Question

I met a man who said if you can guess my age, I will pay you one dollar for each year that I have lived. I will also give you two hints. If you take my age and divide it by any odd number greater than 1 and less than 9 you will get a remainder of 1. But if you take my age and divide it by any even number greater than 1 and less than 9 you will not get a remainder of 1.How much money could you earn?Explain your solution and how you know it is the only correct answer.

Answer 1

$106

Explanation:

The odd numbers greater than 1 and less than 9 are 3, 5, and 7.

The even numbers greater than 1 and less than 9 are 2, 4, 6 and 8.

If we multiply the odd numbers we get:

`3\cdot5\cdot7=105`

To obtain a remainder of 1, we add 1 to the value obtained previously, therefore:

`105+1=106`

Now, being an even number, dividing by any pair will give an exact value, while between 3, 5 and 7 the remainder will be 1.

We know that it is the only correct option because we did it using the least common multiple of the related values in the statement.

So the correct answer is $106