I am a prime number less than 10, Ifyou
add 10 or 20 to me, the results are prime
numbers. What number am I?
The prime numbers less than 10 are 2, 3, 5, and 7.
Adding 10 to these numbers results in 12, 13, 15, and 17, respectively.
Adding 20 to these numbers results in 22, 23, 25, and 27, respectively.
Out of these options, only the number 7 satisfies the condition that both 7 + 10 = 17 and 7 + 20 = 27 are prime numbers.
Therefore, the number you are is 7.
Let's solve this step-by-step:
1. Start by listing all the prime numbers less than 10: 2, 3, 5, 7.
2. Add 10 to each of these numbers: 2 + 10 = 12 (not a prime number), 3 + 10 = 13 (a prime number), 5 + 10 = 15 (not a prime number), 7 + 10 = 17 (a prime number).
3. Now, add 20 to each of the prime numbers less than 10: 2 + 20 = 22 (not a prime number), 3 + 20 = 23 (a prime number), 5 + 20 = 25 (not a prime number), 7 + 20 = 27 (not a prime number).
Based on our findings, the number you are referring to is 3. When you add either 10 or 20 to it, you get a prime number.
To determine the prime number that meets the given criteria, we can follow these steps:
1. Create a list of prime numbers less than 10: 2, 3, 5, 7.
2. Add 10 to each of the prime numbers in the list: 12, 13, 15, 17.
3. Check if any of the resulting numbers are prime numbers.
- 12 is not a prime number (it is divisible by 2 and 3).
- 13 is a prime number.
- 15 is not a prime number (it is divisible by 3 and 5).
- 17 is a prime number.
Based on the given criteria, the prime number less than 10 that, when you add 10 or 20 to it, gives prime numbers, is 3. Adding 10 to 3 gives 13 (a prime number), and adding 20 to 3 gives 23 (also a prime number).