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**Inequality:**

**Reasoning Shortcuts & Tricks**

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Hello
Friends, Today we are going to share a very important Topic of Reasoning
Section that is

**Inequalities.**It is a very common & very Important topic from the competitive exam of view from which there always 5 to 6 questions comes in all competitive exams. In Inequality, we are given some directions, a statements followed by 4 conclusions. We have to find the conclusions which are true according to the given statement.**In Exams mostly questions comes in two forms:**

1) Coded Inequality.

2) Direct Inequality.

In Coded
Inequality form, $, #, %, &, @ symbols are used. In Direct Inequality, they
use direct symbols <, >, =, ≤, and ≥ in the statement.

**Meanings of Different symbols used in the Problems:**

1)
< : Less than

2)
≤ : Less than or Equal to

3)
> : Greater than

4)
≥ : Greater than or Equal to

5)
= : Equal to

Let us take we have given the following directions:

A $ B means A is not smaller than B

A @ B means A is neither smaller
than nor equal to B

A # B means A is neither greater
than nor equal to B

A & B means A is neither
greater than nor smaller than B

A % B means A is not greater
than B

Now first you have to decode the meanings of
different symbols given- Solve it one by one:

1)
First we have Given, A is not smaller than B that means A can
either be equal to A or Greater than B i.e A ≥ B.

2)
A is neither smaller than nor equal to B that means A is Greater
than B i.e A > B.

3)
A is neither greater than nor equal to B that means A is lesser
than B i.e A < B.

4)
A is neither greater than nor smaller than B that means A equal to
B i.e A = B.

5)
A is not greater than B that means A can either be equal to or
lesser than B i.e A ≤ B.

Now form a table before solving this kind of
problems:

1)
Symbols >, ≥, and = should be in Ist row

2)
Symbols <, ≤, and = should be in 2nd row

3)
———-> Right Hand Side Direction.

4)
<———- Left Hand Side direction.

5)
In Row 1, First Priority should go to symbol ‘>’ then
to ‘≥’ & then to ‘=’.

6)
In Row 2, First Priority should go to symbol ‘<’ then
to ‘≤’ & then to ‘=’.

Make Sure you make the table
correct otherwise you will loose all the 5 or 6 marks.

Let us take the following
example:

1).

**Statements:**K & B, B $ W, W # H, H % M**Conclusions:**(1) M @ W. (2) H @ K. (3) W & K.

**Step 1:**First Make a single statement.

K & B $ W # H % M

**Step 2:**Now we have to analyze the given conclusions one by one.

**1)**

**M @ W**

Ã˜ If you go
from M to W, you will go in a Reverse Direction i.e to the Left hand Side.

Ã˜ Between M
and W there are present two symbols, one is % and other is #.

Ã˜ In the above
table both the symbols are present in row 2 & the Highest Priority symbol
is #.

Ã˜ Since the
direction of letters formed was to the Left Hand Side, So In Left Hand Side
case we should note the symbol which is exactly above the symbol #.

Ã˜ The symbol
above to # is @.

Ã˜ And in conclusion
the symbol present between M and W is also @. So M @ W is TRUE.

2)

**H @ K**
Ã˜ If you go
from H to K, you will go in a Reverse Direction i.e to the Left hand Side.

Ã˜ Between H
and K, the symbols present are #, $, and &.

Ã˜ Check these
symbols with the above table, # is in Row 2 and $ is in Row 1.Both the symbols
are in different rows.

Ã˜ So
Conclusion 2 is FALSE.

**3)**

**W**&

**K**

Ã˜ From W to K,
the direction is to the Left hand side,

Ã˜ Between W
and K, the symbols present are $ and & and the higher priority symbol
is $.

Ã˜ Direction is
to the Left-hand side. So we should note the symbol which is opposite to $.
That is %.

Ã˜ But given
conclusion is W & K. So it is FALSE

*Therefore Conclusion 1 alone Follows*
Let us take one more example:

2)

**Statement:**H @ T, T # F, F & E, E % V.**Conclusions:**1) V $ F. 2) E @ T. 3) H @ V. 4) T # V

1)

**V $ F**: Left Hand Side Direction – Symbols present are % and &. Both are in Row 2. Since the direction is Left Hand Side, and highest priority symbol is %, we should note the symbol which is exactly opposite to % which is symbol is $. So the Conclusion 1 is True.
2)

**E @ T**:Left Hand Side Direction. Symbols present are & and #. Both are in Row 2. High priority symbol is #. Symbol opposite to # is @. So E @ T is True.
3)

**H @ V:**Right Hand Side Direction. Symbols present are @, #, & and % but are in different rows. So False.
4)

**T # V:**Right Hand Side Direction. Symbols are #, &, and %. All are present in Row 2. High Priority symbol is #. So T # V is True. (In Right Hand Direction case we should check for the same symbol not the opposite one)

*Therefore, In this Conclusion 1, 2, and 4 are True.*

Thank
You Friends !! J

If you found any problem to understand
anything, you can ask through comment section below.

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