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The factorial operation ! applied to a positive integer n denotes...

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Senior Manager
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The factorial operation ! applied to a positive integer n denotes... [#permalink]

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New post 31 Oct 2017, 19:42
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Difficulty:

  75% (hard)

Question Stats:

45% (01:03) correct 55% (00:51) wrong based on 29 sessions

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The factorial operation ! applied to a positive integer n denotes the product of all integers greater than or equal to 1 and less than or equal to n. If k = 1! + 2! + 3! + . . . + p! , where p is a prime number greater than 10, what is the remainder when k is divided by 4?

A) 0
B) 1
C) 2
D) 3
E) Cannot be determined.
[Reveal] Spoiler: OA

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Kudos [?]: 112 [0], given: 46

Re: The factorial operation ! applied to a positive integer n denotes... [#permalink]

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New post 31 Oct 2017, 20:47
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sasyaharry wrote:
The factorial operation ! applied to a positive integer n denotes the product of all integers greater than or equal to 1 and less than or equal to n. If k = 1! + 2! + 3! + . . . + p! , where p is a prime number greater than 10, what is the remainder when k is divided by 4?

A) 0
B) 1
C) 2
D) 3
E) Cannot be determined.


B will be the answer...

let P = 11
we can write the scenario as:
1! /4 + 2! /4 + 3!/4 ......................11 !/4
Now terms from 4 !/4 will be divided by 4 ..we can neglect those ..

So each time remainder will depend on (1! + 2! + 3! )/4 = 1(Remainder)

Kudos [?]: 112 [0], given: 46

Re: The factorial operation ! applied to a positive integer n denotes...   [#permalink] 31 Oct 2017, 20:47
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