# Solving Inequalities - Quickly and Correctly

I have received a number of requests from you all for this little chapter which comes for 5 marks in any competitive exam – I am talking about bank competitive exams.

Going by the SBI Associate PO that is going on, ensuring that we attempt these and attempt these correctly can really help us with the aggregate – plus it is one of the ‘easy’ chapters.

The method I’m going to share with you is tried and tested – many of you may already know and those who don’t – I sincerely hope this helps!

## My 5 Rules to AGTC (Always Get Them Correct):

### 1: See the signs of change

For ANY given equation, look at what the question asked is and then jot down the signs (<,>, ≤, ≥) in the sequence it is appearing and leave out the ‘=’ sign.

For example :

H>P, P≤T, T=V, V<U

Is H>U correct? Answer is NO, we’ll come to it later, but first we learn the signs.

So, we need to go from H ---- to U. The signs to be written down will be – [ > ≤ < ]

In case H>P, P≤T, V=T and U>V

then, H to U will be written down like this – [> ≤ <]

The last sign is ‘>’ but since we are going from H to U, which mean we will go from T to V to U, we will change the direction – instead of going from left to right like we were initially doing.

We now go from right to left for the last two equations – and since we change direction, we will change the signs too as the relation is now from the point of view of the element in right!

Thus, ignore the ‘=’, jot down the others, and change the signs as per direction in which the equation is needed to go.

### 2: Maximum rules – leave out the rest!

In ANY given question – after you have jotted down the ‘signs’ as per Rule 1 – the sign which appears maximum is your ‘correct’ answer.

T>U, V≤U, V>S, S=K, H<K , what is the relation between T and K?

signs will be – [ > ≥ > > ],
in this, ‘>’ comes maximum number of times, hence T>K is the correct relation, anything else is wrong.

Suppose the question was
T≥U, V≤U, V≥S, S=K, H<K
then the signs would be – [ ≥ ≥ ≥ and > ], which sign comes maximum number of times?

I’m sure you would say ‘≥’, as it comes three times ans ‘>’ come only once. However if you see, ‘≥’ means ‘ greater than or equal to’ which mean it is a combination of two signs, ‘>’ and ‘=’!

Therefore ≥ ≥ ≥ > is actually > =, > =, > =, >= and >   !

Thus the maximum sign is ‘>’      !

Thus in any equation where there are many ‘≥’ or ‘≤’ – if there is even one ‘>’ or ‘<’, the answer will be ‘>’ or ‘<’ respectively.

### 3: Opposites can attract as well as distract!

We will understand this one with an example:

A>B, B≥C, C≤D. Relation between A and D?

the signs - > ≥ ≤.  As you can see the last two signs are opposites to each other – which means any direct relation like ‘>, <, ≥, ≤, or =’ will be incorrect. Thus if in options any of these signs are given answer will be wrong.

however, this classic case is a case of ‘either/or’ option for an answer.

Please Note: This is important. Where you get opposite signs in any combination, [< >, > <, ≥ ≤, ≤ ≥, ≥ <, ≤ >], you have to check for 2 conditions:
(1) if the characters in both the options are same
(2) all the three signs, =, <, > are to be present in any combination
if these 2 cumulatively follow – then answer is either/or. If these don’t follow then answer is none follow or wrong, depending on how the question is given.

thus,
A>B, B≥C, C≤D is given and your to questions are:
(a) A ≤ D (b) A > D

Condition 1 – same characters in both options – A and D.  (yes it meets)
Condition 2 – all 3 signs to be present - <, =, >. (yes, this one meets too)

thus, answer is either (a) or (b) holds true.

### 4: If maximums are opposites?!

Then apply Rule 3 as above!

### 5: Something new?

If any new character is given in the option, which is not given in the question – any relation will be wrong!

A>B, B>C, C>D. but if you are asked is C>G – then it is a big WRONG!

People these are the basic rules of solving inequalities – I myself solve question by these rules and never get any wrong – but the important thing is to practice so that you can remember these rules easily without requiring to mug them up.

Nothing is an alternative to simple, old-fashioned practice and hard work. Tips and Tricks won’t help unless you know them like you know your ABCDs! And that fluency comes only through practice.

So, do some sums today and see if these tips work wonders!

Any doubts or queries – leave ‘em in the comments sections we’ll try to tackle em asap.

Good day for now! 