## Mathematical operation and symbol notation

In such type of questions some relationships are shown with the help of certain symbols/notations and/or mathematical signs. Each symbol or sign is defined clearly in the question statement itself. In other words, each symbol or sign is accorded two values-one real value and another assigned value. You are required to put the assigned value of each symbol or sign and then solve the questions accordingly.

For example: Suppose the triangle ( ∆ ) means addition.

We know that triangle is a plane figure but here it has been assigned the value of addition (-). Thus.
12 ∆ 7= 12 - 7 = 5

In this way, to work out such questions substitute the assigned/implied meanings of the symbol or sign and proceed accordingly.

Example: If '+' means 'minus', '-' means 'multiply', '÷' means 'plus' and 'x' means 'divide', then 10 x 5 ÷ 3 - 2 + 3 = ?
(a) 5    (b) 53/3    (c) 21    (d) 36
Solution: ? = 10 x 5 ÷ 3 - 2 + 3
= 10 ÷ 5 + 3 x 2 - 3
Apply the rule BODMAS
Do things in Brackets First
(Powers, Roots) before Multiply, Divide, Add or Subtract.
Multiply or Divide before you Add or Subtract
= 10 ÷ 5 + 3 x 2 - 3
= 2 + 3 x 2 - 3
= 2 + 6 - 3
Subtraction
= 8 - 3 = 5

Example: If "T" means (x), 'U' means (-) , 'X' means (÷) and W means (+), then what will be the value of the following expression ?
(50 X 2) W (28 T 4 )
(a) 142    (b) 158    (c) 137    (d) 163
Solution: Given expression, (50 x 2) W (28 T 4)
After interchanging the letters with symbols, we get
(50 ÷ 2) + (28 x 4) = 25 + 112 = 137
Hence, option (c)

Example: Which one of the four interchange in signs or numbers would make the given equation correct ?
6 x 4 + 2 = 16
(a) + and x, and 4
(b) + and x, 2 and 4
(c) + and x, 4 and 6
(d) None of these
Solution: Apply all option one by one.
6 x 4 + 2 = 16 ⇒ 4 + 6 x 2 = 16 ⇒ 4 + 12 = 16 ( option c )

Example: If P denotes '÷', Q denotes 'x', R denotes '+' and S denotes '-' then
18 Q 12 P 4 R 5 S 6 = ?
(a) 95    (b) 53    (c) 51    (d) 57
Solution: Given Question is 18 Q 12 P 4 R 5 S 6
After changing the letters in to signs as per given in the question, we have
18 x 12 ÷ 4 + 5 - 6 ,
Apply the BODMAS Rule,
= 18 x 12/4 + 5 - 6
= 18 x 3 + 5 - 6
= 54 + 5 - 6
∴ 59 - 6 = 53
Hence, option (b)

Direction: In these questions, the relationship between different element is shown in the statements. These statements are followed by two conclusions.
(a) If only conclusion I follows
(b) If only conclusion II follows
(c) If either conclusion I or II follows
(d) If neither conclusion I nor II follows
(e) If both conclusion I and II follow.

Example:
Statement: Y < J = P ≥ R > I
Conclusions: I. J > I     II. Y < R
Solution: Correct Option (a)
Y < J = P ≥ R > I
I. J > I is true,
II. Y < R is not true.