Let N be such number which when divided by 6 leaves remainder 1

So, N = 6Q + 1
where;
Q = quotient
R = remainder

For Q = 0, N = 1
For Q = 1, N = 7
For Q = 2, N = 13
For Q = 3, N = 19
For Q = 4, N = 25
For Q = 5, N = 31
For Q = 6, N = 37
For Q = 7, N = 43
For Q = 8, N = 49
For Q = 9, N = 55

motion2020
I suppose the question is asking about one possible value of N??
If it is then the question must read ... then this integer COULD be evenly divisible by what number?

Here is why:
for Q = 0 we get N = 1 - which is not divisible by any of the option choices

For COULD be divisible, the answer could be E