##### What will you learn from this article?

- What is coded inequality?
- Decoding the coded inequalities.
- Solving procedure.

##### ExamConnect

Questions related to coded inequality are an essential part of competitive examinations. Almost all the competitive examinations give much weightage and mark value to questions from coded inequality.

### Coded Inequality

In these types of questions, the relations amongst the numbers are given in a coded form with a set of instructions in which different mathematical symbols replace different symbols of inequality. The examinee is expected to use the given instructions to decode the symbols and then solve the question. Letâ€™s look at some instructions which are provided.

means â€˜ smaller than or equal to.â€™ which is â‰¤*Not greater than*means â€˜ greater than or equal to.â€™ which is â‰¥*Not smaller than*means â€˜smaller than.â€™ which is <*Neither greater than nor equal to*means â€˜ greater than.â€™ which is >*Neither smaller than nor equal to*means â€˜equal to. Which is =*Neither greater than nor smaller than*

**Common mistake:** While attempting questions of coded inequalities, most of the students donâ€™t make a table for decoding wherein all the symbols in the questions are initially decoded; instead, they try to decipher each symbol from each expression individually.

**Example Question:** In the following question, the symbols @, $, &, # and % are used with the following meaning as instructed below.

â€˜Y $ Zâ€™ means â€˜Y is not smaller than Z.â€™

â€˜Y @ Zâ€™ means â€˜ Y is neither smaller than nor equal to Z.â€™

â€˜Y # Zâ€™ means â€˜ Y is neither greater nor equal to Z.â€™

â€˜Y % Zâ€™ means â€˜ Y is not greater than nor smaller than Z.â€™

â€˜Y & Zâ€™ means â€˜ Y is not greater than Z.â€™

Now in each of the following questions assuming the given statement is true, find which of the following conclusions are valid.

**Statements: **N % B, B $ W, W#H, H&M

**Conclusions:**

- M @ W
- H @ N
- W % N
- W # N

**Solution:** Firstly, we will decode the symbols one by one and make a decoding table.

Symbols | $ | & | @ | # | % |

Inequalities | â‰¥ | â‰¤ | > | < | = |

Secondly, we will decode and combine the statements into a single expression of inequality, which will be N = B â‰¥ W < H â‰¤ M.

Lastly, we will take each conclusion and try to find its authenticity.

**Conclusion 1:** M @ W that is M > W, as we can see that this conclusion holds true.

**Conclusion 2:** H @ NÂ that is H > N, as we can see that this conclusion is not true because of Rule 1 of inequality expression.

(To learn more about the various rules governing expression of inequalities check out our article for the same.)

**Conclusion 3:** W % N that is W = N, as we can see that this conclusion is also not true because of Rule 2 of inequality expression.

**Conclusion 4:** W # N that is W < N, as we can see that this conclusion is not true because there is a possibility that W = N, hence we cannot consider this conclusion to be true.

DD