## 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

Addition

= 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.