Question

Oliver has a box of toy cars, but he is not sure how many he has. If he arranges the cars in groups of four, he has three left over. If he arranges them in groups of 3, he has two left over and there are three left over when he puts them in groups of five. Oliver definitely doesn’t have any more than 30 cars, so how many does he have?

Answer 1

x/4 = r3 or 3/4
x/3 = r2 or 2/3
x/5 = r3 or 3/5

we know x is not divisible by 4 3 or 5 and is less than 30.

we know the value ends in 3 or 8 from x/5 = r3

we know the value is greater than 3 from r3

so far we got 13 and 23

13 is eliminated from x/4 = r3 because it is r1 not r3

so the answer is 23