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Mathematical Reasoning and Aptitude || Number series || Letter series || Codes || Relationships
Mathematical Reasoning and Aptitude
UGC NET REASONING
SYLLABUS TOPIC TO BE COVERED
Ø Number series
Ø Letter series
Ø Codes
Ø Relationships
Number series
Most tests include questions about number
sequences. This topic is covered in almost 1-2 questions in the test.
• These
questions are based on number sequences that adhere to a logical rule/pattern
based on basic arithmetic concepts.
• A
specific series is provided from which the pattern must be studied. Following
that, you are asked to guess the next number in the series using the same
approach.
• Some
numbers have been incorrectly entered into the number series, and you must
identify and rectify them.
Tips and Tricks for NTA NET EXAM Number Series
·
Number series questions are questions in
which the numbers in the series are linked to one another. When you recognise
the link, it becomes easier to answer the question.
·
Recognize the pattern posed in the
question. Once you've identified the pattern, it'll be a lot easy to answer the
questions.
·
Once you've recognised the pattern, apply
it to the number preceding/following the missing number in the sequence to get
the solution.
·
Examine the supplied pattern for prime
numbers, perfect squares, cubes, series of known numbers such as Mathematics progression
(AP/GP), and so on.
If
you can't locate the familiar number, try this: -
Ø Calculate
the difference between the supplied series components.
Ø Then
look at the pattern indifference to determine whether they follow any regular
pattern or known numbers, as mentioned earlier.
Ø If the
numbers are steadily increasing, it must be an addition or subtraction series.
Ø If the
numbers are fast increasing, it might be a square, cube, or multiplicative
series.
Ø If the
difference or total do not follow any pattern, it must be an alternative number
series.
Ø Now you
must indicate that the series follows a complicated pattern. Check for
scenarios where you can attain the pattern by multiplying the integer and
adding/subtracting a constant number from it.
How to Spot Common Number Series Patterns
The most frequently requested patterns in
the number series topic include -
Prime numbers
When the integers in a series are prime numbers that are divisible by
themselves and bigger than 1. This number must not have any factors. These are
the numbers 11, 13, 17, 19, and so on.
Squares/Cubes
When the numbers in the series are perfect squares,
perfect cubes, perfect square roots, or perfect cube roots. These numbers
include 81, 100, 121, 144, and so on. These can be of the decimal variety.
Differences reveal a pattern
Calculate the differences between the numbers given
in the question's series. This distinction might be either continuous or
variable. After determining this distinction, you can locate the problem
number, words, or letters in the problem series.
As an example,
what are the numbers 2, 7, 12, 17, 22,?
In this series,
the difference between each number is 5. As a result, the following number will
be 27.
For
instance, A, D, G, J,?
The
difference in position between these letters is three. As a result, the third
letter to J will be M.
Alternate number pattern
If there is a pattern in the alternate numbers, letters, or words in the
sequence, you may quickly discover the problem number, letter, or word using
this alternate pattern.
As an example, what are the numbers 2, 3, 4,
7, 6, and 11?
The alternative
numbers in this series are increased by 2 and 4 steps at a time. As a result,
the following number will be 8. To get the solution, repeat the process with a
letter or word sequence.
Geometric Collection
When the numbers in the series follow the geometric progression, that is,
when each consecutive number in the series is acquired by multiplying or
dividing the preceding numbers with a set ratio, the problem number is simply
determined.
For
instance: 4, 20, 100, 500, etc.
Each
number is multiplied by 5 and then arranged in a geometric sequence. As a
result, the next number will be 2500.
The neighbouring numbers form a pattern.
The following
example demonstrates how neighbouring integers in a series might fluctuate with
a logical pattern.
For
instance: 2, 4, 12, 48,?
In this
series, the first number is multiplied by 2, the second by 3, and the third by
4. As a result, the next number in the series will be 240.
The
odd one out
Except for one, all of the numbers are in the
series. These numbers can be discovered and eliminated.
UGC NET REASONING
SYLLABUS TOPIC TO BE COVERED
Ø Number series
Ø Letter series
Ø Codes
Ø Relationships
|
Number series |
Most tests include questions about number sequences. This topic is covered in almost 1-2 questions in the test.
• These
questions are based on number sequences that adhere to a logical rule/pattern
based on basic arithmetic concepts.
• A
specific series is provided from which the pattern must be studied. Following
that, you are asked to guess the next number in the series using the same
approach.
• Some
numbers have been incorrectly entered into the number series, and you must
identify and rectify them.
Tips and Tricks for NTA NET EXAM Number Series
·
Number series questions are questions in
which the numbers in the series are linked to one another. When you recognise
the link, it becomes easier to answer the question.
·
Recognize the pattern posed in the
question. Once you've identified the pattern, it'll be a lot easy to answer the
questions.
·
Once you've recognised the pattern, apply
it to the number preceding/following the missing number in the sequence to get
the solution.
·
Examine the supplied pattern for prime
numbers, perfect squares, cubes, series of known numbers such as Mathematics progression
(AP/GP), and so on.
If
you can't locate the familiar number, try this: -
Ø Calculate
the difference between the supplied series components.
Ø Then
look at the pattern indifference to determine whether they follow any regular
pattern or known numbers, as mentioned earlier.
Ø If the
numbers are steadily increasing, it must be an addition or subtraction series.
Ø If the
numbers are fast increasing, it might be a square, cube, or multiplicative
series.
Ø If the
difference or total do not follow any pattern, it must be an alternative number
series.
Ø Now you
must indicate that the series follows a complicated pattern. Check for
scenarios where you can attain the pattern by multiplying the integer and
adding/subtracting a constant number from it.
|
How to Spot Common Number Series Patterns |
The most frequently requested patterns in the number series topic include -
Prime numbers
When the integers in a series are prime numbers that are divisible by
themselves and bigger than 1. This number must not have any factors. These are
the numbers 11, 13, 17, 19, and so on.
Squares/Cubes
When the numbers in the series are perfect squares,
perfect cubes, perfect square roots, or perfect cube roots. These numbers
include 81, 100, 121, 144, and so on. These can be of the decimal variety.
Differences reveal a pattern
Calculate the differences between the numbers given in the question's series. This distinction might be either continuous or variable. After determining this distinction, you can locate the problem number, words, or letters in the problem series.
As an example,
what are the numbers 2, 7, 12, 17, 22,?
In this series, the difference between each number is 5. As a result, the following number will be 27.
For
instance, A, D, G, J,?
The difference in position between these letters is three. As a result, the third letter to J will be M.
Alternate number pattern
If there is a pattern in the alternate numbers, letters, or words in the sequence, you may quickly discover the problem number, letter, or word using this alternate pattern.
As an example, what are the numbers 2, 3, 4,
7, 6, and 11?
The alternative numbers in this series are increased by 2 and 4 steps at a time. As a result, the following number will be 8. To get the solution, repeat the process with a letter or word sequence.
Geometric Collection
When the numbers in the series follow the geometric progression, that is, when each consecutive number in the series is acquired by multiplying or dividing the preceding numbers with a set ratio, the problem number is simply determined.
For
instance: 4, 20, 100, 500, etc.
Each number is multiplied by 5 and then arranged in a geometric sequence. As a result, the next number will be 2500.
The neighbouring numbers form a pattern.
The following example demonstrates how neighbouring integers in a series might fluctuate with a logical pattern.
For
instance: 2, 4, 12, 48,?
In this series, the first number is multiplied by 2, the second by 3, and the third by 4. As a result, the next number in the series will be 240.
The
odd one out
Except for one, all of the numbers are in the series. These numbers can be discovered and eliminated.
Complex Sequences
The disparities between numbers in such a series are dynamic rather than fixed, yet there is still a clear logical norm.
For
instance: 3, 8, 15, 24, 33,?
Numbers in this series are increased by +5, +7, +9, and +11. As a result, the following number will be increased by +13. As a result, the solution will be 46.
Complex arithmetic functions
In some series, several operations (+, x, -, and /) are applied sequentially. Such patterns are difficult to discern and might take a long time to identify. As a result, it is best to avoid devoting too much time to such issues. Only attempt the question if you discover the correct answer within the predicted time restrictions; otherwise, go on to the next question.
For instance:
4, 6, 12, 14, 28?
In this series, each prospective number is multiplied by 2 and each prospective number is incremented by 2. As a result, if similar logic is applied to the series, the next number will be 30.
|
Letter series |
One of the simplest rules to solve the alphabetical
series problem is the EJOTY rule. Most of the time, you need to remember the
position of any letter to solve a puzzle. EJOTY rules will help you to easily
find out the position of different letters in the alphabet.
This
sort of question is typically composed of a sequence of little letters that
follow a specific pattern. The series does, however, lack a few letters. These
missing letters are then shown as one of the choices in the correct order. As
the response, the candidate must select this alternative.
There are three sorts of letter series:
Each phrase in the One Lettered Series has one letter and follows a certain pattern. We must determine the following phrase based on that pattern.
Example-1:
What is the next letter in the series B, F, J, N,?
1) R
2) T
3) Q
4) S
Answer: 1) R
Explanation: B = 2; F = 6; J = 10; and N = 14 The difference between the letters is 4 in this case. As a result, the solution is 14 + 4 = 18, which is R.
Example-2: What is the next letter in the series B, C, E, G,?
1) J
2) I
3) K
4) M
Answer: K
Explanation: B = 2, C = 3, E = 5, G = 7 Here the letters are consecutive primes. So, the next prime number is 11 which is K.
Each phrase in the Two Lettered Series has two letters and follows a certain pattern. We must determine the following phrase based on that pattern.
1)
GR
2)
GQ
3)
HQ
4)
HR
Answer: GQ
Explanation: C = 3; D = 4; E = 5; and F = 6.
M is equal to 13, N is equal to 14, O is equal to 15, and P is equal to 16.
As a result, the next term is G = 7 and Q = 17.
Each phrase in the Three Lettered Series has three letters and follows a certain pattern. We must determine the following phrase based on that pattern.
For
instance, what is the next letter in the series CNL, BLI, AJF, and ZHC?
1) XDY
2) YFZ
3) YFA
4)XFY
Answer: YFZ
Explanation: C = 3; B = 2; A = 1; and Z = 26. (Reduced by one) So the following letter is Y,
which equals N = 14, L = 12, J = 10, and H = 8. (Reduced by 2) So the following letter is F,
which is the sixth. L is equal to 12, I is equal to 9, F is equal to 6, and C is equal to 3. (Reducing by 3) So the following letter is Z, which is the 26th.
|
CODE |
Q.1 If NOTE is coded as OQWl and BOA is coded as CQD, then which of the following is coded as NCWGM?
(a) MATCH
(b) MOKEB
(c) MATER
(d) CATCH
Q.2 In one coding language,
the word OFFICE is written as NGGHDD. In that programming language, how is
DENOTE written?
(a) CDMNSD
(b) EDONUD
(c) EPOPUF
(d) EODND
Correct Option: B
Q.3 If "ANANT is coded as "BPDRY", then "MANOJ" will be coded as which of the following options
(a) NCPSO
(b) NDQSO
(c) NCQSO
(d) NCQSP
Correct Option: C
ANANT is coded as BPDRY,
here the logic is A+1 = B, N+2 = P, A+3 = D, N+4 = R, T+5 = Y
Hence, code for MANOJ will
be, M + 1 = N, A + 2 = C, N + 3 = Q, O + 4 = S, J + S = O i.e.
"NCQSO".
Hence, option C is correct.
Q.4 In a certain code language, "YIELD" is written as "YHBGX" and "FORT" is written as "POME". How is "HEIGHT" written in that code language?
(a) NCDFCG
(b) NCCECG
(c) NBCFCG
(d) NCCFCG
Correct Option: D
Q.5 In a certain code of language, "PREVENT" is written as "TNEVERP”. How is "SPECIAL" written in that code language?
(a) LAICPES
(b) LAICEPS
(c) LCAIEPS
(d) LAEICPS
Correct Option: B
The letters of the word are reversed.
Hence, option B is correct.
|
TRICKS FOR RESOLVING FAMILY OR BLOOD RELATIONSHIP QUESTIONS |
Ø Blood Relations Based Questions are quite popular in all sorts of examinations where you have been provided with a relationship among a few members of the family and you need to find the 'Unknown' link that exists meeting the specified requirements based on the supplied facts.
Ø In a roundabout chain, questions illustrate ties among several members of a family.
Ø The applicant is supposed to determine the relationship between two specific people stated in the question.
Ø In
general, the question concerns a hierarchical structure based on seven
generations three above.
Q.1 Saras pointed to a youngster and said, "His father's wife's brother is my sister's father's only sibling." What is the boy's relationship to Saras?
(a) Son
(b) Niece
(c) Cousin brother
(d) Uncle
C is
the correct answer.
The
boy's father's wife is ‘his mother.'
His maternal
uncle' is his mother's brother. Saras' father is Saras' sister's father.
Saras'
father's only sibling is Boy's maternal uncle. Saras' paternal uncle is Boy's
maternal uncle.
This
signifies that the boy is Saras's cousin brother.
Q.2 Pointing to a boy in a photograph, a girl said, "His
father's mother is the mother-in-law of my brother's mother." How is the
person in the photograph related to the girl?
(a)
Maternal Uncle
(b)
Grandfather
(c)
Brother
(d) Paternal Uncle
Correct Option: C
Girl's brother's mother
means girl's 'mother'.
Mother-in-law of girl's mother means her grandmother.
The mother of the father of the boy in the photograph is his 'grandmother'. So, the boy's grandmother is also the girl's grandmother.
This means that the boy is related to the girl as her 'Brother.'
Q.3 pointing to a lady Pankaj Said, her mother's only grandson is my son, “How is that Lady related to Pankaj"?
(a) Aunt
(b) Sister
(c) Mother
(d) Wife
Correct Option: B
Q.4 Introducing a female. "He is the daughter of my
grandfather's only son," Ronit explained. How is that girl connected to
Ronit?
(a) Cousin
(b) Niece
(c) Father in law
(d) Nephew
Option B is the correct answer.
" He is the daughter of my grandfather's only son's
daughter."
My grandfather's only son - Ronit's father.
Ronit's father's daughter, daughter of my grandfather's only
son. It denotes Ronit's sister. Daughter of my grandfather's daughter - Ronit's
sister's daughter.
As a result, the girl is Ronit's niece. As a result, Option B is
right.
Q.5 When a girl points to a lady in a photograph, she states Vinita's grandmother is the lady's mother-in-law. How is the lady in the image linked to Vinita?
(a) Mother
(b) Sister
(c) Aunt
(d) Grandmother
A is the correct answer.
Hence, option A is correct.
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