**Coded Inequality**

Hello Readers

Today’s topic is Coded Inequality.

Coded Inequality topic generally cover 5 questions i.e. 5 marks in competitive exams. This is easy topic if we will understand few concepts related to this topic.

Before starting with the concepts, first we should understand the different types of results which we can get while we compare different types of variables and the types of Coded Inequality/Inequalities.

**TYPES OF INEQUALITIES –**

**Example – **

Let’s take two variables – X person and Y person.

We have to compare weights of both the variables.

**Conclusions – **

- X > Y (X is greater than Y)
- X < Y (X is less than Y)
- X = Y (X = Y)

So, as we have seen that there are three basic conclusions that we can drive, if we compare two variables.

When we combine these conclusions with each other, then it becomes the Types of Inequalities.

- X is neither greater than nor equal to Y. →
**X < Y** - X is neither smaller than nor equal to Y. →
**X > Y** - X is not greater than Y →
**X ≤ Y** - X is not smaller than Y→
**X ≥ Y** - X is neither greater nor smaller than Y. →
**X = Y**

Now, let’s start understanding how to solve the questions in exams with simple trick. With this trick you can easily get the right answer by observing according to this trick.

**Let’s give these inequalities some names –**

**< or > is Ruler****≤ or ≥ is Counsellor****= is Public**

So, from the above we can say.

**Ruler is “< or >” i.e. STRONGEST**

(As he can take the final decision)

**Counsellor is “≤ or ≥” e. Less stronger than Ruler**

(As he can give suggestions but final decision will be taken by Ruler or he can take decision in absence of Ruler)

**Public “=” i.e. less stronger than Ruler and Counsellor**

(As public have to follow the rules and decisions taken by ruler or counsellor)

Let’s take examples to understand how to use this trick –

**Case 1 – RULER(S) </>**

**Example – **

**X > Y > Z < A > D**

**Conclusions- **

i) X > Z

ii) X > D

iii) Y > D

**Solution –**

i) X > Z

This conclusion is True as there is only one **Ruler i.e. >** in between X and Z.

ii) X > D

There are two Rulers i.e. > and < between X and D. And if two rulers will make different conclusion as they are facing each other then, it will result in war. So, NO RELATION can be drawn.

iii) Y > D

This conclusion is False. Same reason as explained in (ii)

**Case 2 – COUNSELLOR(S) ≥/≤**

**Example – 1**

**X > Y ≥ Z ≥ A > D**

**Conclusions – **

i) X > A

ii) Y ≥ A

**Solution – **

i) X > A

This conclusion is True. As there is Ruler > and Counsellor ≥ between X and A. So, the final decision will be taken by X – Ruler.

ii) Y ≥ A

This conclusion is True as there is only one Counsellor between Y and A.

**Example – 2**

**X > Y ≥ Z ≤ A > B**

**Conclusions – **

i) X > B

ii) Y ≥ A

iii) Z ≤ B

**Solution –**

i) X > B

This statement is False. As there is > and ≤ between X and B.

ii) Y ≥ A

There are two Counsellors i.e. ≥ and ≤ between Y and A. And if two counsellors will give different suggestions as they are facing each other then, it will result in conflict. So, NO RELATION can be drawn.

iii) Z ≤ B

No Relation can be drawn. As Ruler and Counsellor is facing each other.

**Case 3 – Public – =**

**Example –**

**X >Y = Z = T > U**

**Conclusions –**

- i) X = T
- ii) Y = T

**Solution –**

i) X = T

This conclusion is False. As there > and = between X and T. So counsellor’s decision will be considered.

ii) Y = T

This conclusion is True.

** **

**Case 4 – Either or**

**Example – **

**X > Y ≥ Z ≥ B**

**Conclusions – **

i) Y > B

ii) Y = B

**Solution –**

These conclusions will result in either or result i.e. both the conclusions are true but only one conclusion can be consider at one time.

As we can see, Y ≥ B

So, Either Y > B or Y = B

So, answer for these kind of conclusion will be Either i or ii.

* If we will check these conclusions individually then, both these conclusions are false.

* In either/or cases, variable to be compared are same.

**Case 5 – Neither nor**

**Example –**

**X > Y ≥ Z ≥ B**

**Conclusions – **

i) Y < B

ii) X < Z

**Solution –**

Both the conclusions of the above statement is False. The correct answer for this is Neither i nor ii is true.

With this we will finish this topic here.

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