Question

: $ 11:17::19:? $
A. $ 29 $
B. $ 27 $
C. $ 21 $
D. $ 23 $

Answer 1

Hint:
Here we need to find the remaining term which is symbolised with a question mark. Here we have the question of logical reasoning where we need to apply our aptitude and the mental ability so that we can find the remaining term. If we see that they all are the prime numbers and between $ 11{\text{ and 17}} $ there is a gap of one prime number which is $ 13 $ . Similarly after $ 19 $ we have the prime numbers as $ 23,29 $ so we can skip $ 23 $ and our required answer is $ 29 $ .

Complete step by step solution:
Here we are given $ 11:17::19:? $ where we need to find the remaining term which is symbolised with a question mark. Here we have the question of logical reasoning where we need to apply our aptitude and the mental ability so that we can find the remaining term.
First of all we need to notice the common thing if present in all of them. If we see them clearly we will notice that they all are the prime numbers. Prime numbers are those who have only two factors out of which one is $ 1 $ and other the number itself.
For example: $ 2,3,5,7 $ are all prime numbers as they are divisible completely only by $ 1 $ and the number itself whereas $ 4 $ is divisible by $ 1,2,4 $ completely so it is not a prime number as it has more than two factors.
Similarly if we see $ 11,17,19 $ are all prime numbers.
Let the number to be found be $ n $
So we have $ 11:17::19:n $
We need to find the same relation between $ 19{\text{ and }}n $ as there is between $ 11{\text{ and 17}} $
So we can notice that between $ 11{\text{ and 17}} $ we have only one prime number which is $ 13 $
Similarly we can skip one prime number between $ 19{\text{ and }}n $
After $ 19 $ the prime number occurring are $ 23, 29, 31,... $
So we have to skip $ 23 $ and get the next prime number as the value of $ n $
So $ n = 29 $
Hence we get the correct answer as $ 11:17::19:29 $

Hence A is the correct result.

Note:
Here we have the problem where we don’t need any mathematical formula but only the logical reasoning and the concept of the prime numbers and we need to find the correct relation between them.