**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.

Thank you nice trick and very handy for direct question but how do we solve it if the orders are changed. I mean if we have

ReplyDeleteH @ T, F # T, F & E, V % E Iinstead of

H @ T, T # F, F & E, E % V.

Do explain please.