Understanding Number Analogy is a crucial step in solving questions on reasoning ability. The reasoning ability is checked mainly by the questions related to Number Analogy. The candidates are asked to identify and point out relationships, similarities or differences, and dissimilarities in a series or between groups of numbers. In the following section, we will try and get acquainted with the concept of analogies.

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## Number Analogy of the First Kind

We shall see how to identify and use this concept to solve some questions. Broadly speaking, the Number analogy based questions may be of two types:

- Find a missing number from a given analogy.
- Find a set of numbers that are related to the same rule as the one given.

If you read newspapers you will find this section very very easy. In these kinds of questions, in bank exams, you will be asked to guess the missing number or complete a series from a given series of numbers. The tricks or the time savers here are to look for the common rules. Check for relations like “is a factor of”, “is a multiple of”, “is a root of”, “is a square of”, or a combination of these rules. Let us again see this with the help of an example:

Q. no. 1: If x = 3 and y = 27, then x : y :: y : _______________

- 19
- 196
- 1968
- 19683

Again, as we have done in the previous examples, we first try to find out the relation between the two given numbers. Here the two numbers are 3 and 27. We see that 3x3x3 = 27. In other words, 33 = 27. Hence 273 is the number that we are looking for. Using the calculator, we see that 273 = 19683. Note: In many bank exams an onscreen calculator is provided.

## Number Analogy of the Second Kind

Q no. 2) What number will follow the given series of numbers: 3, 6, 11, __ _?

- 13
- 16
- 18
- 22

Here let us try and find the rule that generates the given numbers. The first term is 3. The second is 6 and the third is 11. Often times, the number of the term (i.e. whether it is first, second, third or fourth) is very crucial. If we try this [term number]^{2} + 2, then we have:

First term = [1]^{2} + 2 = 3; which is the given first term. Second term of the series = [2]^{2} + 2 = 6; again the second term. And the third term = [3]^{2} + 2 = 11; which is the third term of the given series. Hence the rule is correct and we can use it to find the missing term. The missing term is = [4]^{2} + 2 = 18. Hence the answer is 18.

## Memory-Based Questions

Q. no. 3) 11 : 121 :: 13 : ____

- 156
- 169
- 179
- 216

Answer: The answer is clearly B) 169 as 112 = 121. Therefore, 132 = 169 but if you haven’t memorized the squares of the first few numbers, it will eat into your time. So the main objective is to cut down on the time and for that, you need to commit certain things to the memory. Following is a list of some numbers and their squares that are commonly encountered. Some important squares:

112 = 121; 122 = 144; 132 = 169; 142 = 196; 152 = 225;

162 = 256; 172 = 289; 182 = 324; 192 = 361; 212 = 441;

Q. no. 4) Complete the analogy: 144 : 23 :: 169: _____

- 32
- 24
- 25
- 26

Answer: I will make it easy, the answer here is C) 25. How did I get it? If you look above to the common squared values of a few numbers, you will see that 144 is the square of 12 and 144 – 23 = 121, which is the square of 11 or the square of the number “one” step below 12. Similarly, 169 is the square of 13 and we can reach the answer in two easy steps:

Step 1: Find the square of the number “one” below the given number (which is 13). The number is 12 and 122 = 144.

Step 2: Subtract this value of the squared number from the given number i.e. 169 -144 = 25. Therefore, the answer is 25. You will find a lot of interesting number analogies. Let us try and see an example where you will be asked to guess a pair based on a given pair.

## Pair-Analogy-Based Questions

Q. no. 5) Select the pair that has the same analogy as the given pair: 9876: 12234567

- 34562: 89776
- 123: 122345
- 654321: 922346
- 9993: 8886

Answer: These questions can look very difficult, sometimes even not solvable. This would be true if you hadn’t read this article! If you take a careful look at the given set of numbers, you will find that they are related to a rule. The sum of all digits is 30 in both the numbers. There is no other relation between the two numbers. So start checking the options. You may want to save time and argue that you only need to check the first number of the given pairs. But that would be wrong and dangerous. What if the options followed the rule that the pair should have the same sum of the digits, even if it is different than 30? That said, you should ideally check both the numbers.

## Summary

Follow the following steps to solve the questions based on the number analogy:

- Step 1 – Gather all information from the given pair ( relations, sums, squares etc.)
- Step 2 – Apply the same rules, relations, formulae that you guessed in step 1 to all the options.

## Practice Questions

Q 1: If x = 144 and y = 18, then x : y what

- 96: 12
- 13: 169
- 169: 13
- 256: 16

Answer: A) 96: 12

Q 2: Guess the next number: 19 : 361 :: 66 : ____

- 693
- 256
- 4356
- 5346

Answer: C) 4356.

Q 3: 23 : 506 what 12 : ____

- 132
- 123
- 321
- 312

Answer: A) 132