How To Solve Inequality?

Inequality is one of the most important topic. This topic carries 5 marks in prelims examination. You can easily gain those 5 marks in less than a minute if you know the correct approach of doing this topic questions. There are lot of tips and tricks out there but you don’t have to cram them all because in the examination, you will not remeber anything. So, in this article we will be trying to simplify this topic so that you can understand this better. We will be telling you the concept not the trick. Once you will understand it, you will start solving it in less time.

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The Concept Of Sign

Sign 1 Sign 2 Conclusion
> > >
< < <
< > No Conclusion
< = <
> = >
= = =
> > & = >
< < & = <
> & = < & = No Conclusion

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Priority of Symbols:

1) >  ≥ =
For ex- If    L>M≥Q=N
               Then, L> M and L>N
2)  <  ≤ =
For ex- If    A<B≤C=D
              Then, A<B and A<D
3) >  < (No relation)
For ex- If E>F<G
Then there will be no relation between E and G
4) >  ≤ (No relation)
For ex- If O>J≤H
Then there will be no relation between O and H.
5) <  > (No relation)
For ex- If S<P>M
Then there will be no relation between S and M.
6) <  ≥ (No relation)
For ex- If A<B≥C
Then there will be no relation between A and C.
 
Either- or case:  This is another important concept of In equality. Mostly students make mistakes in this condition. For clear concept we are giving example of “either-or”
1st condition for “either-or” is both conclusions should be wrong.
2nd condition is that variables of both conclusions should be same.

Now let’s Understand this better with an example:

In the following questions, the symbols @, ©, # $ and % are used with the following meanings.
‘P @ Q’ means ‘P is neither smaller than nor equal to Q’.
‘P * Q’ means ‘P is not greater than Q’.
‘P # Q’ means ‘P is neither greater than nor equal to Q’.
‘P $ Q’ means ‘P is neither greater than nor smaller than Q’.
‘P % Q’ means ‘P is not smaller than Q’.
Now, in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is/are definitely true and mark your answer accordingly.
Q4. Statements: L @ W, M # W, M % J
Conclusions: 
I. M * L
II. W % J
III. L @ J
(a) None follows
(b) Only I follows
(c) II and III follow
(d) Only III follows
(e) None of these
 Step 1- Make a table and write down the symbol given in the question with the sign they signify:
@ >
* < & =
# <
$ =
% > & =

Step 2- Now put these sign between the questions

L  >W, M < W, M > & = J

Step 3- Now Look at the options and answer accordingly.

Let’s Take another example:

Statements: F ≥ M > A > R > E
Conclusions: I. M > E
II. F > E
III. F < E
(a) Only I follows
(b) Only I & II follow
(c) Only II and III follow
(d) Only either II or III follows
(e) All follow
Answer- Now here, you don’t have to make a table in this questions as the relationship given is direct.

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