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Calculate the units digit of the following expression:

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Posts: 2313
Calculate the units digit of the following expression:  [#permalink]

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New post Updated on: 13 Aug 2018, 01:22
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

84% (01:23) correct 16% (01:51) wrong based on 92 sessions

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Question:



Calculate the units digit of the following expression:

1! + 2! + 3! +4! +5!….. + 10!

    A) 1
    B) 3
    C) 5
    D) 7
    E) 9
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Originally posted by EgmatQuantExpert on 27 Feb 2018, 09:37.
Last edited by EgmatQuantExpert on 13 Aug 2018, 01:22, edited 2 times in total.
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Re: Calculate the units digit of the following expression:  [#permalink]

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New post 27 Feb 2018, 11:35
EgmatQuantExpert wrote:

Question:



Calculate the units digit of the following expression:

1! + 2! + 3! +4! +5!….. + 10!

    A) 1
    B) 3
    C) 5
    D) 7
    E) 9


5! = 120 and every factorial after 5 ends in 0
thus all we need to is find unit digit of 1! + 2! + 3! + 4! = 1 + 2 + 6 + 26 = 33

(B) imo
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Re: Calculate the units digit of the following expression:  [#permalink]

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New post 28 Feb 2018, 00:46

Solution:



    • The units digit of the expression will depend on the units digits of the factorials
    • While simplifying the factorials of the numbers we will observe the following:
      o \(1! = 1\)
      o \(2! = 2\)
      o \(3! = 6\)
      o \(4! = 24\): Units digit = \(4\)
      o \(5! = 120\): Units digit = \(0\)
      o We do not need to calculate any further since after \(4!\), the value of the next terms will end with zeroes.
         Example: \(6! = 5!*6\) = \(120*6\) = \(720\) : Units digit: \(0\)
         This can be logically deduced because we have a \(5\) and \(2\) in each factorial starting from \(5!\), which gives a zero at the end every time.
    • Since zero added to any number yield the same number, we can ignore it and in turn ignore all terms from \(5!\) to \(10!\).
    • This method helped us eliminate all the terms after \(4!\) and we can re-write the whole expression as shown below:
    \(1! + 2! + 3! + 4!\)
    • To find out the units digit of this expression, let us calculate the value of each term.
      o \(1! = 1\)
      o \(2! = 2\)
      o \(3! = 6\)
      o \(4! = 24\)
    • Hence, \(1! + 2! + 3! + 4! = 33\).
    • Units digit of \(33\) =\(3\).
Since the units digit of the given expression is \(3\), and the correct answer is Option B.
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Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
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Re: Calculate the units digit of the following expression: &nbs [#permalink] 28 Feb 2018, 00:46
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