Question

Currently, Lupe and Hector are 61 and 67 years old, respectively. They have two daughters and a grandson, who are 37, 31 and 7 years old, respectively. Lupe noted that their current ages are all prime numbers. During how many of the next 25 years will it also be true that their ages are all prime numbers?

Answer 1

Answer:

2 years

Step-by-step explanation:

We can check all the possibilities. Necessarily, Hector's age in years must be prime, then we consider the years when this happens and test for the other members of the family.

Hector is 67 years old, so in 25 years he will be 92 years old. The prime numbers between 67 and 92 are 71, 73, 79, 83 and 89.

When Hector is 71 years old, four years have passed the Lupe is 65 years old, so this case fails.

When Hector is 73 years old, six years have passed. Lupe is 67 years old, an their daughters and grandson are 43, 37 and 13 years old. All of these are prime numbers, therefore in this year the statement holds.

When Hector is 79, twelve years have passed. Then, the eldest daughter is 49, which is not a prime number thus this case fails.

When Hector is 83, sixteen years have passed, so Lupe is 77 which is not prime. This case fails too.

Finally, when Hector is 89, 22 years have passed. Lupe is 83, the daughters are 59 and 53 resp; the grandson is 29. All of these are primes, so the statement is true.