Reasoning has everything like tricky questions, calculation based questions, formula-based questions, figure based questions, and many more. There is no right method to solve reasoning questions. All you need to have is enough amount of practice so that you can be comfortable with enough questions before the exam. And today we are going to discuss one of the trickier section of reasoning i.e. coded operations. This topic is considered as scoring as it is based on the fundamentals of mathematics.

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## Coded Operations

Sometimes they are also referred as the coded inequality questions. In this section, various mathematical operators will be represented by symbols. You will have to use these symbols to carry out operations of arithmetics.

Q. Follow the directions given in the question.

‘P © Q’ means that ‘P is greater than Q’.

‘P % Q’ means that ‘P is not greater than Q’

‘P ∆ Q’ means that ‘P is neither smaller than nor equal to Q’

‘P * Q’ means that ‘P is equal to Q’

‘P @ Q’ means that ‘P is neither greater than nor equal to Q’.

Now based on the above question and assuming them to be true find the correct answer from the conclusions given below.

Statement: A * B, B @ C, C © D, D % E

Conclusion: A) C @ A B) C % A C) E * B D) D © B

1. Only A or B is true.

2. Either A or B and C are true.

3. Only C and D are true

4. Either A or B and C and D are true.

5. Either A or B and D are true.

Answer: To solve this question without any confusion, it is better that you prepare a table first. In the tables mention meaning and symbol in the first column. Now add the symbols and meanings respective to the order given in the question. From the symbols, you can see that P © Q is referred to as P is smaller than Q. So it will be written as P<Q.

Symbols | © | % | ∆ | * | @ |

Meaning | > | ≤ | > | = | < |

P * Q or P is equal to Q. Thus, P = Q. Also, P © Q implies P is greater than Q or P > Q

P % Q means P is not greater than Q or P ≤ Q

P ∆ Q means that P is neither smaller than nor equal to Q or P > Q

P @ Q and hence P is neither greater than nor equal to Q. Thus, P < Q.

A = B < C > D ≤ E. Now, the question has become easier and we will only use this table to solve the question. From the question, the statement is: A * B, B @ C, C © D, D % E. This will be decoded into A = B, B < C, C > D, D less than equal to E. On combining the above statements they will be :

Conclusion 1. C @ A ==> C < A. Conclusion 1 is not possible. Because when we combine the statements we found that A is less than C and not the other way around.

Conclusion 2. C % A ==> C ≤ A. This statement is also not possible because A = B and B is less than C, so A < C and it is neither equal to or greater than.

Conclusion 3. E * B ==> E = B. In the combined statements it is given that D ≤ E. Even if we consider that D = E but the other symbols from the statement. And thus this conclusion is also not possible.

Conclusion 4. D © B ==> D > B. C is greater D and B, but there cannot be a direct relationship established between D and B. So this conclusion is also not possible. So the correct answer is the option (5) which is none of this.

**Browse more Topics under Mathematical Operation**

- Interchange Of Signs And Numbers
- Problem-Solving By Substitution
- Mathematical Operations Practice Questions

## Practice Questions

Q 1: In the following questions, the symbols @, CC, $,%, and # are used.

‘X $ Y’ means ‘X is not smaller than Y’

‘X # Y’ means ‘X is not greater than Y’

‘X @ Y’ means ‘X is neither smaller nor equal to Y’

‘X CC Y’ means ‘X is neither greater than nor equal to Y’

‘X % Y’ means ‘X is neither greater than nor smaller to Y’

Now based on the above question and assuming it to be true fond the correct answer from the conclusions given below.

Q. Statements: H % J, J CC N, N @ R.

Conclusions: I) R % J II) H @ J III) N @ H

A. Only I is true B. Only III is true

C. Only II and III are true. D. Only I and III are true

Ans: The correct answer is (2).

Q. Statements: ‘M @ J’, J $ T, T CC N

Conclusions: I) N # J II) T CC M III) M @ N

A. Only I and III are true B. Only II is true

C. Only II and III are true. D. Only III is true

Ans: The correct answer is (B).

Q. Statements: D CC K, K # F, F @ P

Conclusions: I) P @ D II) K @ P III) F $ D

A. Only I and III are true B. Only II is true

C. Only II and III are true. D. Only III is true

Ans: The correct answer is (A).

Q. Statements: X $ Y, Y @ Z, W % Y

Conclusions: I) X $ W II) Z # W III) Z # X

A. I, II and III all are true B. Only II is true

C. Only II and III are true. D. Only III is true

Ans: The correct answer is (D).

+ 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