ned and ted are brothers. Find their ages from these clues: their ages have an even sum but an odd product. ted is 2 years younger than ned

Question

I just need help solving this problem

Answer 1

First lets assign variables to our unknowns

T = Ted's age

N = Ned's age

 

Clues:

their ages have an even sum

T + N = even

but an odd product.

T*N = odd

Ted is 2 years younger than Ned

T = N - 2

 

What this tells us is that both are an odd numbered age, because the sum of two odd numbers is an even number and product odd.

 

Now that we know both their ages are odd, we can write:

N = 2x - 1

which ensures Ned's age is odd

T = 2x - 3

ensures Ted's age is odd and two years younger than Ned

 

Plug in any value ≥ 2 for x

 

N . T

3   1

5   3

7   5

9   7

..

and so any sequential odd number's work and there needs to be more information in order to solve this problem

 

 

 

Answer 2

This is not a very well-phrased question. We need at least one other clue.

 

Let N = Ned's age, and T = Ted's age.

 

Then we know that N = T + 2 (from "ted is 2 years younger than ned").

 

Additionally, we know that N + T = 2*N + 2 is an even number and N*T = an odd number.

 

What this tells us is that N and T are both odd numbers, but we can't conclude anything else without another piece of information, such as the sum or the product of their ages.