Mathematical Operations | CSAT Preparation - UPSC PDF Download

Introduction

Symbols and Notations

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

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:

(a) 7.16
(b) 9.25
(c) 6.23
(d) 8.33

Correct Answer is Option (a).

gives the number inside the circle

 = √16 + √10 = 4 + 3.16 = 7.16

Example 6:

(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

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:

(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:

(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:

(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:

(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:

(a) 4
(b) 6
(c) 5
(d) 7

Correct Answer is Option (c).

The missing number =

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:

(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