• #### FICTITIOUS SYMBOLS

In these types of questions the mathematical operations like +, -, x,  are represented by symbols. Some times the operands like =, , >, <, ,  are also represented by some fictitious symbols in the mathematical equation. The candidate is required substitute these fictitious symbols with the actual signs (mathematical operands) and solved the equation using BODMAS principle.

In the following example, the value can be found by following the BODMAS RULE – i.e. Bracket, Of, Division, Multiplication, Addition and Subtraction.

(8 x 3) /8 – 4 + 2 x 4 = ?

= 24 / 8 – 4 + 2 x 4 = (Solving Bracket)

=3 – 4 + 2 x 4 = ? (Solving Division)

= 3 – 4 + 8 = ? (Solving Multiplication)

= 3 + 8 – 4 = 7 (Solving Addition & Subtraction)

However, if it is given that ‘+’ means ‘divided by’, ‘–‘ means ‘multiplied by’, ‘x’ means ‘minus’ and ‘’ means ‘plus’, then we will have to substitute the symbols given in the above said equation with the real signs. Now our equation after making substitution will read as under:

(8 – 3) + 2 x 2 – 4

= 5 + 2 x 2 – 4

= 5 + 4 – 4

= 5

Similarly certain equations the mathematical signs like = >, <, ,  are represented by fictitious symbols like , , , . So in such cases also we should replace the fictitious symbols with the actual symbols and solve the equations.

#### MATHEMATICAL OPERATIONS

##### 1. If – mean x, x means +, + means  and  means –, then : 40 x 12 + 3 – 6  60 = ?

1) 7.95     2) 16     3) 44     4) 479.95    5) None of these

1. (5): Replacing the fictitious symbols by the correct mathematical operands, we get:
Given expression: = 40 + 12  3 x 6 – 60 = 40 + 4 x 6 – 60 = 40 + 24 – 60 = 4

##### 2. If + means , x means - ,  means x and – means +, then: 8 + 6 x 4  3 – 4 = ?

1) -12     2) -20/3     3) 12     4) 20/3     5) None of these

2. (2): Using the correct symbols, as in Q. 1 above,we have:
Given expression = 8  6 – 4 x 3 + 4
= (4/3)- 4 x 3 + 4 = (4/3) - 12 + 4 = -(20/3)

##### 3. If + means x,  means - , x means  and – means +, what will be the value of 4 + 11  5 – 55 =?

1) - 48.5     2) – 11     3) 79     4) 91     5) None of these

3. (5): Using the correct symbols, we have:
Given expression = 4 x 11 – 5 + 55 = 44 – 5 + 55 = 94.

##### 4. If x means +,  means -, - means x and + means , then: 8 x 7 – 8 + 40  2 =?

1) 1     2) 7(2/5)     3) 8(3/5)     4) 44     5) None of these

4. (2): Using the correct symbols, we have:
Give expression = 8 + 7 x 8 / 40 – 2 = 8 + 7 x(1/5) - 2 = 8 + (37/5) =7(2/5)

##### 5. If + means - , - means x, x means  and  means +, then: 15 x 3  15 + 5 – 2 = ?

1) 0     2) 6     3) 10     4) 20     5) None of these

5. (3): Using the correct symbols, we have:
Give expression = 15 / 3 + 15 – 5 x 2 = 5 + 15 – 5 x 2 = 5 + 15 – 10 = 10.