GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 01 Jun 2020, 05:59

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Calculate the units digit of the following expression:

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3394
Calculate the units digit of the following expression:  [#permalink]

### Show Tags

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

### HideShow timer Statistics

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]

### Show Tags

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: 3394
Re: Calculate the units digit of the following expression:  [#permalink]

### Show Tags

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.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 15034
Re: Calculate the units digit of the following expression:  [#permalink]

### Show Tags

22 May 2019, 10:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Calculate the units digit of the following expression:   [#permalink] 22 May 2019, 10:06