Prime number word problem..

Question

Brenda is thinking of a prime number between 40 and 50. Josh is thinking of a prime number between 10 and 20. The difference between the two numbers is 26. What are the two numbers?

Answer 1

Brenda is thinking of 41, 43, or 47.

 

Josh is thinking of 11, 13, 17 or 19.

 

The solution space is small enough to perform and exhaustive search.

 

Subtract 26 from Brenda's possibilities to see which of Josh's is hit.

 

47 - 26 = 21 composite.

 

Brenda is not thinking of 47.

 

43 - 26 = 17 prime.  Brenda could be thinking of 43.

 

41 - 26 = 15  composite.  Brenda is not thinking of 41.

 

 

Brenda is thinking of 43 and Josh is thinking of 17.

Answer 2

41, 43, 47 are the primes between 40 and 50

11, 13, 17, 19 are the primes between 10 and 20

by trial and error 43-17=26

or...

add 26 to each of the numbers 11, 13, 17, and 19:

11+26=37

13+26=39

17+26=43, which is between 40 and 50

the two primes are 43 and 17