Inequality: Reasoning Shortcuts & Tricks
Shared by: WWW.GovtJobsPortal.IN
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
Ø If you go from M to W, you will go in a Reverse Direction i.e to the Left hand Side.
Ø Between M and W there are present two symbols, one is % and other is #.
Ø In the above table both the symbols are present in row 2 & the Highest Priority symbol is #.
Ø 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 #.
Ø The symbol above to # is @.
Ø And in conclusion the symbol present between M and W is also @. So M @ W is TRUE.
2) H @ K
Ø If you go from H to K, you will go in a Reverse Direction i.e to the Left hand Side.
Ø Between H and K, the symbols present are #, $, and &.
Ø Check these symbols with the above table, # is in Row 2 and $ is in Row 1.Both the symbols are in different rows.
Ø So Conclusion 2 is FALSE.
3) W & K
Ø From W to K, the direction is to the Left hand side,
Ø Between W and K, the symbols present are $ and & and the higher priority symbol is $.
Ø Direction is to the Left-hand side. So we should note the symbol which is opposite to $. That is %.
Ø 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.