Analogy
Simple meaning of analogy is similarity. But, in terms of reasoning, the meaning of analogy is logical similarity in two or more things. This similarity may be on the basis of properties, kinds, traits, shapes etc.
Example:
(i) Student : School : : Patient : Hospital
Explanation: A 'Student' goes to ‘School’ in the same way a 'Patient' goes to 'Hospital', In other words, school (place to take education) is a proper place for a student arid in the same way hospital (place to get treatment) is a proper place for a patient.
1st pair- Student: School (person and proper place relationship).
2nd pair - Patient: Hospital (person and proper place relationship).
Clearly, both pairs show similar relationship in a logical way. Hence, both pairs are analogous or it is said that both pairs exhibit analogy.
(ii) Good : Bad : : Tall : Short
Explanation:
1st pair - Good: Bad (opposite relationship).
2nd pair - Tall: Short (opposite relationship).
Clearly, both pairs show similar relationship (opposite relationship). Hence, both pairs exhibit analogy.
Types of Problems
Problems Based on Synonymous Relationship
In such problems, the words given in one pair have same meaning and the same relationship that is found in another pair of words.
Example 1
Right: Correct:: Fat: Bulky
Explanation:
1st pair - Right: Correct (synonymous relationship).
2nd pair - Fat: Bulky (synonymous relationship).
Example 2
Brave : Bold :: Wrong : Incorrect
Explanation:
1st pair - Brave: Bold (synonymous relationship).
2nd pair - Wrong: Incorrect (synonymous relationship).
Commonly Asked Questions
Select the pair which is related in the same way as the pair of words given in the question.
Tough : Hard \[::\text{ }\_\_\_\_\_\_\text{ }:\text{ }\_\_\_\_\_\_\_\_\]
(a) Rich : Wealthy (b) Rich : Poor
(c) Tall : Short (d) True : False
(e) None of these
Answer (a)
Explanation: Option (a) is correct because ‘Tough’ and 'Hard' are synonymous words. In the same manner 'Rich’ and ‘Wealthy' are synonymous words. Rest of the options is incorrect because words in option (b), (c) and (d) have opposite meanings and option (e) is useless because of the correctness of option (a).
'Start' is related to ‘Begin’ in the same way as ‘Joy’ is related to…………..
(a) Right (b) False
(c) True (d) Delight
(e) None of these
Answer (d)
Explanation: Option (d) is correct because ‘Start’ and ‘Begin’ have same meaning.
Similarly, ‘Joy’ and ‘Delight' have same meaning.
Rest of the options is incorrect because of the correctness of option (d).
Problems Based on Opposite Relationship
In such more...
What is Blood Relation?
Blood relation is biological relation. Remember a wife and husband are not biologically related but they are biological parents of their own children. Similarly, brother, sister, paternal grandfather, paternal grandmother, maternal grandfather, maternal grandmother, grandson, grandmother, niece, cousin etc. are our blood relatives.
Types of Blood Relations
There are mainly two types of blood relations:
(i) Blood relation from paternal side
(ii) Blood relation from maternal side
Now, we will discuss both kind of relations one by one.
Blood Relation From Paternal Side
This type of blood relation can be further subdivided into three types:
Past generations of father
Example: Great grandfather, great grandmother, grandfather, grandmother etc.
Parallel generations of father
Examples: Uncles (brothers of father), aunts (sisters of father) etc.
Future generations of father
Examples: Sons, daughters, grandsons, granddaughters etc.
Blood Relation From Maternal Side
This type of blood relations can also be subdivided into three types:"
Past generations of mother
Examples: Maternal great grandfather, maternal great grandmother, maternal grandfather, maternal grandmother etc.
Parallel generations of mother
Examples: Maternal uncles, maternal aunts etc.
Future generations of mother
Examples: Sons, daughters, grandsons, granddaughters etc.
Some Important Blood Relations
Concept of Direction
In our day to day life we make our concept of direction after seeing the position of the sun. In fact, this is truth that sun rises in the East and goes down in the West. Thus, when we stand facing sunrise then our front is called East while our back is called West. At this position, our left hand is in the northward and the right hand is in the southward. Let us see the following direction map that will make your concept more clear.
Direction Map:
Note: On paper North is always on the top while South is always at the bottom.
Concept of Turn
Left turn = Anti clockwise turn
Right turn = Clockwise turn
Let us understand it through pictorial presentation:"
(i) (ii)
(iii) (iv)
Important Points Regarding Directions
If our face is towards North, then after left turn our face will be towards West while after right turn it will be towards East.
If our face is towards South, then after left turn our face will be towards East and after right turn it will be towards West.
If our face is towards East, then after left turn our face will be towards North and after right turn it will be towards South.
If our face is towards West, then after left turn our face will be towards South and after right turn it will be towards North.
If our face is towards North West, then after left turn our face will be towards South West and after right turn it will be towards North East.
If our face is towards South West, then after left turn our face will be towards South East and after right turn it will be towards North West.
If our face is towards South East, then after left turn our face will be towards North East and after right turn it will be towards South West.
If our face is towards North East, then after left turn our face will be towards North West and after right turn it will be towards South East.
Concept of Minimum Distance
Minimum distance between initial and last point
\[{{h}^{2}}={{b}^{2}}+{{p}^{2}},\] where
h = Hypotenuse
b = Base
p = perpendicular
Remember this important rule is known as 'Pythagoras Theorem'.
Example 1
Pinki starts moving from a point P towards East. After walking some distance she turns her left. Now, her direction is definitely towards North. more...
What is coding-Decoding?
Let us start it with an interesting story.
Suppose you and your father like ice-cream very much. But your mother does not want you two to have it because you both catch cold very easily. Then you and your father make a secret plan to use the word 'Chocolate' for ice-cream. Now, whenever you feel like eating ice-cream you say to your father that you want to eat chocolates. Mother hears it and thinks that you are really demanding chocolates. Therefore, she gives you permission to go out with father and enjoy chocolates. Then you and your father go out, eat ice-cream and comeback.
What do you think happens here? Here, you coded the word Ice-cream' with another word
'Chocolate'. Only you and father know about this code, when you say that you want to eat
'Chocolate', your father hears and easily decodes it that you want to eat ice-cream. This can be presented as below.
\[Ice-cream\xrightarrow{Coded\,as}Chocolate\xrightarrow{Decoded\,as}Ice-cream\]
How to Decode?
In reasoning, words, letters and numbers are coded according to a certain rule. While solving problems, student has to identify that particular rule first and then the same rule is applied to decode other coded words, letters, number etc. The types of coding decoding problems will give you more clear concept about it. But before coming to the actual problems, we must remember the positions of letters in English alphabet in forward order that will help you in solving problems of coding-decoding,
Let us see the positions:
Types of Problems
Coding-Decoding in Forward Sequence
In such problems, letters are coded in forward alphabetical sequence.
Example 1
If 'AB' is coded as ‘BC’, then ‘EF’ will definitely be coded as ‘FG’.
Explanation: Here, letters of ‘AB’ shift one place in forward alphabetical sequence.
Let us see:
Similarly, letters of 'EF' shift one place in forward alphabetical order.
Let us see:
Clearly, code for ‘AB’ is ‘BC’ and code for ‘EF’ is ‘FG’
Example 2
If 'GO' is coded as 'IQ', then 'TO' will definitely be coded as 'VQ'.
Explanation: Here, letters of the word 'GO' shift two places in forward alphabetical sequence.
Let us see:
Similarly, both letters of the word 'TO' will move two places forward
Let us see:
Note: In forward sequence coding-decoding ‘Table 1’ is used.
Commonly Asked Questions
If code of ‘LMN’= 'MNO’, then find the code for 'PQR'.
(a) QRS more...
What is a Letter Series?
A letter series is a sequence of many elements made of letters of English alphabet only. Such sequence is formed by putting the letters one after another from left to right.
Example:
(i) A BCD
(ii)DCB A
(iii) AL BL CB DE
Note: An element of a series is a single member (identity) of that particular series.
For example, in a letter series 'A B C D', each A, B, C and D is a single element. Point to be noted that an element can be made with more than one letter. In a series of 'AB LE BE’, each AB, LE and BE is a single element.
Properties of Letter Series
A letter series can be in forward order
Look at the following:
A BCD
BCDE
Commonly Asked Questions
Find the next letter in the series given below.
L M N…..........
(a) A (b) O
(c) D (d) B
(e) None of these
Answer (b)
Explanation: Option (b) is correct because this is a forward order series of English alphabet in which M comes just after L, N comes just after M and O comes just after N. Rest of the options is incorrect because of the correctness of option (b).
Which of the following options is the next element of the given series?
L N P ........
(a) Q (b) A
(c) S (d) R
(e) None of these
Answer (d)
Explanation; Option (d) is correct because every next letter takes place skipping one letter in forward alphabetical order.
Let us see:
Rest of the options is incorrect because of the correctness of option (d).
A letter series can be in reverse order.
Look at the following:
C B A
D C B A
Commonly Asked Questions
Find the next letter in the following series.
E D C ………
(a) A (b) B
(c) F (d) G
(e) None of these
Explanation: Option (b) is correct because this is a reverse order series of English .alphabet. This series starts with E and then comes D, the next letter in reverse order. Just after D, C will be the next letter in the reverse order. Similarly, B comes just after C to fill the blank space.
Rest of the options is incorrect because of the correctness of option (b).
Find the next element in more...
What is a Number Series?
A number series is a sequence of numbers which follow a particular rule. Each element of a series is called a 'term'. In this chapter, we will analyse the pattern of different kind of number series that a particular series follow and find the missing term to continue the pattern.
Example
Find the missing term in the given series.
2, 8, 32, 128, __.
(a) 512 (b) 510
(c) 516 (d) 520
(e) None of these
Answer (a)
Explanation: Option (a) is correct. The relationship between the terms or the pattern that the given series follows is as below.
Therefore, the next term or missing term of the given series will be
Find the missing term in the following number series.
2, 3, 5, 7, 11, 13__.
(a) 15 (b) 19
(c) 17 (d) 14
(e) None of these
Answer (c)
Explanation: Option (c) is correct. The given number series is the sequence of consecutive prime number. So, the next number or the missing term will be 17,
Commonly Asked Questions
Find the next number.
64, 32, 16, 8, __
(a) 2 (b) 4
(c) 6 (d) 0
(e) None of these
Answer (b)
Explanation: Option (b) is correct because in the given number series, each number is half of its previous number. So the required number or the missing term will be 4.
Rest of the options is incorrect because of the correctness of option (b).
What comes in place of question mark (?) in the series given below?
1, 4, 10, 19, ?
(a) 30 (b) 31
(c) 32 (d) 33
(e) None of these
Answer: (b)
Explanation: Option (b) is correct because the series goes as following-
So the required next term in the series will be
Rest of the options is incorrect because of the correctness of option (b)
A single number series can have more than one series.
Example
Look at the following:
(i) 1 4 2 5 3 6
Clearly,
1st series: 1 2 3
2nd series: 4 5 5
(ii) 4 9 5 3 6 8 7 2 8 7 9 1
Let us see:
Here,
1st series: 4 5 6 7 8 9
2nd series: 9 8 7
3rd series: 3 2 1
Commonly Asked Questions
Find the missing number in the following series
8 2 9 1 10 0…………..
(a) 12 (b) 11
(c) 3 (d) 5
(e) None of these
Answer (b)
Explanation: Option (b) is correct.
Let us see:
more...
Time and clock
Clock is a device which is used to measure and display the time. The face or dial of a clock is divided into 60 equal parts called minute space and it is numbered from 1 to 12, in such a way that each subsequent number is equidistant (5 minutes spaces apart) from the preceding number. A clock has two hands, the smaller one is the hour hand/ while larger one is called the minute hand. When hour hand travels five minutes spaces, the minute hand travels 60 minutes spaces. Therefore, in 60 minutes the minute hand gains 55 minute on the hour hand.
Properties of clock
In 60 minutes/ the minute hand gains 55 minutes on the hour hand,
A clock is said to be too fast, if it shows time more than that of shown by a correct clock.
A clock is said to be too slow, if it shows time less than that of shown by a correct clock.
In every hour, both the hands coincide once.
When the two hands are at right angle, they are 15 minutes spaces apart.
When the two hands are in opposite directions, they are 30 minutes spaces apart, this situation occurs once in a hour.
The hands of a clock are in straight line when they are coincident or opposite to each other.
Hour hand of a clock takes 12 hours to trace the angle of \[360{}^\circ \].
Minute hand of a clock takes 1 hour to trace the angle of \[360{}^\circ \].
Example 1
Choose the time from the following options when the hands of a clock will be in the same straight line.
(a) 4:00 p.m. (b) 8:00 p.m.
(c) 7:00 p.m. (d) 6:00 p.m.
(e) None of these
Answer (d)
Explanation: The two hands of a clock are in the same straight line when they are either coincident or 30 minutes spaces apart from each other.
At 4:00 p.m., the minute hand will be 20 minutes spaces apart from the hour hand.
So option (a) is incorrect.
At 8:00 p.m., the minute hand will be 20 minutes spaces apart from the hour hand.
So option (b) is incorrect.
At 7:00 p.m., the minute hand will be 25 minutes spaces apart from the hour hand.
So option (c) is incorrect.
At 6:00 p.m., the minute hand will be 30 minutes spaces apart from the hour hand.
So option (d) is correct.
Therefore, the correct answer is 6 : 00 p.m.
Between 2 O'clock to 10 O'clock, how many times the hands of a clock are at right angle?
(a) 14 (b) 12
(c) 16 (d) 15 more...
What is Non-verbal Reasoning
Non-Verbal reasoning is a figure based reasoning. It has no language at all. To solve non-verbal problems one has to find out the pattern of pictorial presentation in the given figure. To get a more clear concept about non-verbal reasoning. Let us see the types of problems coming before you.
Types of Problems
Problems Based on Mirror Image
In a mirror image, left part of an object becomes right part and right part becomes left part.
Remember the rule given below,
Left Hand Side (LH.S.) \[\overset{{}}{leftrightarrows}\] Right hand Side (R.H.S.)
Example 1
Number System
A system of naming or representing numbers.
Number
A number is a mathematical object which is used to count, label and measure,
Example
1, 5, 19, 325
Main Type
Natural numbers/whole-numbers, integers, rational numbers, irrational numbers, real numbers.
Natural Numbers
Counting numbers 1, 2, 3, 4, 5, 6... are called natural numbers. These numbers are also referred to as the positive integers.
Properties
The set of natural numbers, commonly denoted by N.
1 is the smallest natural number.
No largest natural number can be found because the set of natural numbers is infinite,
The successor of a natural number is 1 more than the number.
The predecessor of a natural number is 1 less than the number.
Whole Numbers
The natural numbers along with zero form the collection of whole numbers.
Example 0, 1, 2, 3, 4, 5, 6 ....
Properties
The set of whole numbers, commonly denoted by W.
0 is the smallest whole number.
No largest whole number can be found because the set of whole numbers is infinite.
The successor of a whole number is 1 more than the number
The predecessor of a whole number is 1 less than the number.
Factors
A factor of a number is an exact divisor of that number.
Example 1
Factors of \[4=1,\,2,\,4\]
Example 2
Factors of \[15=1,\,3,\,5,\,15\]
Properties
1 is the factor of every number.
Every number is a factor of itself.
The factors of a number are smaller or equal to the number.
Numbers of factors of a given number are finite.
Every factor of a number is an exact divisor of that number.
A number for which sum of all of its factors is equal to twice of twice the number is called a perfect number.
1 is the only number which has exactly one factor, namely itself.
Multiple
A multiple of any natural number is a number formed by multiplying that number by any whole number or a multiple is the product of any quantity and an integer or a number is said to be multiple of any of its factors.
Example 1
First three multiple of 4 are \[4\times 1= 4,4\times 2 = 8\] and \[4\times 3 =12\]
Example 2
First three multiple of 19 are \[19\times 1=19,19\times 2=38\] and \[19\times 3=57\]
Properties
0 is the multiple of everything.
Every number is a multiple of itself,
Every multiple is greater than or equal to that number
The number of multiples of a given number is infinite.
A number is a multiple of each of its factors,
Prime Numbers
The numbers which have exactly two factors, 1 and the number itself, are called prime numbers.
Example more...
Algebra
Algebra is generalized arithmetic in which unknown or unspecified numbers are represented by using letters known as literals.
Constant and variable: A symbol having a fixed numerical value is called a constant and a symbol which takes on various numerical values is known as variables.,
Example: \[8,-25,\text{ }6\frac{6}{11},\,3\frac{1}{2}\] are examples of constants whereas a, b, c, u, u x and y are examples of variables.
Algebraic expression: An algebraic expression composed of arithmetic numbers, letters and signs of operation.
Example: \[5x+8,\text{ }9y+3x\] and 8z are examples of algebraic expressions.
Terms of an expression: Various parts of an algebraic expression separated by the signs plus (+) or minus (-) are known as the terms of the expression.
Example: The algebraic expression \[6x+8y+9\] have three terms, 6x, 8y and 9.
Monomial: An algebraic expression having only one term is known as monomial.
Example: \[2,5x,6xy\] and\[-89xyz\] are examples of monomials.
Binomial: An algebraic expression having two terms is known as binomial.
Example: \[2x+y,3z+5y\] and \[x+8\]are examples of binomials,
Trinomial: An algebraic expression having three terms is known as trinomial
Example: \[x+y-9,\text{ }5a+6b+c\] and \[5x+xy+9\] are examples of trinomials.
Polynomial: An algebraic expression containing two or more terms is called polynomial,
Example: \[5x+6,\text{ }7x+8y+9\]and \[15+xy+9y+8x\] are examples of polynomials,
Factor: A factor is any one of two or more numbers that are multiplied together.
Example: 5 and x are factors of 5x.
Coefficients: In a product of numbers and literals, any of the factors is called the coefficient of the product of other factors.
Example: In 7xy, the coefficient of x is 7y and the coefficient of y is 7x.
Like terms: The terms which have the same literal factors are called like or similar terms.
Example: 7x, 9x, x are examples of like terms.
Unlike terms: The terms which have different literal factors are called unlike or dissimilar terms.
Example: \[5x,3xy,7xz\] are examples of unlike terms.
Algebraic equation: An equation is a mathematical statement equating two quantities.
Example: \[x+9=15,\text{ }5x-8=3x\] and \[3x-7=4\] are examples of algebraic equations.
Solution of equation: The value of the variable in an equation which satisfies the equation is called solution of the equation.
Example: \[x+9=20\], here the value \[~x=11\] satisfies the equation/ therefore \[~x=11\] is the solution of the equation \[x+9=20\].
Ratio
The ratio of two quantities of the same kind and in the same units is a fraction which shows how many times the one quantity is of other.
Example
If a and b are two physical quantities of same kind and in the same units, then the fraction \[\frac{a}{b}\]is called the ratio of a to b and denoted as a : b. Here a and b are called terms of the ratio.
The former 'a' is called the first term or antecedent and the latter b is called second term of consequent
Note 1: A ratio is unchanged if the two more...