How to Solve Inequality Question? Concept & Tips

About the Inequality

Inequality is a common topic for all competitive exams. We can expect 5 or 6 questions from this topic in Reasoning section. It is one of the easy topics for people who are slightly comfortable with elementary mathematics.

Let us consider A and B as two variables, then Inequalities can be shown as following:

Inequalities Golden Rules

The combination between two inequalities can be established, if they have a common term.

For e.g.

(i) A > B, B > C – combination can be easily established as: A > B > C. Here we can make conclusion – A > C or C < A

(ii) A < B, B < Q – combination can be easily established as: A < B < Q. Here we can make conclusion – A < Q or Q > A

(iii) A > B, B > C combination can be easily established as: A > B > C. Here we can make conclusion – A > C or C < A

The combination between two inequalities cannot be established, if they don’t have a common   term.

For e.g. 

(i) A > B, B < C – combination cannot be established. (Here relationship between A & C cannot be established.)

(ii.) A D – combination cannot be established. (Here relationship between A & C cannot be established.)

(iii.) A > B, B < C combination cannot be established. (Here relationship between A & C cannot be established.)

The combination between two inequalities can be established, if and only if the common term is greater than (or ‘greater than or equal to’) one and less than (or ‘less than or equal to’) the other.

For e.g.

(i) A > B, C < B. (Here common term B is less than or equal to one term A, and greater than other term C.So here combination between the elements can be easily established.)

A > B, C < B

Possible inequality – A > B > C or C < B < A

Note: Here we can make conclusion as: A > C or C < A

(ii) P > Q, Q < C – (Here common term Q is less than both the term, so combination between the elements cannot be established.)

(iii) N > M, L > N (Here common term N is greater than or equal to one term M, and less than other term L. So here combination between the elements can be easily established.)

N > M, L > N

Possible inequality – L > N > M or M < N < L

Note: Here we can make conclusion as: L > M or M < L

(iv) N > M, N > L (Here common term N is greater than both the term, so combination between the elements cannot be established.)

If we combined the inequality – L < N > M; so here we cannot make combined inequality.)

Complementary Pairs: (Either & or) – Either and or cases only takes place in complementary pairs. We cannot combine two elements with common elements in which no relation is established.

For e.g.

A > B, B < C

1. Statement: A > B < C

Conclusion:  I. A > C               II. A < C

Here we cannot establish relation between A and C. We can only draw conclusion i.e. A is either greater than or equal to C or we can say A is either smaller than C.

From the given above conclusions, it is easy to understand that one of the given conclusions must be true, which is represented by option either (i) or (ii). These types of pairs are called complementary pairs.

One more complementary pair is < and >. These two relations covers the entire possibility same as > and <.

2. Statements: A = B > C > D < E

Conclusions: I. A > C           II. A = C

Conclusion doesn’t form the complementary pairs but still here the answer is either-or because only two relations can be established between A and C. Here conclusion either I or II follows, because here we can say A is either greater than C or equal to C.

3. Statements: A = B > C > D < E

Conclusions: I. A > E           II. A < E

Here, conclusion either I or II follows. We don’t know the exact relation between A and E. Here A can be either greater than E or Smaller or equal to E.

Points to remember 

1. If similar signs are there between two or more elements, relationship can be easily established between the elements. 

For e.g.

A > B > C > D

Here we can draw a conclusion – A > D, B > D, A > C or D < A, D < B or C < A, C < B

2. If similar signs are not there between two or more elements, relationship cannot be established between the elements. In these cases you have to put extra care seeking either-or cases type conclusions.

For e.g.

A > B < C > D

Here relationship cannot be established between – A & C, A & D, B & D.

Now, since you have understood the Inequalities Concepts and Shortcuts,

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