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A number is called flippy if its digits alternate between two distinct digits. For example, 2020 and 37373 are flippy, but 3883 and 123123 are not. How many five-digit flippy numbers are divisible by 15?
A 3
B 4
C 5
D 6
E 8

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Answer:

A

Step-by-step explanation:

The number of five-digit flippy numbers are divisible by 15 is;

Option B; 4 Numbers

  • We want 5 digit flippy numbers that are divisible by 15.

For a number to be divisible 15, it has to be divisible by 3 and 5.

Also, for a number to be divisible by 5, it's last digit has to be 0 or 5.

  • Since it is a flippy digit and 0 cannot start it as it is a five digit number, then the first and last digits must be 5. Also, the center digit must be 0 or 5 to fulfill both conditions.

  • Thus, the format of the number should be;

       5N5N5

For it to be divisible by 3, since 5 + 5 + 5 = 15 is divisible by 3, the N + N can be equal to 0, 6, 12, or 18 since N is identical.

  • Thus, possible numbers are; 50505, 53535, 56565, 59595.

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