest possible value of b so that 7^b is a factor of n!?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6 Assuming a value for n, suppose n = 25 Number of 5s in 25! = \(\frac{25}{5}\) + \(\frac{25}{{5^2}}\) = 5+1 = 6 The maximum value of n can be 29 because if n=30, no. of 5s become \(\frac{30}{5}\) + \(\frac{30}{{5^2}}\) = 6+1 = 7 The largest value of b so that 7^b is a factor of 29! is \(\frac{29}{7}\) = 4 Answer C.
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If 5^a is a factor of n!, and the greatest integer value of a is 6, wh
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Updated on: 19 Sep 2018, 09:15
If 5^6 is a factor of n i.e. n! has to have 5*5*5*5*5*5 in it. as a result 25=<n=<29 to include every 5 (of 5^6) in it. In the form of: 5,10,15,20,25 And we have take 29 as it can not be 30 since that would mean 5^7. Now once we know in where n could lie, we see the second part of the question, which asks us the value of b in 7^b That is the greatest possible value for 7^b in 25=<n=<29 Now lets check, all values of 7 possible with n are: 7,14,21,28 i.e 4 values of 7 Therefore the largest possible value of b is 4 Answer is C which is 4 Thanks for pointing out my mistake CAMANISHPARMAR
Originally posted by Natty97 on 14 Sep 2018, 22:18.
Last edited by Natty97 on 19 Sep 2018, 09:15, edited 1 time in total.



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Re: If 5^a is a factor of n!, and the greatest integer value of a is 6, wh
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19 Sep 2018, 09:02
Given the constraints since the greatest integer value of a is 6  n could take max value of 29. For 29! to be divisivle by 7^b  the max value which b can take is 4. Correct Ans is option C
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Re: If 5^a is a factor of n!, and the greatest integer value of a is 6, wh
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19 Sep 2018, 09:05
Natty97 wrote: It is very simple. Just try and understand the concept. If 5^6 is a factor of n i.e. n! has to have 5*5*5*5*5*5 in it. as a result 30=<n=<34 to include every 5 (of 5^6) in it. In the form of: 5,10,15,20,25,30
Don't forget 25 is 5^2. Hence the max value of n could be 29. Think over it, in case if you have further doubts, please feel free to revert.
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Re: If 5^a is a factor of n!, and the greatest integer value of a is 6, wh
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19 Sep 2018, 09:38
patnaiksonal wrote: If 5^a is a factor of n!, and the greatest integer value of a is 6, what is the largest possible value of b so that 7^b is a factor of n!?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6 OA:C5! = 5*4*3*2*1 (\(5!\) is divisible by \(5^1\)) 10! = 10*9*.....* 5*4*3*2*1 (\(10!\) is divisible by \(5^2\)) 15! = 15*14*13*........* 10*9*.....* 5*4*3*2*1 (\(15!\) is divisible by \(5^3\)) 20! = 20*19*....* 15*14*13*........* 10*9*.....* 5*4*3*2*1 (\(20!\) is divisible by \(5^4\)) 25! = 25*24*....* 20*19*....* 15*14*13*........* 10*9*.....* 5*4*3*2*1 (\(25!\) is divisible by \(5^6\)) 30!= 30*29*...* 25*24*....* 20*19*....* 15*14*13*........* 10*9*.....* 5*4*3*2*1 (\(30!\) is divisible by \(5^7\)) largest value of \(n\) such \(5^6\) is a factor of \(n!\) is \(29\). largest possible value of \(b\) so that \(7^b\) is a factor of \(n!= \frac{29}{7}=4\)
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Re: If 5^a is a factor of n!, and the greatest integer value of a is 6, wh
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20 Sep 2018, 09:34
Natty97 wrote: Thanks for pointing out my mistake CAMANISHPARMARYou are most welcome. Please feel free to get in touch with me in case if I could be of any other help! Wishing you all the very best for your GMAT!
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Re: If 5^a is a factor of n!, and the greatest integer value of a is 6, wh &nbs
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