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Introduction

The basic approach for the problems of this type is more or less similar to that of coding and decoding. One has to study the symbols or the geometrical figures and their meanings carefully. Then, the meanings are to be used in place of those symbols in answering the questions. The questions can be categorized into two types

Symbols and Notations

Symbols for these types of questions stand for mathematical operations like +, –, ×, ÷, > , <, ³, £, = and #. So, the students must replace the symbols bymathematical operations and apply the BODMAS’ rule to find the value f the given expression. Other symbols which can be used are DÑ, *, @, $, etc, with proper definitions. 

Solved Examples

Example 1: If ‘+’ means ‘–’, ‘–’ means ‘×’, ‘×’ means and ‘means’ ‘÷’, and ‘÷’ mean ‘+’ then 15 × 3 ÷ 15 + 5 – 2 = ?
(a) 0
(b) 10
(c) 20
(d) 6

Correct Answer is Option (b).
after changing the signs = 15 = 3 + 15 – 5 × 2 = 5 + 15 – 10 = 10


Example 2: If 2 * 3 = 12, 3 * 4 = 20 and 4 * 5 = 30, then 2 * 6 is
(a) 18
(b) 12
(c) 21
(d) None of these

Correct Answer is Option (c).

The numbers on both sides of * are increased by one and then multiplied to get the answer. 2*6 = 3 × 7 = 21


Example 3: If x $ y = (x + y + xy –1) (x + y + xy + 1), then the value of (4 $ 10) is.
(a) 2915
(b) 2195
(c) 2951
(d) 2955

Correct Answer is Option (a).
As per the definition of $, (4$10) would be (4 + 10 + 4 × 10 - 1) (4 + 10 + 4 × 10 + 1) = 2915. So, answer is (a)


Example 4: If* means “is greater than”, @ means `is less then’; and $ means “is equal to” and if a $ b and b @ c, then
(a) c * b
(b) b * c
(c) c * a
(d) Both (a) and (c)

Correct Answer is Option (d).
Replace the symbols with the meaning given against them. If a $ b and b @ c would become a = b and b < c, then c > b or c > a ie, c * b, c * a are true from the given options.

Geometrical Figures

These figures will be divided and subdivided into a number of parts, each part is filled with a number or a letter except one part. The numbers or the letters in the figures follow certain pattern. The objective is to identify the pattern and find themissing number or letter. The problems based on geometrical figures are of various types.

Type 1
Based on circles: In these type of, three circles with numbers outside the circle will be given.In the first two circles, the number inside the circle is written according to a particular pattern. The objective of the student is to find the missing number of third circle.

Example 5:
Mathematical Operations | CSAT Preparation - UPSC
(a) 7.16
(b) 9.25
(c) 6.23
(d) 8.33

Correct Answer is Option (a).

Mathematical Operations | CSAT Preparation - UPSCgives the number inside the circle

Mathematical Operations | CSAT Preparation - UPSC = √16 + √10 = 4 + 3.16 = 7.16


Example 6:
Mathematical Operations | CSAT Preparation - UPSC
(a) 14
(b) 10
(c) 6
(d) 4

Correct Answer is Option (d).
Cube root of the sum of the numbers outside the circle given the number inside the circle
Mathematical Operations | CSAT Preparation - UPSC


Type 2
Circle divided into parts: In such questions, circle is divided into three parts. An arithmetic operation on the numbers gives the missing number.

Example 7:
Mathematical Operations | CSAT Preparation - UPSC
(a) 2
(b) 11
(c) 33
(d) 44

Correct Answer is Option (b).
60 + 40 = 10, 20 + 29 = 7
The missing number is 55 + 66 = 11


Example 8:
Mathematical Operations | CSAT Preparation - UPSC
(a) 9
(b) 6
(c) 8
(d) 4

Correct Answer is Option (d).
(11 – 4)2 = 49, (3 – 2)2 = 1
The missing number is (20 – 18)2 = 4

Type 3
Problems based on triangles: In such questions, three triangles are givenwith numbers inside and outside. The number inside the triangle is obtained by operating some arithmetic operators on the numbers outside the triangle.

Example 9:
Mathematical Operations | CSAT Preparation - UPSC
(a) 2
(b) 1
(c) 0
(d) None of these

Correct Answer is Option (d).
(5 + 7 + 4) ÷ 4 = 4
The missing number is (1 + 2 + 1) ÷ 4 = 1.

Example 10:
Mathematical Operations | CSAT Preparation - UPSC
(a) 70
(b) 80
(c) 90
(d) 1

Correct Answer is Option (c).
(4 × 5 × 6) = 120.
The missing number is (5 × 6 × 3) = 90


Type 4
Problems based on squares: Such questions consist of three squares with five numbers inside the square of the 5 numbers, 4 numbers are at the four corners of the square and one middle number follow some arithmetic operation.
Examples 11:
Mathematical Operations | CSAT Preparation - UPSC
(a) 4
(b) 6
(c) 5
(d) 7

Correct Answer is Option (c).

Mathematical Operations | CSAT Preparation - UPSC
The missing number = Mathematical Operations | CSAT Preparation - UPSC


Type 5
Problems based on matrix: In such questions, a square divided into nine parts, three rows and three columns, out of the nine parts, eight parts are filled with one part left vacant. The students need to apply some arithmetic operation to find out the missing number.
Examples 12:

Mathematical Operations | CSAT Preparation - UPSC
(a) 8
(b) 9
(c) 13
(d) 12

Correct Answer is Option (d).
(6 + 1) = 7, (4 + 2) = 6, -4 column wise
The missing number = 7 + 5 = 12

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FAQs on Mathematical Operations - CSAT Preparation - UPSC

1. How do you perform mathematical operations?
Ans. Mathematical operations can be performed using various mathematical symbols such as addition (+), subtraction (-), multiplication (*), and division (/). These symbols are used to manipulate numbers and solve mathematical problems.
2. What is the order of operations in mathematics?
Ans. The order of operations in mathematics is a set of rules that determine the sequence in which mathematical operations should be performed. The order is as follows: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
3. What is the difference between addition and multiplication in mathematics?
Ans. Addition is an operation that combines two or more numbers to give a total, while multiplication is an operation that combines two or more numbers to give a product. In addition, the order of numbers doesn't matter, but in multiplication, the order of numbers affects the result.
4. How do you solve a mathematical equation with multiple operations?
Ans. To solve a mathematical equation with multiple operations, you need to follow the order of operations. Start by solving any operations inside parentheses, then simplify any exponents. Next, perform multiplication and division from left to right, and finally, perform addition and subtraction from left to right.
5. Can you explain the concept of PEMDAS in mathematics?
Ans. PEMDAS is an acronym for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It represents the order of operations in mathematics. By following the PEMDAS rule, you ensure that mathematical expressions are evaluated correctly.
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