Mathematical Operations

Friends, today we shall discuss another important model of Reasoning Section Mathematical Operations. Of course, even these questions are asked under reasoning section these are mainly dependent on mathematical operations. All calculations will be performed using BODMAS Rule. We can divide these problems in three types.Those are,

1. Symbol Substitution
2. Mathematical Logic
3. Interchange of Signs & Numbers

Now lets discuss these types with detailed examples.

1st Type : Symbol Substitution



In this type, to find the value of the given expression you should replace the symbols by mathematical operations. Then apply the BODMAS Rule (i.e., Brackets, of, Division, Multiplication, Addition, Subtraction).



For the detailed understanding, lets have a look at an example



Example : 42% (9-2) + 6 x 3 - 4



Solution :

42 % (9-2) + 6 x 3 - 4

= 42 % 7 + 6 x 3 - 4

= 6 + 6 x 3 - 4

= 6 + 18 - 4

= 24 - 4 = 20



2nd Type : Mathematical Logic



In this type, they just give you some logical statements followed by some mathematical operations. You should solve the given mathematical operations with the help of given logical statements.



Example : If % stands for greater than, x stands for addition, + stands for division, - stands for equal to, > stands for multiplication, = stands for less than, < stands for minus, then which of the following alternatives is correct ?

1. 3 + 2 < 4 % 6 > 3 x 2 
2. 3 x 2 < 4 % 6 + 3 < 2
3. 3 > 2 < 4 - 6 x 3 x 2 
4. 3 x 2 x 4 = 6 + 3 < 2 

Usually for these type of questions people tend to make direct decisions with the help of given statements. But confusion arises when you tried to  coordinate given mathematical symbols with the logical statements mentioned above. It is because lack of coordination between eyes and brain. So, to avoid confusion you just should make a note of given logical statements in simple mathematical equations format. So that it will be easier for your eye to pick the correct operation.

by using above logical statements, you can use a rough sketch like this,

now you can calculate the values of given operations mentally by picking the right hand side symbols instead of left hand side. Or you just can replace the symbols by taking the reference of above rough sketch.

Solution : Using the symbols correctly as given in the above operations, for the option (2) you will get, 3+2-4>6%3-2. Using BODMAS rule in this inequality, we will get 5-4>2-2 or, 1>0, which is correct.

3rd Type : Interchange of Signs & Numbers

In this type they just give you some random set of numbers and mathematical symbols. And then ask you to choose the correct of symbols to fit the given equation.

Example : Select the correct set of symbols which will fit in the given equation 5  0  3  5  = 20

1. x, x, x
2. =, +, x
3. x, +, x
4. +, -, x

Solution : Using the set of symbols given in options, you will get the Option 2 as the correct answer.

Using the set of symbols given in option 2, you will get the equation,

5-0+3x5 = 20

Using BODMAS rule you will get,

5-0+15=20 or 20-0 = 20 which is correct

Now lets have a look at some examples,

1. '<' means subtraction, '>' means Addition, '+' means Multiplication and '$' means Division. Then what will be the value of 27 > 81 $ 9 < 6 ?

Solution :

27+81%9-6 = 27+9-6 = 36-6 = 30

2. If % means +, - means x, x means -, + means %, then what will be the value of 15 - 2 % 900 + 90 x 100 ?

Solution :

15x2+900%90-100 = 30 + 10 - 100 = -60

3. Q means Addition, J means Multiplication, T means Subtraction, K means Division then what is the value of 30K2Q3J6T5 ?

Solution :

3%2+3x6-5  =  15 + 18 - 5 = 28

4. P means x, R means +, T means %, S means -, then what will be the value of 18T3P9S8R6 ?

Solution :

By substituting the given symbols, you will get the answer 52

5. P means Multiplication, T means Subtraction, M means Addition, B means Division then what will be the value of 28B7P8T6M4 ?

Solution :

28 % 7 x8 - 6 + 4 

= 4 x 8 - 6 + 4 

= 32 - 6 + 4 

= 36 - 6 = 30

Thats all for now friends. In our next post we shall discuss some more problems of Mathematical Operations with higher difficulty level. Happy Reading :)