Marcy found two numbers that satisfy the following rules:
● Has one prime number
● Has one composite number
● The sum of the numbers is prime
Problem
Which two numbers could be the numbers that Marcy found?
A
23 and 27
B
11 and 20
C
8 and 16
D
13 and 15
one is even, the other is odd if you want the sum to be prime (that is, odd)
Only B works for that
B
Because:
In answer A
23 and 27
Both numbers are prime.
In answer C
8 and 16
Both numbers are composite numbers.
In answer D
13 and 15
13 is prime 15 is composite, but their sum 13 + 15 = 28 is not prime.
So in answer B:
11 is prime, 20 is composte.
Their sum 11 + 20 = 31 is prime.
My typo.
In answer A
23 and 27
23 is prime 27 is composite, but their sum 23 + 27 = 40 is not prime.
A
To find the two numbers that meet the given criteria, we can go through each option and check them one by one.
Option A: 23 and 27
- 23 is a prime number, and 27 is a composite number since it can be factored into 3 * 3 * 3.
- The sum of 23 and 27 is 50, which is not prime.
Option B: 11 and 20
- 11 is a prime number, and 20 is a composite number since it can be factored into 2 * 2 * 5.
- The sum of 11 and 20 is 31, which is a prime number.
Option C: 8 and 16
- 8 is not a prime number; it is a composite number because it can be factored into 2 * 2 * 2.
- 16 is also not a prime number; it is a composite number because it can be factored into 2 * 2 * 2 * 2.
- The sum of 8 and 16 is 24, which is not a prime number.
Option D: 13 and 15
- 13 is a prime number, and 15 is a composite number since it can be factored into 3 * 5.
- The sum of 13 and 15 is 28, which is not a prime number.
Based on the analysis above, the only option that meets all the given criteria is Option B: 11 and 20.