# (Online Course) CSAT Paper – II : General Mental Ability: Mathematical Operations

General Mental Ability

## Mathematical Operations

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. Some examples are given below

Example 1: If ‘+’ means ‘–’, ‘–’ means ‘×’, ‘×’ means and ‘means’ ‘÷’,
and ‘÷’ mean ‘+’ then 15 × 3 ÷ 15 + 5 – 2 = ?
(a) 0
(b) 10
(c) 20
(d) 6
Solution. (b) 15 × 3 = 15 + 5 – 2
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
Solution. (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
Solution. (a) As per the definition of \$, (4\$10) would be (4 + 10 + 4 ×
10 – 1) (4 + 10 + 4 × 10 + 1) = 2915. So,

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)
Solution. (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
Solution. (a) ÖTop
number + Bottom number
+ ÖLeft
number + Right number
gives the number inside the circle

Ö8
+ 8
+ Ö5
+ 5
= Ö16 + Ö10 = 4
+ 3.16 = 7.16

Example 6:

(a) 14
(b) 10
(c) 6
(d) 4
Solution. (d) Cube root of the sum of the numbers outside the circle
given the number inside the circle
3Ö(20
+15 +11)
= 3Ö64 = 4

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

Example 8:

(a) 9
(b) 6
(c) 8
(d) 4
Solution. (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
Solution. (b) (5 + 7 + 4) ÷ 4 = 4
The missing number is (1 + 2 + 1) ÷ 4 = 1.

Example 10:

(a) 70
(b) 80
(c) 90
(d) 1
Solution. (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
Solution. (c) Ö1
+ 1 + 3 + 4
= 3, Ö1
+ 4 + 5 + 6
= 4
The missing number = Ö4
+ 5 + 6 + 10
= 5

## 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
Solution. (d) (6 + 1) = 7, (4 + 2) = 6, -4 column wise
The missing number = 7 + 5 = 12