**Mathematical Reasoning Notes for UGC NET 2024**

**Mathematical reasoning :-** Mathematical reasoning is a branch of the Math’s where we can evaluate the reliability of the assertions which are delivered. Our daily lives are highly depend on Mathematical Reasoning and Aptitude .

Assume a class contains student of the subject Math, English and Management. And now it is said that, all the management subject student are being removed from the class, it follows logically that the only left in the class are Math and English student.

**Types of reasoning**

There are two types of reasoning :- (A) Verbal Reasoning (B) Non – Verbal Reasoning

A) Verbal Reasoning :- A verbal reasoning test may include questions that evaluate your ability to identify letter sequences, interpret codes based on letters and numbers, follow written instructions, interpret texts, find words inside words, and find the missing letter to complete words.

Topic we cover under Verbal Reasoning are:-

**(a) Number series**

**(b) Letter series**

**(c) Codes and Relationships**

(B) Non – Verbal Reasoning :- An Non – Verbal Reasoning involves using diagrams and images to solve problems. It measures the capacity to evaluate visual data and resolve issues through verbal reasoning.

(a) Number series :- A series of numbers that follow a pattern is referred to as a number series. Applicants need to identify the incorrect or missing number in the given series.

1 What number comes after 10, 20, 30, and 40 ?

Ans :- In the sequence 10, 20, 30, and 40 follow the pattern of increasing the number 10 every time so final answer is 10, 20, 30, 40 and 50 .

2 What number comes after 17, 34, 51, and 68 ?

Ans :- In the sequence 17, 34, 51, and 68 follow the pattern of multiplying the number 17*1 every time so final answer is 17, 34, 51, 68 and 85 .

17*1 = 17

17*2 = 34

17*3 = 51

17*4 = 68

17*5 = 85

3 What number comes after 7, 14, 28, and 56 ?

Ans :- In the sequence 7, 14, 28, and 56 follow the pattern of Double the number of last one

so final answer is 7, 14, 28, 56 and 112 .

4 What is the next number 3,5,7,11,13 ?

Ans :- In the sequence 3, 5, 7, 11, and 13 follow the pattern of increasing the Prime number

so final answer is 3, 5, 7, 11, 13 and 17

5 What number comes after 15, 30, 45, and 60 ?

Ans :- In the sequence 15, 30, 45, and 60 follow the pattern of multiplying the number 15*1 every time so final answer is 15, 30, 45, 60 and 75.

15*1 = 15

15*2 = 30

15*3 = 45

15*4 = 60

15*5 = 75

6 What is the next number 30, 20, 60, and 40 ?

Ans :- In the sequence 30, 20, 60, and 40 follow the pattern of increasing the alternate number every time so final answer is 30, 20, 60, 40 and 120

7 What number comes after 25, 31, 38, and 46, ?

A In the sequence 25, 31, 38, and 46 follow the pattern of increasing the number in ascending order so final answer is 25, 31, 38, 46 and 55 .

25+6 = 31

31+7 = 38

38+8 = 46

46+9 = 55

(b) **Letter series :-** A letter series is a logical grouping of the alphabet’s letters that follow a predetermined order. A list of letters and sequences of numbers and letters are provided in this section.

shortcut :-** E J O T Y**

we have to remember the alphabetical position as below :-

E as 5,

J as 10,

O as 15,

T as 20 and

Y as 25

1 What is the value of “?” in the sequence of the letter series (A, F, K, P, ?)

Ans :- In the letter series (A, F, K, P, ?) follow the pattern of increasing the letter 4 every time

so final answer is A, F, K, P, U

2 What is the value of “?” in the sequence of the letter series (A, C, E, G, ?)

Ans:- In the letter series (A, C, E, G, ?) follow the pattern of increasing the every alternative letter so final answer is A, C, E, G, I

3 What should come in place of the “?” in the letter series (A, C, F, J, O ?)

In the letter series (A, C, F, J, O ?) follow the pattern of increasing the letter in ascending order so final answer is A, C, F, J, O , U

4 What is the value of “?” in the sequence of the letter series (E, G, I, K, ?)

Ans :- In the letter series (E, G, I, K, ?) follow the pattern of increasing the every alternative letter so final answer is E, G, I ,K , M

5 What should come in the place of question mark (?) in the following letter series BE GJ LO QT ?

Ans :- In the letter series (BE GJ LO QT ?) follow the pattern of increasing the every alternative letter and gap of two letter in between so final answer is BE , GJ , LO , QT , VY

(c) **Codes and Relationships :**– Problems involving understanding an interaction that is coded in a specific way and matching it. The relationship and specified in the inquiry are known as coded relationship.

Directions (Q. 1-2) − Read the following information to answer the questions.

‘P # Q’ means ‘Q is father of P’

‘P ∗ Q’ means ‘Q is mother of P’

‘P £ Q’ means ‘Q is brother of P’

‘P $ Q’ means ‘Q is sister of P’

1. Which of the following means ‘X is the grandfather of Y’?

1 Z $ X ∗ K # L £ Y

2 Y £ L ∗ K # X $ Z

3 Y ∗ K # L £ Y

4 can’t be determined

5 None of these

**Solution :-**

Need to Proof:- X is the grandfather of Y

Option 1 Z $ X ∗ K # L £ Y

Z $ X means X is sister of Z

X ∗ K means K is mother of X

K # L means L is father of K

L £ Y means Y is brother of L

Not possible because , Z $ X means X is sister of Z so X cant be grandfather.

Option 2 Y £ L ∗ K # X $ Z

Y £ L means L is brother of Y

L ∗ K means K is mother of L

K # X means X is father of K

X $ Z means Z is sister of X

Possible because , L is brother of Y, and K is mother of L , so K is mother of Y also

now X is father of K so X is the grandfather of Y and L.

Option 3 Y ∗ K # L £ Y X is not available so cant find relations.

So Answer will be Option 2

Write the answer on comment :-

1 What number comes after 16, 20, 28, and 40 ?

2 What number comes after 12, 20, 36, and 60 ?

For More Question Go to Quiz Section