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# Calculate the units digit of the following expression:

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3386
Calculate the units digit of the following expression:  [#permalink]

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Updated on: 13 Aug 2018, 01:22
00:00

Difficulty:

15% (low)

Question Stats:

75% (01:21) correct 25% (01:35) wrong based on 162 sessions

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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.
Current Student
Joined: 07 Jan 2016
Posts: 1082
Location: India
GMAT 1: 710 Q49 V36
Re: Calculate the units digit of the following expression:  [#permalink]

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27 Feb 2018, 11:35
1
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
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3386
Re: Calculate the units digit of the following expression:  [#permalink]

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28 Feb 2018, 00:46
1

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

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22 May 2019, 10:06
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Re: Calculate the units digit of the following expression:   [#permalink] 22 May 2019, 10:06