 # Problem-Solving By Substitution

In problem-solving by substitution, mathematical operators are substituted with symbols. This exercise checks the candidate’s ability to rewire their brain and improvise to solve problems. A convenient method to solve such problems is to create a mental map of such symbols. Here we will discuss the concepts, see various types of questions that the candidate may face.

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### Suggested Videos        ## Questions on Problem-Solving By Substitution

This topic is also known as symbol substitution. Symbols of different mathematical operations like addition, division, greater than, lesser than, etc are interchanged or substituted to find the correct answer. Almost all the competitive exams like IBPS PO, IBPS clerk, SSC asks the questions related to the mathematical operations. There are four types of topics that come under mathematical operations. But today our sole focus will only be on substitution based questions.

In this type of questions, you will be provided with various mathematical signs and symbols. The substitute for these signs itself will be provided in the question. You need to change the signs with that given in the equation and then find the answer. Or you will also be asked to find the correct/incorrect equations. You just need to solve the equation based on these signs and symbols.  Now, we will show you some of the examples and approach on how to solve the questions. Source: Wikimedia Commons

### Examples

Q. If ‘+’ means ‘÷ ‘, ‘-‘ means’x’. ‘÷ ‘ means ‘+’ and ‘x’ means ‘-‘, then 36 x 8 + 4 ÷ 6 + 2 – 3 = ?

A. 2

B. 18

C. 43

D. 6 1/2

Now, in this question instead of remembering the signs make a table like this. Fill this table with the interchanging signs as given in the first half of the question.

 Symbols + – ÷ x Meaning ÷ x + –

From the table replace the signs in the given equation.

The equation will be as follows: 36 – 8 ÷  4 + 6 ÷  2 x 3 = 36 – 2 + 3 x 3 = 34 + 9 = 43.

So the correct answer is (C). You must have noticed while solving this question your self as to how much there is confusion regarding the interchanging signs. And that is why it is important that you make a table.

Q. It is given that: ‘>’ denotes ‘+’, ‘<‘ denotes ‘-‘, ‘+’ denotes ‘÷ ‘, ‘-‘ denotes ‘=’, ‘=’ denotes less than’ and ‘x’ denotes ‘greater than’, find which of the following is correct statement?

A. 3 + 2 > 4 = 9 + 3 < 1

B. 3 > 2 > 4 = 18 + 3 < 2

C. 3 > 2 < 4 x 8 + 4 < 2

D. 3 + 2 < 4 x 9 + 3 < 1

In this question, there are many signs and symbols. You need to find the correct statement out of the following given options. First, make the following table as per the symbols given in the question.

 Symbols > < + – = x Meaning + – ÷ = < >

Now put all the interchanged signs and symbols in the question and check them one by one.

Equation 1. After interchanging the signs equation will be:

3 ÷ 2 + 4 < 9 ÷ 3 – 1 = 11/2 < 3 – 1 = 11/2 < 2 . This is not possible. So, option A is not the correct answer.

Equation 2. After the signs are interchanged, the equation will become:

3 + 2 + 4 < 18 ÷ 3 – 2 = 9 < 6 – 2 = 9 < 4. This is also not possible. So option B is also not the correct answer.

Equation 3. The equation 3 will be become: 3 + 2 – 4 > 8 ÷ 4 – 2 = 5 – 4 > 2 – 2 = 1 > 0. This is possible and it satisfies the conditions. So option C is the correct answer.

Equation 4. This equation will be like: 3 ÷ 2 – 4 > 9 ÷ 3 – 1 = 3/2 – 4 > 3 – 1 = -5/2 > 2. This condition is also not possible.

So the correct answer is (C). To solve this type of questions it is important that you remember the BODMAS rule. It is a basic mathematical rule in which for the given equation, the division between the two numbers is solved first, after that multiplication, this will be followed by addition and subtraction. Every question in this section is solved using this rule.

## Practice Questions

Q. If P = 6, J = 4, L = 8, M = 24 then M x L ÷ L + J = ?

A. 8

B. 36

C. 16

D. 0

Q. If L denotes ‘x’, M denotes ‘divide’, P denotes ‘+’ and Q denotes ‘-‘, than 8 P 36 M 6 Q 6 M 2 L 3 = ?

A. 13/6

B. -1/6

C. 14 1/2

D. 5

Q. If ‘-‘ means ‘x’; ‘x’ means ‘÷ ‘; ‘÷’ means ‘+’ and ‘+’ means ‘-‘, then 40 x 12 + 3 – 6 ÷ 60 = ?

A. 44/5

B. 79/5

C. 116/3

D. 136/3

Q. If ‘+’ means ‘÷ ‘; ‘-‘ means ‘x’; ‘÷ ‘ means ‘+’  and ‘x’ means ‘-‘ then 20 ÷ 12 x 4 + 8 – 6 = ?

A. 8 2/3

B. 29

C. 32

D. 26

Q. If ‘x’ stands for ‘addition’, ‘<‘ for ‘subtraction’, ‘+’ stands for ‘division’, ‘>’ for multiplication’,’-‘ stands for ‘equal to’, ‘÷’ for ‘greater than’ and ‘=’ stands for ‘less than’, state which of the following is true?

A. 3 x 2 < 4 – 16 > 2 + 4

B. 5 > 2 + 2 = 10 < 4 x 2

C. 3 x 4 > 2 – 9 + 3 < 3

D. 5 x 3 < 7 – 8 + 4 x 1

The correct answet is (B).

Q. If L denotes ‘÷’, M denotes ‘x’, P denotes ‘+’ and Q denotes ‘-‘, then which of the following statements is true?

A.  32 P 8 L 16 Q 4 = -3/2

B. 6 M 18 Q 26 L 13 P 7 = 173/13

C. 11 M 34 L 17 Q 8 L 3 = 38/3

D. 9 P 9 L 9 Q 9 M 9 = – 71

Q. If P denotes ‘+’, Q denotes ‘-‘, R denotes ‘x’ and S denotes ‘÷’, which of the following statements is correct?

A. 36 4 S 8 Q 7 P 4 = 10

B. 16 R 12 P 49 S 7 Q 9 = 200

C. 32 S 8 R 9 = 160 Q 12 R 12

D. 8 R 8 P 8 S 8 Q 8 = 57

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