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Updated on: 13 Aug 2018, 02:22
Originally posted by EgmatQuantExpert on 27 Feb 2018, 10:37.
Last edited by EgmatQuantExpert on 13 Aug 2018, 02:22, edited 2 times in total.
Last edited by EgmatQuantExpert on 13 Aug 2018, 02:22, edited 2 times in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
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Question Stats:
75% (01:13) correct
25%
(01:27)
wrong
based on 467
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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
Question 7 of The e-GMAT Number Properties Marathon
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27 Feb 2018, 12:35
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EgmatQuantExpert
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
28 Feb 2018, 01:46
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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.
• 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 \(4! = 24\)
• Units digit of \(33\) =\(3\).
