Question

Suppose we have x apples.
When we distribute them equally to 4 people, 2 apples are left.
When we distribute them equally to 5 people, 3 apples are left.
When we distribute them equally to 7 people, 5 apples are left.
What is the minimum value of x?

Answer 1

Well, here's a hint to start. Multiples of 5 end in 5 or 0. So if you distribute apples in multiples of 5 and there are 3 left, this means that the amount of apples has to end in a 3 or 8. Any multiply of 5:
15
20
25
30.
If you have those multiples and 3 are left, this forces the amount of apples you have to end in a 3 or 8. If that makes sense.
If we distribute apples equally in multiples of 4, then no matter what we will distribute an even number of apples. So if we distribute an even number of apples and there are 2 left, then this means the amount of apples total has to be an even number. Which means we can narrow down our choices of apples and know that the amount ends in the number 8. Now its just going from there :3

Answer 2

Would yo mind explaining why we know that the amount ends in the number 8?

Answer 3

*Would you mind