the sum of 2 odd number is 42 they are both prime numbers and the difference of the two numbers is 16 what are the 2 numbers?
A. 20 and 22
B. 17 and 25
C. 9 and 33
D. 13 and 29
Here's a list of prime numbers.
http://www.mathsisfun.com/prime_numbers.html
To solve this problem, we need to use a process of elimination based on the given conditions.
The sum of two odd numbers is 42. Since odd numbers can only be either even plus one or even minus one, we can rewrite this as:
x + y = 42
Where x and y represent the two odd numbers.
Next, we are told that both numbers are prime numbers. Prime numbers are numbers greater than one that are divisible only by 1 and themselves. To determine if a number is prime, we need to check if it is divisible by any number less than itself.
Let's look at the possible answers and check if both numbers are prime:
A. 20 and 22
Neither 20 nor 22 is prime. 20 is divisible by 2 and 22 is divisible by 2 and 11.
B. 17 and 25
17 is a prime number, but 25 is not. 25 is divisible by 5.
C. 9 and 33
Neither 9 nor 33 is prime. 9 is divisible by 3 and 33 is divisible by 3 and 11.
D. 13 and 29
Both 13 and 29 are prime numbers. Let's check if their sum is 42 and if their difference is 16:
13 + 29 = 42 (The sum is correct)
29 - 13 = 16 (The difference is also correct)
Therefore, the correct answer is D. 13 and 29.
x+(x+2)=42
2x+2=42
2x=40
x=20
A.20 and 22