## Aug 19, 2015

### INEQUALITY: REASONING SHORTCUTS & TRICKS

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:
Important Points to be remember while solving 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)    & 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
Modified Single Statement: H @ T # F & E % 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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