- I am a two digit number - The digit at ten's place is multiple of 2 and digit at units place is multiple of 3.  - The sum of the two digit is a prime number which is a factor of 52.  The number is ?

Option 3 : 49

Given:

 I am a two digit number

The digit at ten's place is multiple of 2 and digit at units place is multiple of 3. 

The sum of the two digit is a prime number which is a factor of 52. 

Calculation:

Let two digit no. = 10 n + m

According To Question,

Tens place is multiple of 2 and ones place is multiple of 3.

The number is (n + m) = prime number

n can be 2,4,6,8

And m can be 3,6,9.

Sum of digit is prime number and factor of 52(given)

Lets check, 

⇒ 2 + 3 = 5

⇒ 4 + 3 = 7 

⇒ 6 + 6 = 12 

⇒ 8 + 3 = 11

⇒ 4 + 9 = 13

In all of these 5, 7, 11, 13 are prime number.

In all only 13 is factor of 52.

∴ The number is 49.

∴ Option 3 is correct.