Question

How many three-digit numbers have the property that the sum of that number and the three-digit number written with the same digits in reverse order is a multiple of 5?

Answer 1

There are 1000 three-digit numbers that have the property described.

Step-by-step explanation:

To find the numbers with the desired property, we need to consider all possible three-digit numbers and check if their sum with the number written in reverse order is a multiple of 5.

Let's consider a three-digit number ABC, where A, B, and C represent the hundreds, tens, and units digit, respectively.

The number written in reverse order is CBA.

The sum of ABC and CBA is (100A + 10B + C) + (100C + 10B + A) = 101(A + C) + 20B.

This sum will be a multiple of 5 if and only if (A + C) is a multiple of 5.

Therefore, we can choose any two-digit number for B, and for each choice of B, there are 10 options for A and 10 options for C.

Therefore, the total number of three-digit numbers with the desired property is 10 * 10 * 10 = 1000.

Learn more about three-digit numbers with a specific sum property