# Online Coaching For RRB Exam Reasoning (Arithmetical Reasoning)

## Reasoning (Arithmetical Reasoning)

First we should know some mathematical operations. They are add (+), subtraction (–), multiply (×) and division (÷), greater than (>), less than (<). This test is set up to test candidates skill in mathematical operations. The questions involving these operations are set using artificial symbols. You are required to substitute the real signs and solve the questions accordingly, to get the answer.

## Different Type of Questions

There are three types of questions based on mathematical operations which are asked in various competitive examinations. They are,

### Problem-Solving by Substitution

In such type of questions you have some substitutes for various mathematical symbols or numerals followed by a question involving calculation of an expression or choosing the correct/incorrect equation.

### Rule BODMAS

Brackets
Of
Division
Multiplication
Addition
Subtraction
While solving a mathematical operations proceed according to the BODMAS’ formula.

Example 1: If ‘+’ means ‘minus’ ‘×’ means ‘divided by’ ‘÷’ means ‘plus’ and ‘–’means ‘multiplied by’ then which of the following will be the value of expression 7 × 3.5 ÷ 2 – 4 + 5 ?

(a) 4
(b) 5
(c) 11
(d) None of these

Solution. (b) Using the proper notations in the given expression, we have

= 7 × 3.5 ÷ 2 – 4 + 5 = 7 ÷ 3.5 + 2 × 4 – 5
= 2 + 2 × 4 – 5 = 2 + 8 – 5 = 10 – 5 = 5

Example 2: If × means +, + means ÷, – means × and ÷ means –, then 6 × 4 – 5 + 2 ÷ 1 =?

(a) 10
(b) 11
(c) 12
(d) 15

Solution. (d) Using the proper notations in the given expression, we have

6 × 4 – 5 + 2 ÷ 1

= 6 + 4 × 5 ÷ 2 – 1
= 6 + 4 × 2.5 – 1
= 6 + 10 – 1
= 16 – 1 = 15

Example 3: If P denotes ‘multiplied by’ T denotes ‘subtracted from, M denotes ‘added to’ and B denotes ‘divided by’, then

12 P 6 M 15 T 16 B 4

(a) 70
(b) 83
(c) 75
(d) 110
(e) None of these

Solution. (b) 12 P 6 M 15 T 16 B 4

= 12 × 6 + 15 – 16 ÷ 4

= 12 × 6 + 15 – 4
= 72 + 15 – 4
= 87 – 4 = 83

### Interchanging of Signs and Numbers

This type of question certain signs or numbers interchanging with each other. The candidate is required to change the given signs or change the given numbers with each other and select which of the equation is correct of the given alternatives.

Example 4: If signs + and –and numbers 4 and 8 interchanges with each other, which one of the following four equations would be correct?

(a) 4 – 8 + 12 = 0
(b) 8 – 4 ÷ 12 = 8
(c) 4 ÷ 8 – 12 = 16
(d) 8 ÷ 4 – 12 = 24

Solution. (a) On interchanging signs + and – and numbers 4 and 8 in equation (a)

8 + 4 – 12 = 0
12 – 12 = 0
0 = 0

Example 5: Which one of the four interchanges in signs and number would make the given equation correct?

6 × 4 + 2 = 16

(a) + and ×, 2 and 4
(b) + and ×, 4 and 6
(c) + and ×, 2 and 6
(d) None of the above

Solution. (b) On interchanging signs + and × and 4 and 6,

4 + 6 × 2 = 4 +12 = 16

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