**MATHEMATICAL OPERATIONS**

This section deals with questions on simple mathematical operations. Here, the four fundamental operations — addition, subtraction, multiplication and division and

also statements such as less than 'greater than', 'equal to', 'not equal to1, etc. are represented by symbols, different from the usual ones. The questions involving these operations are set using artificial symbols. The candidate has to substitute the real signs and solve the questions accordingly, to get the answer.

**TYPE 1: PROBLEM-SOLVING BY SUBSTITUTION**

In this type, you are provided with substitutes for various mathematical symbols, followed by a question involving calculation of an expression or choosing the correct/ incorrect equation. The candidate is required to put in the real signs in the given

equation and then solve the questions as required.

Note : While solving a mathematical expression, proceed according to the rule BODMAS — i.e., Brackets, Of, Division, Multiplication, Addition, Subtraction.

eg., (36 -12) + 4 + 6 + 2x3 = 24 + 4 + 6 + 2x3 (Solving Bracket)

= 6 + 3x3 (Solving Division)

15 (Solving Multiplication)

15 (Solving Addition)

**ILLUSTRATIVE EXAMPLES'**

Ex. 1. If V means 'divided by 1,4- means 'multiplied by', V means 'minus and V means 'plus', which of the following will be the value of the expression 16+ 8- 4 + 2x4?

(a) 16 (b) 28 (c) 32 (d) 44 (e) None of these

Sol. Putting the proper signs in the given expression, we get :

16+ 8x4 + 2- 4 = 16+ 8 x 2 - 4 = 16+ 16 - 4 = 32 - 4 = 28. So, the answer is (b).

Ex. 2. If + means +, - means x, + means + and x means then 36 x 12 + 4 + 6 + 2 - 3 = ?

(a) 2 (6) 18 (c) 42 (d) 6 (e) None of these

Sol. Using the proper signs, we get :

36- 12 + 4 + 6 + 2x3 = 36-3 + 3x3 = 36-3+9 = 45-3=42. So, the answer is (c).

Ex. 3. If A means 'plus', B means 'minus', C means 'divided by' and D means 'multiplied by', then 18 A 12 C 6 D 2 B 5 = ?

(a) 15 (b) 25 (c) 27 (d) 45 (e) None of these

Sol. Using the proper signs, we get :

Given expression = 18+12+ 6 x 2 - 5 = 18+ 2 x 2 - 5 = 18 + 4- 5 - 2 2 - 5 = 17.

So. the answer is (e).

(a)3 + 2 + 4 <9 + 3 - 2 (b) 3 + 2 + 4 < 18 + 3 - 1 ( c ) 3 + 2 - 4 > 8 + 4 - 2 (d)3 + 2 - 4 > 9 + 3 - 3

Sol. Using proper notations, we have :

(а) Given statement is3 + 2 + 4 < 9 + 3- 2 or — < 1, which is not true.

(b) Given statement is 3 + 2 + 4< 18 + 3 - 1 or 9<5, which is not true.

(c) Given statement is3 + 2- 4 > 8 + 4- 2 or 1>0, which is true.

(d) Given statement is3 + 2- 4 > 9 + 3- 3 or -1 > 0, which is not true.

So, the statement (c) is true.

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