Number Properties

[swerve]

Calculate the units digit of the following expression:

1! + 2! + 3! +4! +5!….. + 10!

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

The OA is B

Source: e-GMAT

[RaghavKhanna]

1! + 2! + 3! + 4! + 5! + 6! + 7! + 8! + 9! + 10! = S

5! = 120 and after this, every number will have 0 in the unit's place.

=> Unit's digits of (S) = Unit's digit of (1!+2!+3!+4!) = Unit's digit of (1+2+6+24) = 3

[Scott@TargetTestPrep]

Calculate the units digit of the following expression:

1! + 2! + 3! +4! +5!….. + 10!

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

The OA is B

Solution:

Recall that the units digit of n! is 0 if n ≥ 5. Therefore, we only need to calculate the units digit of 1! + 2! + 3! + 4!. Since 1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33, the units digit is 3.

Answer: B