Question

Direction : In each question the numbers / letters / figure on both side of ‘:’ have a definite relation between them and the pair of numbers / letters/ figure on both side of ‘::’ follow the same pattern. Choose the correct option to replace the ‘?’.10 : 111 :: 12 : 157 :: 13 : 183 :: 15 : ?

Answer 1

Explanation:

I hope my efforts are useful to you

Answer 2

Answer:

Concept:

Analogy is a key stage in answering inquiries about one's capacity for reasoning. Questions about number analogy mostly test the ability to think. A sequence of relationships, similarities and differences, and discrepancies within or between sets of numbers are to be identified and noted by the applicants. We shall attempt to familiarise ourselves with the idea of analogies in the part that follows.

Explanation:

Given:

A number sequence based on analogy.

To find:

A number that follows the same pattern as given pairs.

Solution:

• Find the pattern followed among given pairs to know in what way the first number in the pair relates to the second one.

• $1^{st}$ pair - $10:111$

The above pair can be written as $10:(10^{2} )+11$  which can be generalized as $x:x^{2} +(x+1)$       ⇒  A

• $2^{nd}$ pair - $12:157$

Check whether this pair follows the same pattern as A

The second pair can be written as $12:12^{2}+13$  i.e. $x:x^{2} +(x+1)$

• $3^{rd}$  pair - $13:183$

Check whether this pair follows the same pattern as A

The third pair can also be written as $13:13^{2}+14$   i.e. $x:x^{2} +(x+1)$

• So,it is clear from the above analysis that every pair follows the  same pattern as $x:x^{2} +(x+1)$.
• To find the second number of the given last pair use the derived pattern as follows:

$15:?$  ⇒  $x:x^{2} +(x+1)$

Here $x=15$ ,

          $15:15^{2}+(15+1)$

         $15:(225+16)$

          $15:241$

Hence, $241$ replaces the question mark and its the second number of the  last pair  ⇒ $15:241$

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