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. Some examples are given below
Example 1: If ‘+’ means ‘–’, ‘–’ means ‘×’, ‘×’ means ‘÷’, and ‘÷’
mean ‘+’ then 15 × 3 ÷ 15 + 5 – 2 = ?
- 0
- 10
- 20
- 6
- None of these
Solution. (2) 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
- 18
- 12
- 21
- 24
- None of these
Solution. (3) 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
- 2915
- 2195
- 2951
- 2955
- None of these
Solution. (1) As per the definition of $, (4$10) would be (4 + 10 + 4
× 10 – 1) (4 + 10 + 4 × 10 + 1) = 2915. So, answer is (1)
Example 4: If * means “is greater than”, @ means `is less than’; and $
means “is equal to” and if a $ b and b @ c, then
- c * b
- b * c
- c * a
- Both 1 and 3
- None of these
Solution. (4) 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 the missing 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.
- 7.16
- 9.25
- 6.23
- 8.33
- None of these
- 14
- 10
- 6
- 4
- None of these
Solution. (4) Cube root of the sum of the numbers outside the circle
gives 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.
- 2
- 11
- 33
- 44
- None of these
- 9
- 6
- 8
- 4
- None of these
Solution. (4) (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 given with numbers inside and outside. The
number inside the triangle is obtained by operating some arithmetic operators on
the numbers outside the triangle.
- 2
- 1
- 0
- 3
- None of these
Solution. (2) (5 + 7 + 4) ÷ 4 = 4
The missing number is (1 + 2 + 1) ÷ 4 = 1.
- 70
- 80
- 90
- 1
- None of these
Solution. (3) (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.
- 4
- 6
- 5
- 7
- None of these
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.
- 8
- 9
- 13
- 12
- None of these
Solution. (4) (6 + 1) = 7, (4 + 2) = 6. The missing number = 7 + 5 =
12
