Chapter 4.5, Problem 20E

To determine

The number in the conversation below.

DMS: Calculators are neat, but there are lots of ways to work with numbers without having to use one. The trick is to keep the numbers small by working with remainders.

Friend: What do you mean?

DMS: I’m thinking of a three-digit number. When I divide it by 12, I get a remainder of 4.

Friend: So what?

DMS: When I divide the same number by 25, I get a remainder of 15.

Friend: So what?

DMS: What was my number? I’ll give you a hint. It’s bigger than 200.

Friend(10 minutes later): I give up.

DMS: It’s easy. I’ll show you how to do it.