Mathematics - Chapter - 5 (Logical Reasoning)

Coding & Decoding

Coding is a method of transmitting a message between the sender and the receiver that no third person can understand it. The coding and decoding one’s ability of deciphering the rule and breaking the code to decipher the message will be tested to know.  Some words are stand for some another words which is known code of the word. Process of replacing some word by code word is known as Coding. Decoding is reverse of Coding. Coding and Decoding test is set up to judge candidates’ ability to decipher the rule.

Approach

1.      Observe alphabets or numbers given in the code keenly.

2.      Find the sequence it follows whether it is ascending or descending.

3.      Detect the rule in which the alphabets/numbers/words follow.

4.      Fill the appropriate letter/number/word in the blank given.

Letter coding

Alphabets in a word are replaced by other alphabets according to a specific rule to know its code. So the common rule should be detected first. Some examples are given below.

1.      ‘ZYXW’ as coded as ‘ABCD’ then ‘STUV’ is coded as...........
Answer: Z – A, Y– B, X – C, W – D
V – E, U – F, T – G, S – H
STUV = HGFE
Answer = HGFE
Rule= front alphabet= back alphabet.

2.      ‘bcd’ is coded as ‘def’ then ‘True’ is coded as..........
Answer: b – d (+2)
c – e (+2)
d – f (+2)
+2 letters are considered in this code.
True – Vtwg
Answer = Vtwg.

3.      ‘Hyderabad’ is coded as ‘Ixedszcze’ then ‘Chennai’ is coded as..............
Answer: H – I (+1)
Y – X (1–)
D – E (1+)
E – D (1-)
R – S (1+)
A – Z (1–)
B – C (1+)
A – Z (1– )
D – E (1+)
Here if we observe alternatively the letter increasing and one letter decreasing.
Chennai =dgfmozj
Answer = dgfmozj

Number Coding

In this each alphabets or words are assigned to the numeric values we should observe the given letters and the assigned values and use the same rule to find the value to of given code. Some examples are given below:

1.      Apple is coded as 25563, Rung is coded as 7148. Then purple is coded as
Answer:

PURPLE – 517563
Answer = 517563.

2.      In a language A is coded as 1, B is coded as 2, ….. then FACE is coded as
Answer:

Then FACE = 6135
Answer = 6135.

3.      PUSH is coded as 1234, ROUGH is coded as 65274. Then SOUP is coded as
Answer:

SOUP = 3521
Answer = 3521.

Substitution

In this section an object names are substituted with different object names. We should carefully trace the substitution and answer given question. Some examples are given below.

1.      ‘book’ is coded as ‘pencil’, ‘pencil’ is coded as ‘mirror’, ‘mirror is coded as ‘book’. Then what is useful to write on a paper?

Answer: Pencil is coded as mirror
Answer = mirror.

2.      ‘Man’ is coded as ‘woman’, woman is coded as ‘girl’, and ‘girl’ is coded as boy ’,‘ boy is coded as ‘worker’ then 6 years female is known as?
Answer: 6 years female = girl, but ‘girl’ is coded as ‘boy’.
Answer = boy.

3.      ‘Reds’ are ‘blues’, ‘blues’ are ‘whites’, ‘whites’ are ‘yellows’, ‘yellows’ are ‘oranges’, ‘oranges’ are ‘pinks’, then what is the colour of the sky?
Answer: Sky is blue, but blues are whites
Answer = white.
Exercise questions

4.      In a certain code, COMPUTER is written as RFUVQNPC. How is MEDICINE written in the same code ?
a) MFEDJJOE            b) EOJDEJFM
c) MFEJDJOE            d)EOJDJEFM
Ans: Option d
The letters of the word are written in reverse order and expect the first and the last letter all other letters are
move one step forward

5.      In a code language, A is written as B, B is written as C, C is written as D and so on, then how will SMART be written in that code language ?
a) TLBSU                   b)SHBSU
c)TNBSU                    d)SNBRU
Ans: Option c
The letters are coded by moving them 1 step forward.

6.      In a certain code , RIPPLE is written as 613382 and LIFE is written as 8192. How is PILLER written in that code?

a) 318826                    b)776655
c)786543                     d)156724
Ans: Option a:
Word : R I P P L E  L I F E  P I L L E R
Code :  6 1 3 3 8  2  8 1 9 2  3 1 8 8  2 6

7.      In a certain code FLOWER is coded as 36 and SUNFLOWER is coded as 81, then how to code FOLLOWS?
a) 42                b)49
c)63                 d) 36
Ans: Option b
The word FLOWER has 6 letters . 6² is 36
The word SUNFLOWER has 9 letters. 9² is 81
Like FOLLOWS has 7 letters. So 7² is 49

8.      In a certain code ,'il be pee' means 'roses are blue','sik hee' means 'red flowers' and 'pee mit hee' means 'flowers are vegetables', How is 'red' written in that code?
a) hee
b) sik
c) be
d) cannot be determined
e) none
Ans: Option b
Code Sentence
Il be pee roses are blue
Sik hee red flowers
Pee mit hee flowers are vegetables
In II and III code ‘hee’ stands for ‘flowers’. So ‘sik’ stands for ‘red’

9.      In a certain code language : ‘dugo hui mul zo’ stans for ‘work is very hard’ ‘hui dugo ba ki’ for ‘Bingo is very smart’; ‘nano mul dugo’ for ‘cake is hard’; and ‘mul ki gu’ for ‘smart and hard’ Which of the following word stand for Bingo ?
a) Jalu
b) Dugo
c) Ki
d) Ba
Ans: Option d
Code Sentence
1.dugo hui mul zo work is very hard
2.hui dugo ba ki bingo is very smart
3.nano mul dugo cake is hard
4.mul ki gu smart and hard
From second code and its sentence neither ‘ba’ is repeated nor is ‘Bingo.

10.  If rain is called water, water is called air, air is called cloud, cloud is called sky, sky is called sea, sea is called road, where do the aeroplanes fly ?
a) Water
b) Road
c) Sea
d) Cloud
Ans: Option c
Aeroplanes fly in sky and as per given codes sky is sea

11.  If Orange is called Lemon, Lemon is called Flower, Flower is called Fish, Fish is called Tail and Tail is called Pen, what is Rose ?
a) Pen
b) Lemon
c) Flower
d) Fish
Ans: Option d
Rose is a flower and as per given codes flower is fish.

12.  In a certain code language $#* means ‘Shirt is clean’, @ D# means ‘Clean and neat’ and @ ? means ‘neat boy’, then what is the code for ‘and’ in that language.

a) #
b) D
c) @
d) Data inadequate
Ans: Option b
Code sentence
$#* ‘Shirt is clean’,
@ D# ‘Clean and neat’
@ ? ‘neat boy’
Here # stands for clean and @ stands for neat. D stands for ‘and’

13.  If A stands for +, B stands for -, C stands for x, what is the value of (10C4)(A) (4C4)B6 ?
a) 60
b) 50
c) 56
d) 46
Ans: Option b
(10C4)(A) (4C4)B6 = (10 * 4) + (4*4) –6 = 50

Mathematical Operations

This section deals with questions on simple mathematical operations. Here, the four fundamental operations -- addition, subtraction, multiplication and division and also statements such as 'less than', 'greater than', 'equal to', 'not equal to', etc. are represented by symbols, different from the usual ones. The questions involving these operations are set using artificial symbols. The candidate has to substitute the real signs and solve the questions accordingly, to get the answer.

1.      E.g. In following alphabet series, one term missing as shown by question mark. Choose missing term from options.

Z, U, Q, ?, L

 Option:

A. I

B. K

C. M

D. N

 Answer: D . N 
 Justification:

The first, second, third,... letters of the series are respectively moved one, two, three,... steps forward to obtain the successive terms.

2.      In following alphabet series , one term missing as shown by question mark . Choose missing term from options.

A, C, F, H, ?, M

 Option:

A. L

B. K

C. J

D. I

 Answer: B . K 
 Justification:

The letters are alternately moved two and three steps forward to obtain the successive terms.

3.      In following alphabet series, one term missing as shown by question mark. Choose missing term from options.

A, Z, X, B, V, T, C, R, ?, ?

Option:

A. P, D

B. E, O

C. Q, E

D. O, Q

E. Q, O

 Answer: A. P, D 
 Justification:

The first, fourth and seventh letters are in alphabetical order.
So, tenth letter would be the letter after C  i.e. D.
Also, the second and third letters are alternate and in reverse order and so are the fifth and sixth letters and the eighth and ninth letters.

4.      In following alphabet series, one term missing as shown by question mark . Choose missing term from options.

R, M,?, F, D, ?

 Option:

A. C, B

B. J, H

C. B, H

D. H, C

E. I, C

 Answer: E. I, C 
 Justification:

Letter is in reverse order in which from the last 0, 1, 2, 3 and 4 letters are missing between two consecutive letters.

Number Coding

In Number coding type of questions, either numerical code values are assigned to a word or alphabetical code letters are assigned to the numbers. The candidate is required to analyse the code as per the directions.

1.      If ROSE is coded as 6821, CHAIR is coded as 73456 and PREACH is coded as 961473, what will be the code for SEARCH?

Option:

A. 246173

B. 214673

C. 214763

D. 216473

Answer: B. 214673 
Justifications:

The alphabets are coded as shown:

R	O	S	E	C	H	A	I	P
6	8	2	1	7	3	4	5	9

So, in SEARCH,
S ia coded as 2,
E as 1,
A as 4,
R as 6,
C as 7,
H as 3.
Thus, the code for SEARCH is 214673.

2.      If the letters in PRABA are coded as 27595, and THILAK are coded as 368451, how can BHARATHI be coded?

 Option:

A. 37536689

B. 57686535

C. 96575368

D. 96855368

 Answer: C . 96575368 

 Justification:

The alphabets are coded as shown:

P	R	A	B	T	H	I	L	K
2	7	5	9	3	6	8	4	1

So, B is coded as 9,
H as 6,
A as 5,
R as 7,
T as 3   and
I as 8.
Thus, the code for BHARATHI is 96575368.

Logical Venn Diagram

Introduction

The main aim of this section is to test your ability about the relation between some items of a group by diagrams. In these questions some figures of circles and some words are given. You have to choose a figure which represents the given words.

Some critical examples are given below:

Example 1:

If all the words are of different groups, then they will be shown by the diagram as given below.

Dog, Cow, Horse

All these three are animals but of different groups, there is no relation between them. Hence they will be represented by three different circles.

Example 2:

If the first word is related to second word and second word is related to third word. Then they will be shown by diagram as given below.

Unit, Tens, Hundreds

Ten units together make one Tens or in one tens, whole unit is available and ten tens together make one hundreds.

Example 3:

If two different items are completely related to third item, they will be shown as below.

Pen, Pencil, Stationery

Example 4:

If there is some relation between two items and these two items are completely related to a third item they will be shown as given below.

Women, Sisters, Mothers

Some sisters may be mothers and vice-versa. Similarly some mothers may not be sisters and vice-versa. But all the sisters and all the mothers belong to women group.

Example 5:

Two items are related to a third item to some extent but not completely and first two items totally different.

Students, Boys, Girls

The boys and girls are different items while some boys may be students. Similarly among girls some may be students.

Example 6:

All the three items are related to one another but to some extent not completely.

Boys, Students, Athletes

Some boys may be students and vice-versa. Similarly some boys may be athletes and vice-versa. Some students may be athletes and vice-versa.

Example 7:

Two items are related to each other completely and third item is entirely different from first two.

Lions, Carnivorous, Cows

All the lions are carnivorous but no cow is lion or carnivorous.

Example 8:

First item is completely related to second and third item is partially related to first and second item.

Dogs, Animals, Flesh-eaters

All the dogs are belonging to animals but some dogs are flesh eater but not all.

Example 9:

First item is partially related to second but third is entirely different from the first two.

Dogs, Flesh-eaters, Cows

Some dogs are flesh-eaters but not all while any dog or any flesh-eater cannot be cow.

1.      In a country three persons A, B and C live. They are three different persons. This information can be represented as:

Here, we can see that A, B and C are different elements so they’ve represented by different circles.

2.      If we were to represent information in which two elements are intermingled while the third one is different we’ll do that a bit differently.

For example: Hindu, Indian and Parrot. Now, logically we know that Some Hindus are Indian (as some Hindu might be living abroad and be Australian or any other country’s citizen) and also, no Parrot is Hindu (as animals have no religion) also no Parrot is Indian (as no animal has ethnicity). This information of Hindu, Indian, Parrot can be represented as follows:

Here, the shaded area shows those Hindus who are Indians at the same time. Parrot are represented in a different circle.

3.      Suppose, we need to convey this: Dog, Animal and Cow.

Now we know that all dogs are animals (clearly no dog is human) so the circle of ‘dog’ will have to be completely surrounded by circle of animal though circle of animal can have some spare space aside from dog as dog isn’t the only animal. Similarly, all ‘cows’ are animals so the circle of ‘cow’ will have to be completely surrounded by circle of animal though circle of animal can have some spare space aside from cow as cow isn’t the only animal. This information can be represented as:

Here, we can see that ‘Animal’ has been represented by a big circle which encompasses the circles for both ‘cow’ and ‘dog. Notice, the circle for ‘animal’ has some spare space as this can contain other types of animals because ‘cow’ and ‘dog’ aren’t the only type of animal.

Types of questions asked in Competition Exam

Let’s have a look at the type of questions asked specifically in SSC exam. There are basically two types of questions:

Finding relationship

To solve these kinds of questions, we need to have a strong grip on common relationships that exist in the world around us. Like to define the relationship between Catholics & Christian we need to know that Catholics are the type of Christians hence we can easily conclude that all Catholics are Christian but some Christians will not be Catholics as they will be the other type of Christians. This information can be represented as:

 A typical question might look like this: Dean, Painter, Singer.

We live in a diverse world where people can be multi-talented also people possess just one talent so this info can be represented by 7 categories of people:

a) Who are only Dean

b) Who are only Painter

c) Who are only Singer

d) Who are both Dean & Painter

e) Who are both Painter & Singer

f) Who are both Singer & Dean

g) Who are all Dean, Painter & Singer

This information can be represented by Venn - diagram as follow: (for reader’s convenience, the different regions have been labeled as named above but in exams, questions aren’t marked this way)