I am a number less than 100. I am a product of two prime numbers. If you reversemy digits, I am a prime. The sum of my digits is a 1-digit prime. One of my digits is a square number. What number am I?

You are number 34

Step-by-step explanation:

* Lets explain how to solve the problem

- The number is less than 100

∴ The number is 2-digit number

- The number is the product of 2 prime numbers

∴ The two prime numbers could be two of these numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43

∵ The number is less than 100

∴ The two prime numbers are 1-digit numbers OR one of them

is 1-digit and the other is 2-digit

- The sum of its digits is a 1-digit

∴ The sum of its digits is less than 10

- One of its digit is a square number

∴ One of its digit is 1 or 4 or 9 because they are square numbers

* Look to the prime number above the number and chose two of

them try to find the answer

- Start with the product of 1-digit prime numbers

∵ 2 and 7 are prime numbers

∵ 2 * 7 = 14 and the sum of its digits is less than 10 (1 + 4 = 5)

∵ 14 < 100

∵ The reversed of its digits obtained 41 which is a prime number

∵ 4 and 1 are a square number (1² = 1 or 2² = 4)

∴ The number is not 14

- Chose one of them 1-digit and the other 2-digit

∵ 2 and 17 are prime numbers

∵ 2 * 17 = 34 and the sum of its digits is less than 10 (3 + 4 = 7)

∵ 34 < 100

∵ The reversed of its digits obtained 43 which is a prime number

∵ 4 is a square number (2² = 4)

∴ The number is 34

* You are number 34