Math quiz question

Question

A child has fewer than 70 baseball cards. If he puts them in piles of 3​, 4​, 6​, 12​, or 18 he has one card left over each time. How many baseball cards does he​ have?

Answer 1

x < 80

x = number of cards which are put in piles of 3,4, 6, 12, or 18

with 1 left over

if 79

if in piles of 3 there are 26 piles and 1 left over

if piles of 4, 19 piles, 3 left over

if piles of 6, 13 piles and 1 left over

if piles of 12, 6 piles with 7 left over

if piles of 18, 4 piles with 7 left over

could be 79 cards total

with all piles of 3, or all piles of 6

or 6 piles of 12, and 2 piles of 3

or 4 piles of 18 and 2 piles of 3

or other combinations

79 is the largest number of cards possible and put in piles with 1 left over

7 is the smallest number, where there are 2 piles of 3, with 1 left over

he has somewhere between 7 and 79 cards