# can you work out the question below ?

Tim, Sam and John are each thinking of a number.

Tim says, “My number is a prime number between 15 and 30.”

Sam says, “My number has prime factors of 3 and 5.”

John says, “My number is an odd number less than 30 which is

a total of 3 prime numbers.”

The total of all 3 numbers is between 70 and 100. Investigate

what the three numbers might be. Find two possible answers.

Relevance
• Here's one set:

Tim: 29 (Prime between 15 and 30)

Sam: 45 = 3x3x5 (Has prime factors of 3 and 5)

John: 19 = 3 + 5 + 11 (Odd number less than 30 and a total of 3 prime numbers)

29 + 45 + 19 = 93 (Total of the three is between 70 and 100)

• "total" means sum?

Tim: primes arre 17 19 23 29

Sam: 15, 45, 135, 405 ..., 75, 375, 1875 ...

only possible ones are 15 45

john: primes are all odd except 2, so 2 not must be a factor

3+5+7 = 15

3+5+11 = 19

3+5+13 = 21

3+5+17 = 25

3+5+19 = 27

3+7+11 = 21

3+7+13 = 23

3+7+17 = 27

3+7+19 = 29

3+11+13 = 27

3+11+15 = 29

sum between 70 and 100

sums are, lowest to highest...

17+15+15 = 47 low

17+45+15 = 77 ok

17+15+19 = 51 low

17+45+19 = 81 ok

19+15+15 = 49 low

19+45+15 = 79 ok

19+15+19 = 51 low

19+45+19 = 81 ok

etc

primes:      2 3 5 7 11 13 17 19 23 29

31 37 41 43 47 53 59 61 67 71