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What is the right most nonzero digit in the value of 15!
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23 Aug 2019, 23:34
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28% (01:36) correct 72% (01:52) wrong based on 39 sessions
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What is the right most nonzero digit in the value of 15! A. 1 B. 2 C. 4 D. 6 E. 8
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What is the right most nonzero digit in the value of 15!
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Updated on: 24 Aug 2019, 03:27
EncounterGMAT wrote: What is the right most nonzero digit in the value of 15! A. 1 B. 2 C. 4 D. 6 E. 8 Asked: What is the right most nonzero digit in the value of 15! 15! = 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1 15! has 3 0s. To find out right most nonzero digit in 15! we can find unit digit of 15!/1000 To remove 0s from 15! 5*2*10 = 10*10= 100 15 * 4= 60 2*4*5*10*15 = 6000 = 6*1000 We can remove 2,4,5,10,15 and replace them with 6 Unit digit of 15! /1000= Unit digit of (6*4*3*2*1*9*8*7*6*3) = 8 after removing tens digits from 14,13,12,11 The right most nonzero digit in 15! is 8 IMO E
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Originally posted by Kinshook on 23 Aug 2019, 23:51.
Last edited by Kinshook on 24 Aug 2019, 03:27, edited 1 time in total.



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Re: What is the right most nonzero digit in the value of 15!
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24 Aug 2019, 02:43
Kinshook wrote: EncounterGMAT wrote: What is the right most nonzero digit in the value of 15! A. 1 B. 2 C. 4 D. 6 E. 8 Asked: What is the right most nonzero digit in the value of 15! 15! = 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1 To remove 0s from 15! 5*2*10 = 10*10= 100 15 * 4= 60 We can remove 2,4,5,10 ,15 and replace them with 6Unit digit of 15! = Unit digit of (6*4*3*2*1*9*8*7*6*3) = 8 after removing tens digits from 14,13,12,11 IMO E Kinshookplease explain the highlighted part of your solution why digit 6 has been placed?
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Re: What is the right most nonzero digit in the value of 15!
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24 Aug 2019, 02:52
This way might not be the shortest way but it can be used to solve to find for any value of n in n! first write all the primes below N. and then find the powers of those primes in n! for example, here the primes less than N are 2,3,5,7,11,13 The powers of 2 are 11, powers of 3 are 6, powers of 5 are 3 powers of 7 are 2 power of 11 is 1 and powers of 13 is 1. now since 2^3 * 5^3 gives the powers of 10. so remove those. we need to check the rightmost non zero digit, so essentially we need the unit digit.now 2 and 3 have a cyclicity of 4. so the remaining 2^8 = 2^4 which gives a unit digit of 6. and 3^6 = 3^(4+2) so it becomes 3^2 which gives a unit digit of 9. now 7^2 has a unit digit of 9. the product reduces to 6*9*9*1*3, after performing this calculation we get the answer as 8. Option E satisfies that. If you like my solution, do give kudos!



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Re: What is the right most nonzero digit in the value of 15!
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24 Aug 2019, 02:52
Archit3110 wrote: Kinshook wrote: EncounterGMAT wrote: What is the right most nonzero digit in the value of 15! A. 1 B. 2 C. 4 D. 6 E. 8 Asked: What is the right most nonzero digit in the value of 15! 15! = 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1 To remove 0s from 15! 5*2*10 = 10*10= 100 15 * 4= 60 We can remove 2,4,5,10 ,15 and replace them with 6Unit digit of 15! = Unit digit of (6*4*3*2*1*9*8*7*6*3) = 8 after removing tens digits from 14,13,12,11 IMO E Kinshookplease explain the highlighted part of your solution why digit 6 has been placed? Archit3110To find out right most nonzero digit we have to remove 0s and then find out unit digit of remaining number. To remove 0s We have to eliminate 5,10 & 15 with power of 2s. Let us choose 5*2, 10 & 15*4 randomly 2*4*5*10*15 = 6000 = 6*1000 Then remove these numbers from 15! and replace them with 6 and then find out unit digit of 15!/1000.
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What is the right most nonzero digit in the value of 15!
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Updated on: 29 Aug 2019, 17:34
KinshookI deleted my explanation. I think it is wrong. Sorry about that.
Originally posted by chondro48 on 29 Aug 2019, 16:34.
Last edited by chondro48 on 29 Aug 2019, 17:34, edited 3 times in total.



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Re: What is the right most nonzero digit in the value of 15!
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29 Aug 2019, 17:11
chondro48 wrote: EncounterGMAT and Kinshook, kindly evaluate my solution. Q. What is the right most nonzero digit in the value of 15!? A. 1 B. 2 C. 4 D. 6 E. 8 After reading the question, I immediately know what the question really asks: what is the units digit of multiplication of factors of 2 in 15! (2x4x6x...x14) 15! has 7 multiples of 2 (2, 4,...,14) and therefore, factors of 2^11. So the units digit of multiplication of 2^11 is 8. Answer is (E) @chondo48 If I use this logic, right most non zero digit in 6! = 720 Should have been 2*4*6 = 48 or 8 which is incorrect But if you remove 2*5 = 10 from 6! Then 1*3*4*6 = 72 will provide correct answer Posted from my mobile device
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Re: What is the right most nonzero digit in the value of 15!
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