Hello Friends! In every competitive exam, logical reasoning is one of the scoring sections. In this article, we are going to discuss important concepts and short tricks on inequality reasoning step-by-step. Using this simple inequality reasoning rules you can solve inequality reasoning questions in minimum time.
These concept and trick help you answer quickly inequality reasoning questions in the exam like IBPS PO, SBI PO, IBPS RRB, IBPS Clerk, SBI Clerk, IBPS RRB, SSC CGL, SSC CGL, SSC MTS, NICL AO, LIC AAO, SBI Associate Clerk, SBI Associate PO and others. You can see our article on Quantitative Aptitude-Simplification with Digital Root or Digital Sum
To make this chapter easy for you, we are providing some inequality reasoning questions with answers.
Let us consider P and Q as two variables, and then inequalities can be shown as follows:
- P>Q – P is greater than Q
- P<Q – P is less than Q
- P≥Q – P is greater than or equal to Q
- P≤Q – P is less than or equal to Q
There are two types of statement or relation in inequality from which you need to make a conclusion.
In this type of statement contains directional signs, either statement includes >, ≥, = or <, ≤, =.
For example, 1. A>B≥C=D>E≥F 2. P≤Q=R<S<T
This type of statement contains complementary pair signs or opposite directional signs.
1. A>B≤C>D≥E 2. P<Q<R≥S<T=U
How to combine statement?
In every Competitive exam related to banking or insurance, inequality reasoning questions are given in a split manner. To solve this type of question we need to combine them in a single relation.
Statement- X≥G=H, G>J≥L, J≥K<Y
Generally, you find questions like above. To find conclusions from the statement first we need to make a relation between the variables. To find the relations you need to combine statement through a common term.
If we find a conclusion between G and L, we have to combine the first two statements through common term G.
Therefore, We get our derived statement like X≥G>J≥L.
Similarly, if you try to find a conclusion between X and Y, you can combine three statements through their terms in common, G and J. And you get X≥G>J≥K(type #2 statement).
How to draw a conclusion from the statement?
From any statement of inequality reasoning questions, we can make two types of conclusions.
- Definite Conclusion
- Indefinite Conclusion(Cannot say)
In a definite conclusion, we find a particular inequality(>, ≥, <, ≤ and =)between variables. For example, Statement – A>B≥C=D
Conclusions – 1.A>B 2.B≥D
The first conclusion, we can draw directly from our statement. But in the second conclusion we don’t have a direct relation between B and D. So we made our conclusion by “Preference Of Sign” method.
What is Preference Of Sign?
If signs >, ≥ and = or <, ≤ and = comes between variables then the order of inequalities exists between them is → ≥ → = or < → ≤→ =.
The preference order is > → ≥ → = or < → ≤→ =
Similarly, for the second conclusion, you find both ≥ and = in the given statement. Hence by giving sign preference, you find that “≥” is the only inequality exists between B and D. So the second conclusion is correct.
Let see another example and you get a clear idea.
Statement – P≥Q>R=S>T
In the above statement, the only inequality exists between P and T is P>T. We find the following signs in order from P to T is ≥,>,=,>. Giving sign preference, we find “>” is the only inequality exists between P and T.
This method of finding a conclusion from a statement is very easy and quick and save a lot of time.
If we see a type#2 statement where signs are complementary, we cannot say anything about what inequalities exists between variables.
Statement – P<Q<R≥S<T=U
In this statement, you cannot draw any conclusion between variables like P, S or R, U as complementary pairs of inequalities present in the statement.
Note – If you cannot find any definite conclusion it does not mean that there is no relation or you cannot make any possible inequality.
How to verify a conclusion from Inequality Reasoning Questions?
In the paper, our answer would be the verification of the given conclusions with the following condition –
- ”If only conclusion 1 is true”
- “If only conclusion 2 is true”
- ”if either conclusion 1 or conclusion 2 is true”
- ”if neither conclusion 1 or conclusion 2 is true”
- ”If both the conclusions are true”
To answer a question first we need to verify whether the given conclusion is true or false. We can verify it by a step-by-step process.
Statement – L>I=N>P; I≥R>K; N≤E<Z
Conclusions – 1.E>P 2.R≤L
Combine statements using the common term.
To verify the first conclusion you need to combine statement using the common term N. And you get derived statement, E≥N>P.
Find the inequality between variables using “Preference Of Sign” method.
Here applying Preference of sign method we get conclusion E>P. Hence our 1st conclusion is true.
Similarly, for the 2nd conclusion derived statement is L>I≥R and after applying “Preference Of Sign” method the right inequality between L and R is L>R or R<L. So the answer is false.
Sometimes you came across a situation when both conclusions are false. Then you are in a confusion that whether the answer is “Either-Or” or “Neither-Nor”. We can distinguish both types very easily.
“Either-Or” type of inequality can be derived from both type#1 and type#2 statements.
How to solve “Either-Or” type conclusions?
There are some prerequisite conditions required to be a case of “Either or”
- Both the conclusions must be normally wrong.
- Subject and predicate should be same for both conclusions.
- There should be minimum and maximum only one “=” in conclusion.
- Lastly, we have to check our statement, whether it is supporting the conclusions or not.
If any of the above four condition is not satisfied then our answer will be “Neither-Nor”.
Statement – A≥B≥C
Conclusions –1.A>C 2.A=C
In the first step, we find that both the conclusions are wrong. So our 1st condition is satisfied.
Both the conclusions, subject and predicate(A and C) are alike, hence it satisfies our 2nd condition.
Both the conclusions contain only one “=”. So it satisfies our 3rd condition.
From the statement, you find that the right conclusion is A≥C which means “A is greater than C” or “A is equals to C” so our 4th condition is also satisfied. Hence the answer will be ”if either conclusion 1 or conclusion 2 is true”.
Let see another example,
Conclusions –1.P>R 2.P=R
In this example both the conclusion satisfies 1st, 2nd and 3rd conditions for “Either-Or” but does not support the actual statement so “Neither-Nor” will be the answer.
For type#2 statement, condition for either or is almost same. Conclusions must satisfy the first three conditions for “Either-Or”. As the opposite signs exist, we cannot say any definite inequalities between variables but it does not mean that there is no relation. So “either or” may be the answer if both the conclusions must follow this Particular condition.
Both the conclusions must contain all the three basic sign in form of > and ≤ or < and ≥. Both the combination of the sign has all the basic inequality that is >, <, =.
Note – For type#2 statement, we have to verify the first three conditions for type#1.
Statement – R≥S≥P=Q>T≤U<V<W
Conclusions A–1.R>V 2.R=V B–1.R>V 2.R≤V
For the A, both the conclusion is false as there is no definite inequality exists between R and V(Type#2 statement). Both the conclusions satisfy all the three conditions for a case of “Either-Or”. But they do not contain all the three basic signs that are >, <, = combined in them. So “Neither-Nor” will be the answer. Similarly for the B, Both the conclusions satisfy all three conditions for a case of “Either-Or”. And both the conclusions contain all the three basic signs >, < and = in the inequalities > and ≤. Hence definitely our answer is “Either or”.
finally, you have learned all the concepts and tricks to solve inequality reasoning questions for the upcoming exam.
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