# Inequality Reasoning: Concept, Questions & Answers

## Introduction of Inequality:

In such types of questions of Inequality, a group of elements is given with a certain coded relationship denoted by <, >, =, ≤, ≥ and ≠.

To understand the symbols, let us discuss the meaning of the given symbols:

- ‘X > Y’; Here, the symbol ‘
**>**‘ means ‘greater than’, hence the relation shows that X is greater than Z. - ‘X < Y’; Here, the symbol ‘<‘ means ‘smaller than’, hence the relation shows that X is smaller than Z;
- ‘X = Y’; Here, the symbol ‘=’ means ‘equal to’, hence the relation shows that X is equal to Z;
- ‘X ≤ Y’; Here, the symbol ‘≤’ means ‘either smaller than or equal’, hence the relation shows that X is smaller than or equal to Z;
- ‘X ≥ Y’; Here, the symbol ‘≥’ means ‘either greater than or equal’, hence the relation shows that X is greater than or equal to Z;
- ‘X ≠ Y’; Here, the symbol ‘≠’ means ‘not equal’, hence the relation shows that X is not equal to Y.

**Tips and Tricks: **

**To solve the tricky question of inequality, the candidate must understand the four tricky concepts:**

- If in a question, K < M < L is given, then K < M, M < L and K < L are considered to be true.
- If in a question, K > M ≥ L is given, then K > L is considered to be true and K ≥ L is not true.
- If in a question, K ≥ L = M is given, in that case, either K > M or K = M is true.
- If in a question, K < M > L is given, then no relation can be found between K and L because of opposite symbols.

## Types of Inequality:

**a) Single statement Inequality:**

**a) Single statement Inequality:**

In this type of question, the relation between the elements is given in a single series by coded relationship symbols i.e. <, >, =, ≤, ≥ and ≠. For example;

**Q. Statement: **

A < N = U > F > B > H

Conclusion:

I. H < N (true)

II. F > A (false)

**Q. Statement:**

T < D > G < F > B > H

Conclusion:

I. G < H (false)

II. F > T (false)

**b) Multiple statements Inequality:**

**b) Multiple statements Inequality:**

In this type of question, the relation between the elements is given in two or more different series. To get the exact relation, we have to arrange it by matching the similar elements in a single series. For example;

**Q. Statement:**

T < D > G, P < F = T

Conclusion:

I. P < G

II. G > T

**Solution:**

Here, first, we have to arrange it in a single series to get the definite relation.

P < F = T < D > G

I. P < G (false)

II. G > T (false)

**Q. Statement: **

T < S < D = F, F ≥ Q > E = R

Conclusion:

I. R < D

II. Q > T

**Solution:**

Here, first, we have to arrange it in a single series to get the definite relation.

T < S < D = F ≥ Q > E = R

I. R < D (true)

II. Q > T (false)

**c) Not equal types Inequality:**

**c) Not equal types Inequality:**

In this type of question, the **‘≠’** **(not equal)** relation are given between the elements. The not equal symbol is meant to show a comparison between the two quantities which are unequal hence, among the two quantities one will be either greater or smaller than the other quantity. To get the exact relation, we have to consider the both possibilities i.e. either ‘>’ or ‘<‘. For example;

**Q. Statement: **

T < S < D = Q, T ≠ P = X < Z < R,

Conclusion:

I. X < D (False) (≠ means either > or <)

II. Q > P (False) (≠ means either > or <)

**Q. Statement:**

R ≠ S > Y ≠ Q, P < F = R = E < T,

Conclusion:

I. P < T (true)

II. S < F (false)(≠ means either > or <)

**d) Filler Inequality:**

**d) Filler Inequality:**

In this type of question, the relation between the elements is not given and in the place of coded symbols (which represented by <, >, =, ≤, ≥ and ≠) blank or space was/were given. You have to find out the proper coded symbol/s to fill the blank or space according to a certain conditions which generally mentioned with the questions. For example;

**Q. Which of the following order of letters (from left to right) in the blanks makes the expression, C > P definitely true?**

____ = ____ > ____ ≤ ____=____

a) Z, T, C, D, P

b) T, P, D, C, Z

c) P, T, C, D, Z

d) D, C, T, Z, P

e) None

**Solution: **(e)** **None

**e) Conditional Inequality:**

**e) Conditional Inequality:**

It is an inequality which is true for some variables or for a particular condition but not true for all values of variables. And the solution of inequality consists of only real numbers as the term ” Less than or Greater than” are not defined for establish a certain relation. For example;

**Q1. Which of the following statements prove that ‘W > F’ is definitely true?**

I. A ≥ J < K = W ≥ L > Z; J > N = S ≤ F

II. W < P < Q ≤ K > J > Z; Z = H ≥ S = A < F;

III. S < J < W = O ≤ L < Q; S = P ≤ K < F =J

Solution: III

**Q2. Which of the following statements prove that ‘K > S’ is definitely true?**

I. A ≥ J < K = W ≥ L > Z > N = S ≤ H

II. W < P < Q ≤ K > J > Z; C = H ≥ S = A < L < W;

III. S < J < W = O ≤ L < Q = P ≤ K > D =J < L

Solution: I, II and III

**f) Coded Inequality: **

**f) Coded Inequality:**

In case of coded inequality, questions consists of a couple of statements with some logical and arithmetic relationship between them. Such type of Inequality followed by a couple of conclusions and you’ll have to find out which conclusion follows the given statements. For example;

**Q. In these questions, the relationship between different elements is shown in the statement. The statement is followed by two conclusions. Choose the correct answer on the basis of the information given below.**

a) If only conclusion I is true.

b) If only conclusion II is true.

c) If either conclusion I or II is true.

d) If both conclusions I and II are true.

e) If neither conclusion I nor II is true.

In the following questions, the symbols %, @, #, &, $ are used. All the symbols define the following meanings.

Y # Z means that ‘Y is equal to Z’

Y & Z means that ‘Y is greater than Z’

Y $ Z means that ‘Y is greater than or equal to Z’

Y % Z means that ‘Y is smaller than Z’

Y @ Z means that ‘Y is smaller than or equal to Z’

For example;

**Q. Statements: **

O $ M; P # M; R % P;

Conclusions:

I) P % O

II) P # O

**Ans: c**

**Solution:**

Step 1 – Decode the given symbols as shown below:

Symbols | % | @ | # | & | $ |

Meaning | < | ≤ | = | > | ≥ |

Step 2 – Now decode the given statements with the help of the above table:

So, after decoding the statements, we have;

O ≥ M; P = M; R < P.

After arranging, we have;

R < P = M ≤ O

Step 3 – Now based on the given statement; we can conclude that either O > P or O = P will be true.

So, the correct answer is c.

**For ****Basic level Inequality Questions & Answer.**

**For Advanced level Inequality Questions & Answer.**