Question

I met a man who said, "if you can guess my age, 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.

Answer 1

The age is 106

Explanation:

The hints are:

HINT 1

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.

Let the age be A

There odd numbers between 1 and 9 are: 3, 5 and 7.

Then

A/3 = B remainder 1

A/5 = C remainder 1

A/7 = D remainder 1.

HINT 2

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.

The even number between 1 and 9 are: 2, 4, 6 and 8.

A/2 = P remainder l

A/4 = Q remainder m

A/6 = R remainder n

A/8 = S remainder o

Where l ≠ 1, m ≠ 1, n ≠ 1, and o ≠ 1.

From the first hint, notice that 3, 5, and 7 would have been factors of his age, if not for the remainder 1. It will make sense to say the number after 3, 5 and 7 are factors of the number before his age.

Example: 3 and 5 are factors of 3×5 = 15 right?

Add 1 to 15, we have 16.

16/3 = 5 remainder 1

16/5 = 3 remainder 1.

So, 5 and 3 are factors of the number before 16.

Now, back to our work

3, 5, and 7 are factors of 3×5×7 = 105

Dividing 105 by 3 or 5 or 7 give a number without remainder.

Now dividing 105 + 1 = 106, by any of these number will give a remainder of 1.

The second hint, dividing 106 by any of 2, 4, 6, and 8 will not give a remainder of 1.

Then the age is 106

Answer 2

Question:

I met a men 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?

Answer:

The man's age is 106 years

Amount earned is $ 106.00

Explanation:

Here we have

3 × a = Age +1

5 × b = Age +1

7 × c = Age +1

Age is even, therefore, a, b and c are odd numbers

Since 3, 5 and 7 are factors of Age + 1

Then, 3 × 5 × 7 is a factor. That is 3 × 5 × 7 = 105

Therefore, 105 + 1 or 106 is a possible solution as an even number divided by another even number will not have a remainder of 1.

The age of the man is 106 years

Therefore, the amount earned = $ 1.00/year × 160 years = $ 106.00