Bunuel wrote:
If n! and (n + 1)! have the same units digit, then n can be which of the following?
I. n = 10
II. n = 1
III. n = 0
A. I only
B. II only
C. III only
D. I and III
E. I, II, and III
Given: n! and (n + 1)! have the same units digits
Let us first write down the factorials of different numbers:
0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
If we notice here, all the numbers after 4! will end with a 0.
Here is why:
If we multiply any number by 10, a 0 is added to that number
And a 10 is formed by a 5 and a 2, 10 = 5*2
Till 4!, we do not have a "5" in multiplication. But after that, we will have atleast one "5" in the multiplication.
Hence the units digits will be same after 5! and for 0! and 1!
Now checking the statements
I. n = 10
Yes, the units digits of 10! and 11! are same and = 0. TRUE
II. n = 1
units digit f 1! = 1 and units digit of 2! = 2. FALSE
III. n = 0
Units digit of 1! = 1 and units digit of 0! = 1. TRUE
Correct Option: D