On each of the 18 cards, only one number is written: 4 or 5. the sum of the numbers on all the cards is divisible by 17. how many cards are there with a number "5"?

So number of cards with 5 written on it = 13

Step-by-step explanation:

On each of the 18 cards, only one number is written: 4 or 5. The sum of the numbers on all the cards is divisible by 17.

Let the number of cards with 5 written on it be x. Then the number of cards with 4 written on it will be (18 - x).

Sum of all numbers is divisible by 17.

Sum of numbers = 5x + 4 (18 - x) = x + 72

The multiple of 17 closest to 72 is 85.

Hence the sum of numbers = 85

x + 72 = 85

x = 13

So number of cards with 5 written on it = 13