Answer: B: 4
Step-by-step explanation:
A number is divisible by 15 if the number ends on a 0 or a 5, and the sum of its digits is divisible by 3.
We want to find a 5 digit flippy number, this can be: modeled with:
N = ababa
Where a and b are single digit numbers.
If we impose that N must end with a zero, then we will have:
N = 0b0b0 = b0b0
This is a 4-digit number, so we can discard all the options that end with a zero.
Then the only option that we have are the numbers like:
B = 5b5b5
This number will be only divisible by 15 if:
5 + b + 5 + b + 5 = K is divisible by 3.
Then let's try find the possible values of b.
K = 3*5 + 2*b
K has two terms, the left term is already divisible by 3, then K will be divisible by 3 only if the other term is also divisible by 3.
Then we want 2*b to be divisible by 3.
And 2 is a prime number, then b must be divisible by 3, and we know that b is a number between {0,1 , 2, 3, 4, 5, 6, 7, 8 ,9}
The options are:
2*0 = 0 is divisible by 3.
2*3 = 6 is divisible by 3.
2*6 = 12 is divisible by 3
2*9 = 12 is divisible by 3.
Then we have four values of b such that:
N = 5b5b5 is divisible by 15.
Then the correct option is: B: 4
