Simple Inequality Problems


 
 
Concept Explanation
 

Simple Inequality Problems

Type - I rightarrow Simple Inequality Problems :  In such questions one or more than one statements will be given and two or more than two conclusions will be given according to statement you have to find which of these conclusion is right (follow).

Basics of Inequality : The various operators that are used inequalities are

> and < are single (definite) inequality symbols.

geqslant and leqslant are double (possible) inequality symbols.

= is neither single nor double inequality symbols presence of = in statement doesn't make any difference.

neq concept is totally different so we have to study separately.

Rules for Conclusions are:

There are certain rules that can be used to reach to a particular conclusion

S.No Statement  Possibility Conclusion
 1   A > B > C  

No possibility of statement

 A > C
 2  A geqslant B > C  A > B > C  rightarrow A > C

 From both possibility

we are getting A>C

so the conclusion will be A>C

 A = B > C  rightarrow A > C
3. A>B geqslantC A >B > C rightarrow  A > C

From both possibilities

we are getting A>C

So conclusion will be A>C

A > B  = Crightarrow A > C
 4.  A geqslant B geqslant C A > B > C rightarrow A > C

From first three possibilities

we are  getting A > C

but from last one we are getting A=C

So combination of these two AgeqslantC will be conclusion.

 

A = B > C rightarrow A > C
A > B = Crightarrow A > C
A = B = C rightarrow A = C 
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Sample Questions
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Question : 1

In the question below, statements are given followed by Conclusions numbered I and II. The candidate has to assume all the statements to be true even if they seem to be at variance from the commonly known facts and then decide which of the given two Conclusions logically follows from the information given in the statements and mark the option best suited.

Statements:    

 A > B = C ≥ D, V ≥ G ≤ H = D

Conclusion:

I. C ≥ D       

II. A > H      

III. B ≥ G        

IV. C < V

Right Option : C
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Question : 2

In the question below, statements are given followed by Conclusions numbered I and II. The candidate has to assume all the statements to be true even if they seem to be at variance from the commonly known facts and then decide which of the given two Conclusions logically follows from the information given in the statements and mark the option best suited.

Statement:  

  M ≥ P < H,  V > T = M

Conclusions:  

 I. V > P    

II. T ≥ H

Right Option : A
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Explanation
Question : 3

Which of the following expressions is true, if the given expression is true?

P < R  S = M > N = K > L

Right Option : A
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Explanation
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