@ : Home > Reasoning > Coded Inequalities > Tricks and Shortcuts Coded Inequality is an important topic for competitive exams especially for banking exams like IBPS and SBI PO and Clerk exam. Reasoning section usually carries 5-6 questions from this topic. In order to ensure that the candidate is able to solve questions on coded inequalities in less than a minute, we have compiled this article which will bring forth the concept and tricks.

## Decoding inequality signs:

Before, we proceed further, we should know how to correctly decode the signs. The following table shows different signs and their meanings:-

SIGNSMEANING
>

means Greater than,

Neither smaller nor equal

<

Smaller than, less than,

Neither greater nor equal

=

Equal to,

Neither greater nor smaller

Either smaller or equal to,

Not greater than

Either greater or equal to, Not smaller than

## How to solve questions on coded inequalities in reasoning section?

When solving inequalities, we will consider the following cases:-

### Case 1: Equal to

The first step in every equation is to ignore equal. Yes ignore. Please read the following example to know why we want you to ignore ‘equal to’ sign:

Example 1: A =B <C =D

Therefore, B < D

Example 2: A < B =C

Therefore, A < C. (A is the smallest)

### Case 2: Same Sign

When same sign repeats itself again and again, then such sign would be the answer.

Example 3: A < B < C < D

Therefore, A < D. (A is the smallest)

Example 4: A= B ≥ C = D ≥ E

Therefore, A ≥ E

### Case 3: Common Sign

(= is never considered as a common sign). So, the first thing to be done is to ignore (=) as ignore told in Case 1.

Example 5: A < B ≤ C

Therefore, A < C.(A is the smallest)

Example 6: A ≥ B > C = D ≥ E > F

Therefore, A > F.

### Case 4 : Opposite sign

Whenever there are opposite sign there are 3 possibilities.

For instance, A > B ≤ C (No relation), there will be 3 possibilities:

A = C

A > C

A < C

We can even understand it in another way

A > B

C ≥ B

So, no relationship can be found between A and C.

 SIGN POSSIBILITIES ≤ <, = ≥ ≥, = = <, >, =

Example 7: A < B ≤ C = D ≤ E

Conclusion 1: A < E

Conclusion 2: A ≤ E

Conclusion 3: A > D

Conclusion 4: B = E

Which conclusion(s) follow(s)?

In this example, only Conclusion 1 follows.

Conclusion 2 is wrong because common sign between A and E is <.

Conclusion 3 is wrong because A < D.

Conclusion 4 is wrong because B ≤ E. ( B = E is just a possibility)

## How to solve Possibilities?

There can be 2 cases:

1. Either - or

If two possibilities are given in the conclusions and both such conclusions have the same variable, we apply ‘either or’ between the conclusions. This means at a time one of the two conclusions will surely be true.

This is the most tricky type of snaswer. Let's have a look at the following example in order to understand this point:-

Example 8: A < B ≤ C > D = E ≤ F

Conclusion 1: A ≤ D

Conclusion 2 : A > D

Conclusion 3: A =D

Conclusion 4: A ≤ C

In this case correct answer will be Either 1 or 2 follows because there are opposite signs between A and D ( <, ≤, >). So, in this case there will be 3 possibilities as explained earlier.

Since all the three possibilities are present in conclusion 1 or 2, we apply either or case.

Let us now consider another example:

Example 9: A < B ≥ C =E = F > D

Option 1: A < C

Option 2: A > C

Option 3: F ≥ B

Option 4 : D < F

In this correct answer will be Option 4.

In option 1 & option 2, we cannot apply either or case because only 2 possibilities are given but according to the questions, there can be 3 possibilities between A and C.

1. Wrong

If all the possible possibilities are not given the conclusion i.e only some of the possibilities are given, then those conclusions will be considered wrong.

## Solved Examples of Coded Inequality for Reasoning Section:

Now, we solve one miscellaneous question to thoroughly understand the concept:

Example 10:

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 than nor greater than Y

X # Y means X is neither greater than nor equal to Y

X * Y means X is neither smaller than nor equal to Y

Statements: W % E, P % E, P @ S.

Conclusions:

I: S * E.

1. W \$ S
 A. Only conclusion I follows B. Only conclusion II follows C. Both conclusion I and conclusion II follow D. Neither conclusion I nor conclusion II follows E. Either conclusion I or conclusion II follows

Correct Ans: D

W % E implies W < E

P % E implies P < E

P @ S implies P > S

Hence, the consolidated relationship is E > P > S and E > W

Conclusion I: S * E implies S > E, which is definitely false.

Conclusion II: W \$ S implies W = S, which may or may not be true as the relationship between S and W cannot be established.

Hence, neither conclusion follows.

Hence, option 4.