If n is an integer and n^4 is divisible by 10, which of the following could be the remainder when n ...
If n is an integer and n^4 is divisible by 10, which of the following could be the remainder when n is divided by 10?
Answer/Solution
10
Steps/Work
option 1
Remainder 2 means 10+2=12
n^4= 12^4= 12*12*12*12/10 is not an integer
option 2
Remainder 5 means 10+5=15
n^4= 15^4= 15*15*15*15/10 is not an integer
option 3
Remainder 6 means 10+6=16
n^4= 16^4= 16*16*16*16/10 is not an integer
option 4
Remainder 8 means 10+8=18
n^4= 18^4= 18*18*18*18/10 is not an integer
option 5
Remainder 10 means 10+10=20
n^4= 20*20*20*20/10 is an integer means n^4 is divisible by 10 if we take n=10
so E is correct
Remainder 2 means 10+2=12
n^4= 12^4= 12*12*12*12/10 is not an integer
option 2
Remainder 5 means 10+5=15
n^4= 15^4= 15*15*15*15/10 is not an integer
option 3
Remainder 6 means 10+6=16
n^4= 16^4= 16*16*16*16/10 is not an integer
option 4
Remainder 8 means 10+8=18
n^4= 18^4= 18*18*18*18/10 is not an integer
option 5
Remainder 10 means 10+10=20
n^4= 20*20*20*20/10 is an integer means n^4 is divisible by 10 if we take n=10
so E is correct