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For an integer n = 2^16*3^13*5^5*7^5*11^3, what is the value of the

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For an integer n = 2^16*3^13*5^5*7^5*11^3, what is the value of the  [#permalink]

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New post 23 Mar 2019, 08:49
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A
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D
E

Difficulty:

  85% (hard)

Question Stats:

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For an integer n = 2^16*3^13*5^5*7^5*11^3, what is the value of the first non-zero digit from the right?

A. 1
B. 2
C. 4
D. 6
E. 8
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Re: For an integer n = 2^16*3^13*5^5*7^5*11^3, what is the value of the  [#permalink]

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New post 24 Mar 2019, 10:06
kiran120680 wrote:
For an integer n = 2^16*3^13*5^5*7^5*11^3, what is the value of the first non-zero digit from the right?

A. 1
B. 2
C. 4
D. 6
E. 8


Its too tricky question.. Experts please explain this question.
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For an integer n = 2^16*3^13*5^5*7^5*11^3, what is the value of the  [#permalink]

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New post 28 Mar 2019, 17:19
1
2^16*3^13*5^5*7^5*11^3 = (2 * 5)^5 *(3 * 7)^ 5 * 2^11 * 3^8 * 11^3
We need to figure out the last digit of this product after get rid of 10^n.

21^5 -> last digit: 1 (numbers ending with 1 will have its power with last digit is 1)
11^3 -> last digit 1
2^11 -> last digit 8
3^8 -> last digit 1

Therefore the answer is 8 -> E
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Re: For an integer n = 2^16*3^13*5^5*7^5*11^3, what is the value of the  [#permalink]

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New post 29 Mar 2019, 00:00
Given, n = 2^16*3^13*5^5*7^5*11^3

Here's how I did it..

n = 2^16*3^13*5^5*7^5*11^3
= (2*3)^13 *(5*7)^5 *(2*11)^3
= 6^13 *35^5 *22^3

Last digits of each term..
6^13 = 6
35^5 = 5
22^3 = 8

Which on multiplying, I get 240. So, 4 is the non zero term. C is my answer.
Please help..
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Re: For an integer n = 2^16*3^13*5^5*7^5*11^3, what is the value of the  [#permalink]

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New post 30 Mar 2019, 10:30
1
kiran120680 wrote:
For an integer n = 2^16*3^13*5^5*7^5*11^3, what is the value of the first non-zero digit from the right?

A. 1
B. 2
C. 4
D. 6
E. 8


n = 2^16*3^13*5^5*7^5*11^3
pair the no
n=10^11 * 21^5 *2^11*3^8*11^3
10^11 * 21^5*11^3 ; all hav unit digits as 1;
2^11*3^8= use cyclicity ; we get 8*1
so non zero integer ; 8
IMO E
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For an integer n = 2^16*3^13*5^5*7^5*11^3, what is the value of the  [#permalink]

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New post 04 Apr 2019, 03:04
From given primes, 2^5 * 5^5 will get consumed into creating trailing zeros.

Remaining:
2^11: Unit digit is 8
2 has unit digit cyclicity of 4: 2-4-8-6

3^13: Unit digit is 3
3 has unit digit cyclicity of 4: 3-9-7-1

7^5: Unit digit is 7
7 has unit digit cyclicity of 4: 7-9-3-1

11^3: Unit digit is 1
1 has unit digit cyclicity of 1: 1

Product of UD= 8*3*7*1= 168
Hence first non zero integer from right is 8

Ans E
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For an integer n = 2^16*3^13*5^5*7^5*11^3, what is the value of the   [#permalink] 04 Apr 2019, 03:04
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