The Interchange of Signs and Numbers section will have questions that are based on arithmetical reasoning ability of the candidate. In such questions, the mathematical operations will be put in random and you will have to guess which symbol represents what operation. These questions form an important category in the IBPS PO, SO, SBI and other such exams. Hence here we will see types of questions that you are most likely to see in your exam. Let us begin!

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### Types of Questions in Mathematical Operations

1. Making the equation balanced.

2. Substituting the symbols.

3. Interchange of numbers and signs

4. Mathematical operations questions based on tricks.

Out of these topics, today we are going to discuss in detail about the interchange of numbers and signs only. Rest of the topics will be covered in other articles.

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### So, what type of questions are the interchange of signs and numbers?

Generally, in these questions, you need to interchange the numbers with the signs or vice versa. You need to find the right sign or number so that the equation can be balanced on both the sides Sometimes even artificial symbols are also used to denote the real signs. You need to use trial and error method to find the answer. Along with this, you need to have an approach beforehand so that you can practice questions accordingly. And that is why we are here to discuss the tricks and concepts concerning today’s topic. We will also help you with some practice questions afterwards.

## Solved Examples

Q. 12 – 4 + 11 x 3 ÷ 6 = 6

A. -, x, +, and –

B. +, -, x, and +

C. x, ÷, -, and +

D. ÷, +, x, and ÷

Answer: Now in this question, we need to find the correct symbols which will fit on the left side of the question so that the answer must be 6 on both the sides. We will try and apply each option one by one and see which one fits better. When we use option 1 the equation will be, 12 – 4 x 11 + 3 – 6 = 8 x 33 – 6 = 264 – 6 = 258. This is no where near 6.

For 2^{nd} option the equation will be 12 + 4 – 11 x 3 + 6 = (16) – (33) + 6 = -17 + 6 = -11. Again, this is nowhere close near the required answer.

Now, let’s check for the option 3^{rd}, equation will be 12 x 4 put ÷ sign 11 – 3 + 6 = (48) ÷ sign (8) + 6 = 6 + 6 = 12. Thus this is also not a correct option. So, the 4^{th} option will be the correct answer. Let’s find out using the symbols from the option 4. 12 ÷ 4 + 11 x 3 ÷ 6 = (3) + (33) ÷ 6 = 36 ÷ 6 = 6 which is the required answer.

### Number Based Questions

Q. In the given question, interchange the two numbers to form a correct equation.

8 x (4/3) + 9 – 5 = 10

1. 5, 3 2. 8, 4

3. 9, 3 4. 4, 3

Answer: In this question, we need to find the two numbers that after interchanging will balance the equation on both the sides. We will go through each and every option and try it to put it into the equation and see which one fits better.

Option 1. In option 1 you need to replace 5 and 3. After replacing the equation will be something like this: 8 x (4/5) + 9 – 3 = 8 x (4/5) + 6. This answer will be an irrational number.

Option 2. For 2nd option, we have to replace 8 and 4. So the equation will become 4 x (8/3) + 9 – 5. Here again, the answer will be in the form of irrational. So this option is also not possible.

Option 3. When you replace in the above equation the answer will be once again in irrational form.

Option 4. In this option you need to interchange 4 and 3 of their respective positions. So you will get an equation like this, 8 x (3/4) + 9 – 5 = 6 + 9 – 5 = 6 + 4 = 10. So the correct answer is option (4).

## Practice Questions

Q. Which one of the following equation will be possible when you interchange the 4 and 5 numbers and + and x signs?

A. 5 x 4 + 10 = 30

B. 10 x 4 + 5 = 50

C. 20 + 5 x 4 = 104

D. 5 + 15 x 4 = 90

Ans: The correct answer is (3).

Q. What two signs in the following equation need to be interchanged so that the equation will be mathematically correct? 5 + 3 x 8 – 12 ÷4 = 3

A. – and +

B. x and ÷

C. ÷and –

D. None of these

Ans: The correct answer is (3).

Q. What will be the correct equation when the signs – and ÷and numbers 4 and 8 are interchanged?

A. 4 ÷8 – 2 = 6

B. 6 – 8 ÷4 = -1

C. 4 – 8 ÷6 = 2

D. 8 – 6 ÷4 = 1

Ans: The correct answer is (1).

+ means ‘ is greater than’

– Means ‘ is less than’

× means ‘ is not greater than’

÷ means ‘ is not less than’

p – q – r implies

1.p – q + r

2.q + p – r

3.r × q + p

4. q + p ÷ r