Question

The difference between ages of two brothers is a prime number. the sum of their ages is also a prime number. if elder brother is 28 years old, how many values can age of younger brother take

Answer 1

Prime numbers between 1 to 28 = 2, 3, 5, 7, 11, 13, 17, 19, 23
Now the difference and sum of their ages are prime numbers. 
From subtracting these numbers from the age of elder brother we can get the age of younger brother. 
We get 3 possibilities in this calculation. 
They are 25, 15 and 9
Hence the answer is 3.

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Answer 2

Solution :-

Prime numbers between 1 to 28 = 2, 3, 5, 7, 11, 13, 17, 19, 23

Now, we will adopt Trial and Error method. 

Elder Brother's    Difference is       Younger             Sum        Sum is a Prime 
Age                     Prime Number    Brother's Age                    Number or not

28                              2                      26                    54                No
 
28                              3                      25                    53                Yes

28                              5                      23                    51                 No

28                              7                      21                    49                 No  

28                             11                     17                    45                 No

28                             13                     15                    43                Yes

28                             17                     11                    39                 No

28                             19                      9                     37                Yes  

28                             23                      5                     33                 No


We can see that there are only 3 possible numbers for younger brother's age. These are 25, 15 and 9.

Hence, younger brother's age can take 3 values.

Answer.