# Number Series

Number Sequence in the missing number section is a bit different than the sequences that we see in the number series tests. For example, in number Sequence we have numbers put into patterns like squares, triangles, swastikas etc. and there is a missing number somewhere. There is an algebraic or a non-algebraic rule that governs the assembly of the numbers. You have to find this number by guessing the pattern from other sections of the arrangement. Here we will see number series questions of this kind and develop some important methods and tricks that will help you solve it conveniently. Let us begin!

## Number Sequences And The Hint Number

Let us first see how these number sequences may be present in the paper. The following is a number sequence question from the SSC paper. The numbers may be different but the rule is exactly the same.

Directions: In the following square, numbers have been arranged following a specific order. Can you guess the missing number?

 6 9 11 3 4 7 27 65 ?

This is how the questions look. Sometimes the numbers are in the square, sometimes on the vertices of a triangle. The rule is that there is some mathematical or non-mathematical logic that governs this arrangement of numbers. This rule is like the key to the lock, once you have it you can predict any number of the patter. Usually, one pattern will have a unique rule. Let us solve these examples beginning with the one present above.

## Examples of Interest

Example 1: Directions: In the following section, numbers have been put in order. Find the missing number. The missing number is marked with the help of a ‘?’.

 6 9 11 3 4 7 27 65 ?

A) 63Â  Â  Â  Â  Â  Â  Â  Â  Â  B) 34Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â C) 9Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â D) 72

Answer: The rows go from left to right and the columns go from top to bottom. The rule may be either in the rows, the columns, or the diagonals. However, it will be only one. The first thing to do, or in other words the rule of the thumb to solve this pattern is to take a row or a column and select the largest number. For example, consider the following two tables.

 6 9 11

and

 6 3 27

## The Largest Number Method

The numbers in the first table are 6, 9 and 11. So the largest number of the row is 11 and we have to figure out how to generate this number 11 from the other two numbers i.e. 6 and 9. The difference between the two numbers is 3 and their sum is 15. There seems to be no way of getting 11. Let us see the column then.

In the column, the largest number is 27. We have to generate this number from 6, and 3. 27 can be written as 3Ã—3Ã—3 or 9Ã—3. It is difficult to see a rule here. But we have another row too. In the second row, the largest number is 65. 65 can be written as 13Ã—5. Do you see the rule now?

In the first column, the sum of 6 and 3 is 9. When we multiply this by 3 which is the difference between the first and the second number in the column, we get 27. In the second column, we see the same rule 9 + 4 = 13Â Ã— 5 = 65. Thus we have found the rule and will apply this to the third column to find the final result. The missing number therefore is 11 + 7 = 18Â Ã— 4 = 72. Thus the answer is D) 72.

## Combination of Arithmetic And Reasoning

Sometimes you may have to use a combination of reasoning and arithmetics as we will see in the following example. The example is from the graduate level exams and is very similar to the ones that you will encounter in the banking exams. In the following question, numbers have been arranged in a pattern. Find the pattern and with the help of the rule, fill in the missing number of the final arrangement.

### The Pattern of Ludo!

Example 2: Find the missing number:

 7 5 9 9 65 6 4 45 9 7 ? 8 8 2 11

A) 55Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â B) 15Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â C) 85Â  Â  Â  Â  Â  Â  Â  Â  Â  Â D) 75

Answer: Again we will apply the same fundamental method. Take the largest number and try to get it from the other numbers that are left behind. We have two complete patterns, one to guess the rule from and the other to try it on. Once we have found a rule that works for both the arrangements we can use it to detect the missing number in the final one. Let us begin with the first arrangement. The largest number is 65 and we have to somehow get 65 from the numbers surrounding it i.e. 6, 7, 8 and 9.

One of the things that you check the sum. the sum of the four numbers 6, 7, 8 and 9 is 30.Â  How to connect 30 to 65? Well 6Ã—5 = 30. Sounds like we have a rule here. Let us see if this works for the second pattern.

In the second arrangement, the largest number is 45. The other numbers that are left are 2, 4, 5, and 9. The sum of these numbers i.e. 2+4+5+9 = 20. We can express 20 as 4Ã—5 which can be written as 45. Thus we see that the rule works fine. Let us try this for the last one. 7 + 8 + 9 + 11 = 35. here we will have to take the help of the options now. Which option can represent 35? 7Ã—5 = 35 which is option D) and is the correct answer.

## Number Series Questions

Q 1: From the following table, find the missing number?

 10 5 75 6 4 20 13 7 ?

A) 40Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  B) 60Â  Â  Â  Â  Â  Â  Â  Â  C) 80Â  Â  Â  Â  Â  Â  Â  Â  D) 100

Ans: C) 80

Q 2: In the space below, the pattern has a missing number. Pick that number from the options below:

 3 11 10 11 4 11 40 11 ?

A) 12Â  Â  Â  Â  Â  Â  Â  Â  Â  B) 13Â  Â  Â  Â  Â  Â  Â  Â  C) 14Â  Â  Â  Â  Â  Â  Â  Â  D) 15

Ans: A) 12 [Hint: The rule can be in the rows, columns or the diagonals]

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### One response to “Alphabet Series”

1. Alan Livesey says:

In example 2:
“You can see that each of the numbers is a square and that the sequence is a perfect square series. 1, 22, 32, 42 (=16). The alphabet that corresponds to 16 is P. ”
“You can see that each of the numbers is a square and that the sequence is a perfect square series. 1, 2×2, 3×3, 4×4 (=16). The alphabet that corresponds to 16 is P. ”
(I suspect that the original text from which this was prepared used superscript but this has not been reflected in the online version, so use “2×2” or “2^2” which most people are familiar with from Excel)

In Circular Arrangement Series:
“These type of questions are similar to the ones we saw earlier. But there our numbering scheme would stop at 26 with X.”
“These type of questions are similar to the ones we saw earlier. But there our numbering scheme would stop at 26 with Z.”

In example 3:
“Answer: The lesser the number of alphabets present, the greater the difficulty of the question. Here you see that V and A have a difference of 4 alphabets between them. Similarly, A and H have a difference of 6 alphabets between them if we follow the circular order of the alphabets. Thus the next alphabet will have to have a difference of 8 alphabets with H. This alphabet is Q. Thus the series is V, A, H, Q. Therefore the correct option is s) P.”
“Answer: The lesser the number of alphabets present, the greater the difficulty of the question. Here you see that V and A have a difference of 4 letters between them. Similarly, A and H have a difference of 6 letters between them if we follow the circular order of the alphabets. Thus the next alphabet will have to have a difference of 8 letters with H. This letter is Q. Thus the series is V, A, H, Q. Therefore the correct option is d) P.”

In example 4:
“Answer: We will have to figure out the rule to every sequence. If you use the table, you will see that it becomes much more convenient to guess the rule. For example, in the first series, Q = 17; T = 20, X = 24; C = 29 [circular alphabet order]. Thus it forms a series under the rule. Similarly for the second option, F 6, P = 16, Z = 26 and J = 36. It also forms a correct sequence. Let us see the third one i.e. W = 23; U = 21; R = 18; and N = 14. So it is a wrong sequence. In place of N = 14, we should have had O.

That means the only series here that has a wrong term should be d). Let us check it. We have A = 1, L = 12, W = 23, H = 34.
Answer: We will have to figure out the rule to every sequence. If you use the table, you will see that it becomes much more convenient to guess the rule. For example, in the first series, Q = 17; T = 20, X = 24; C = 29 [circular alphabet order]. Thus it forms a series under the rule. Similarly for the second option, F 6, P = 16, Z = 26 and J = 36. It also forms a correct sequence. Let us see the fourth one i.e. A = 1, L = 12, W = 23, H = 34 which is a correct sequence.

Let us see the third one i.e. W = 23; U = 21; R = 18; and N = 14. So it is a wrong sequence. In place of N = 14, we should have had O.

Kind regards,
Alan

PS If you have other material that needs proof-reading I am frequently called upon to spot typos and grammatical errors in texts of all types including dense technical ones.