Numerical Reasoning

Series

This type of series questions are based on the English letters. In this we have to find out the pattern of the series and then find out the missing letter from the series.

To solve these questions quickly you should remember following points:

1. Learn the place values of all the English alphabets.

A	B	C	D	E	F	G	H	I	J	K	L	M
1	2	3	4	5	6	7	8	9	10	11	12	13

N	O	P	Q	R	S	T	U	V	W	X	Y	Z
14	15	16	17	18	19	20	21	22	23	24	25	26

2. Learn the pairs of opposite letters. (The letters whose sum of place values is 27.)

Types of Alphabet Series

1. One Lettered Series

In One lettered series each term contains one letter and follows a certain pattern.

For eg: A, C, E, G, I, ?

Ans. We know that the place values of the given letters are A = 1, C = 3, E = 5, G = 7, I = 9

So, we can see that there is a difference of 2 between the place values of the corresponding letters.

Thus, the place value of the missing letter will be 11.

Hence, the correct answer is K.

2. Two Lettered Series

In Two lettered series each term contains two letters and follows a certain pattern.We have to find out the next term according to that pattern.

Example: AC, FH, KM, ?

Here, we can see that there is a gap of one letter between the letters of each group and there is a difference of two letters between the last letter of one group and the first letter of the consecutive group.

Now, M + 2 = P, and P + 1 = R.

Hence, the correct answer is PR.

3. Three Lettered Series

In Three lettered series each term contains three letters and follows a certain pattern.We have to find out the next term according to that pattern.

Example: What is the next letter in the series CNL, BLI, AJF, ZHC, _______ ?

(1) XDY

(2) YFZ

(3) YFA

(4) XFY

Ans. If we check the place values of the letters in each pair.

So,

C = 3, B = 2, A = 1, Z = 26. (Decreasing by 1) So, the next letter will be 25, which is Y.

N = 14, L = 12, J = 10, H = 8. (Decreasing by 2) So, the next letter will be 6, which is F.

L = 12, I = 9, F = 6, C = 3. (Decreasing by 3) So, the next letter will be 26, which is Z.

Hence, the correct answer is YFZ.

4. Continuous Pattern Series

In this type, a series of small/capital letters are given which follow a particular pattern. However, some letters are missing from the series. The series follows a specific pattern and we have to find the letters which should come in place of the blank spaces or question marks.

In each of the following letter series, some of the letters are missing which are given in that order as one of the alternatives below it. Choose the correct alternative.

1._ stt _ tt _ tts _

(a) tsts

(b) ttst

(d) tsst

Ans. By observing the given series we can say that the pattern 'tst' is repeated. The series is tst/tst/tst/tst. Thus, the correct answer is ‘tsst’.

Coding Decoding

1. Coding is a process used to encrypt a word, a number in a particular code or pattern based on some set of rules. Decoding is a process to decrypt the pattern into its original form from the given codes.

2. There are various types of coding:

(i) Letter Coding: In this type of questions, alphabets of a word are replaced by some other alphabets according to a specific rule to form code.

(ii) Number Coding: In this type of questions, a word is replaced by certain numbers according to some specific rule.

(iii) Symbol Coding: In this type of questions, letters/numbers are replaced by certain symbols.

(iv) Substitution Coding: In this type of questions, some particular words are assigned with certain substituted names.

(v) Mixed Letter Coding: In this type of questions, three or four sentences are given in a coded language and the code for a particular word is asked. To analyse such codes, any two sentences bearing a common code is picked up. The common code will mean that word.

(vi) Matrix Coding: In this type of questions, letters are written down in matrix form and the code of the letters are denoted by the corresponding row and column of the matrix to which the letter belongs.

3. Points to remember while solving coding/decoding:

(i) To solve pattern based questions, we should learn the position values of the English alphabet. E-J-O-T-Y is the simplest way of remembering the position values. Position values of these letters are E - 5, J – 10, O – 15, T – 20, Y- 25. With these five landmarks, the position value of all the other letters can be easily found.

(ii) Sometimes, in such questions, reverse letter coding is followed i.e. the letters are coded in reverse alphabetical order, where, Z = 1, Y = 2, … , B = 25, A = 26.

(iii) In coding-decoding questions, always try to find the difference between the given letters and their corresponding codes. The difference can be positive or negative.

(iv) The letters/numbers can be shifted in both forward and backward direction.

(v) In matrix coding, first, write all the possible codes of each letter and then compare the given codes with the options.

(vi) Opposite of each alphabet should be known. A is opposite to Z, B is opposite to Y and so on.

(vii) In number coding, the pattern can be based on the sum of the digits of the numbers/letters, squares of natural numbers, cubes of natural numbers, the sum of the digits of letters in reverse alphabetical order, the difference between the place value of the letters.

(viii) To answer questions based on random coding-decoding, you just have to check for the code of an individual letter/number from the given word, and place the corresponding code for every letter.

Relationship and Blood relations

1. To solve the problems in blood relation, one should know how to draw a family tree. Important points in a family tree:

(i) Females are denoted by (-) sign and males by (+) sign. There can be other notions too.

(ii) The relation between two members of the family is shown by connecting a double-headed arrow.

(iii) The spouse relation is represented by the two ends of a double-headed arrow.

(iv) The family members of the upper generation are represented above in the family tree.

(v) Members of the same generation are represented along the same line.

(vi) Members of the lower generation are represented below in the family tree.

(vii) We use different symbols for different relations while drawing a family tree. Normally, a downward arrow is used to show different generations of the family.

Indirect relation	Direct relation
Father or Mother’s Daughter	Sister
Father or Mother’s Son	Brother
Father or Mother’s Sister	Aunt/maternal aunt
Father or Mother’s Brother	Uncle/maternal uncle
Father or Mother’s Father	Grandfather/maternal grandfather
Father or Mother’s Mother	Grandmother/maternal grandmother
Daughter’s husband	Son-in-law
Son’s wife	Daughter-in-law
Husband-or-wife’s brother	Brother-in-law
Husband-or-wife’s sister	Sister-in-law
Brother/Sister’s son	Nephew
Brother/Sister’s daughter	Niece
Aunt’s or uncle’s son or daughter	Cousin
Granddaughter’s or Grandson’s daughter	Great-granddaughter

2. The approach you need to follow to solve questions based on the statement is Backtracking. Backtracking means beginning with the last information and proceeding backwards. For example, if it's given that she is the daughter of the father of my grandmother’s daughter, then we start with the last information provided: ‘Grandmother’s daughter’.

3. In puzzle-based questions, first, the family tree must be drawn and then attributes if given, must be specified.

4. In coding-decoding of blood relations, the relationships among the members of the family are represented by certain specific codes or symbols such as +, -, $, *, /, &, #, @, ! etc. The answers are obtained by decoding the relationships hidden in the symbols.

Calendar

We follow the Gregorian calendar. It is also known as the Christian calendar or the Western calendar. The Gregorian calendar starts on 1st January and ends on 31st December. It is named after Pope Gregorian XIII, who introduced the calendar in October 1582.

There are two types of year in this calendar:

1. Ordinary year: It has 365 days.

2. Leap year: It has 366 days. The extra day is designated as 29 February. It occurs every four years. A year cannot be a leap year if it is not divisible by 4, in the case of a century year, it should be divisible by 400. For example 1600, 2000 are leap years but not 1700, 1800 and 1900, etc.

Calendar Problems can be solved using the concept of odd days.

Odd Days: In a given period, the number of days that are more than the weekly cycle is called odd days.

For example: 9 days = 1 week + 2 days. Then the extra 2 days become odd days.

Similarly, 18 days = 2 weeks + 4 days. Then the extra 4 days become odd days.

Therefore, an ordinary year has 1 odd day and a leap year has 2 odd days.

Reference chart:

Number of odd days	Day
0	Sunday
1	Monday
2	Tuesday
3	Wednesday
4	Thursday
5	Friday
6	Saturday

Odd days in 100 years = 5

Odd days in 200 years = 3

Odd days in 300 years = 1

Odd days in 400 years = 0

Direction Sense Test

1. There are Four primary directions i.e. North, South, East and West.

2. There are Four secondary directions i.e. North-east, North-West, South-East, South-West.

3. The shadow of a person always appears in the opposite direction from the light source.

4. At the time of sunrise, the shadow will always be towards the West.

5. At the time of sunset, the shadow will always be towards the East.

6. If a man is facing north, his shadow will be on his right during sunrise and on his left during sunset.

7. If a man is facing south, his shadow will be on his left during sunrise and on his right during sunset.

8. At noon, there will be no shadow.

9. Always draw a direction diagram to solve questions, based on the movement of a person or a thing.

10. Pythagoras theorem is used often to solve direction based questions. It states that $P^{2} + B^{2} + H^{2}$ , where $P$ is the perpendicular, $B$ is the base and $H$ is the hypotenuse.

11. To solve questions, based on movement, it is better to assume yourself in that position and use gestures to understand the left/right or north/south/east/west movement.

12. In coded direction test, symbols are used to denote direction. Analyse each symbol and solve step by step from the forward direction.

13. If you are facing North, your right will be East and your left will be West.

14. If you are facing South, your right will be West and your left will be East.

In these types of questions we have to find out the terms that have something in common and hence forming a group, or we have to find out the term that are different from the others.

Following are the types of the questions that are asked:

Word Classification

In these questions the same or the different elements are classified on the basis of common properties like name, alphabetical order, etc.

Examples:

1. Four of the following five are alike in a certain way and so form a group. Find the one which does not belong to the group.

(i) MARS

(ii) URANUS

(iii) JUPITER

(iv) MOON

(v) EARTH

Ans. All the given words are planets except Moon as it is a satellite.

Hence, the correct answer is Moon.

2. Four of the following five are alike in a certain way and so form a group. Find the one which does not belong to the group.

(i) ERSO

(ii) ULTOS

(iii) GAERON

(iv) ILYLL

(v) NIASJEM

Ans. Here we can see that all words are jumbled form of the names of flowers. i.e. ROSE, LOTUS, LILLY and JASMINE. But ORANGE is a fruit, so it will be different.

Hence, the correct answer is GAERON.

Letter Classification

In this type of questions, a certain number of letter groups are given and we have to select the one that are same or different from the others.

Example:

1. Four of the following five are alike in a certain way and so form a group. Find the one which does not belong to the group

(i) ZW

(ii) TQ

(iii) NL

(iv) PM

(v) SP

Ans. Here we can see that in these pairs there is a difference of 3 between the place values of the letters,

Z - 3 = W

T - 3 = Q

S - 3 = P

P - 3 = M.

But, in NL the difference is 2.

N - 2 = L.

Hence, the correct answer is NL.

Number Classification

In this type we have to choose the odd number from the given numbers or the numbers that are forming a pair. The numbers can be paired on the basis of odd, even, prime, square, cubes etc.

Examples:

1. Four of the following five are alike in a certain way and so form a group. Find the one which does not belong to the group

(i) 19

(ii) 37

(iii) 47

(iv) 17

(v) 27

Ans. Here all the given numbers are odd. But 19, 17, 47 and 37 are prime numbers. But 27 is a composite number.

Hence, the correct answer is 27.

2. Four of the following five are alike in a certain way and so form a group. Find the one which does not belong to the group

(i) 361

(ii) 441

(iii) 625

(iv) 289

(v) 343

Ans. Here all the given numbers are squares except 343, it is a cubes of 7.

Hence, the correct answer is 343.

Figure Classification

1. In the figure completion series, four-five different figures following a specific pattern are given and we need to analyse the pattern and then find the correct figure accordingly.

2. The figures can be based on the rotation of all the elements in the figure.

3. The figures can be based on the movement of the elements inside the figure.

4. The figures can be based on an incremental number of things.

5. The figures can be given in the form of a matrix and we need to analyse the pattern followed in the other figures.

6. The figures can be based on the clockwise or anti-clockwise movement of the figures.

7. The figures can be based on the shape of the elements.

8. The figures can be based on the shading of elements of a figure.

9. In this figure, in each step, the pin rotates 90 degrees clockwise and the arrow rotates 90 degrees anti-clockwise. Hence, option C is the correct answer.

10. Here, all the elements together move one space to the right in each step and once they reach the rightmost position, then in the next step, they move to the leftmost position. Also, in the first step, the first (uppermost) and the third elements interchange positions; in the second step, the second and the fourth elements interchange positions and in the third step, none of the elements interchange positions. These three steps are repeated to continue the series. Hence, option C is the correct answer.

11. In visual classification, we need to find the odd image or the image which does not follow the same pattern as followed by the other images.

A	B	C	D	E	F	G	H	I	J	K	L	M
1	2	3	4	5	6	7	8	9	10	11	12	13

N	O	P	Q	R	S	T	U	V	W	X	Y	Z
14	15	16	17	18	19	20	21	22	23	24	25	26

A	B	C	D	E	F	G	H	I	J	K	L	M
1	2	3	4	5	6	7	8	9	10	11	12	13

N	O	P	Q	R	S	T	U	V	W	X	Y	Z
14	15	16	17	18	19	20	21	22	23	24	25	26

A	B	C	D	E	F	G	H	I	J	K	L	M
1	2	3	4	5	6	7	8	9	10	11	12	13

N	O	P	Q	R	S	T	U	V	W	X	Y	Z
14	15	16	17	18	19	20	21	22	23	24	25	26

How many numbers from 1 to 100 can be divided by 8 whose at least one digit is 8?

Important Questions on Reasoning (lncluding Mathematical)

Learn and Prepare for any exam you want !

How many numbers from $1$ to $100$ can be divided by $8$ whose at least one digit is $8$ ?