Inequality is a concept used to compare two or more quantities using specific symbols to show their relationship.
In such types of questions, a group of elements is given with a certain coded relationship denoted by <, >, =, ≤, ≥, ≠.
To understand the symbols, let us discuss their meanings:
- X > Y means “greater than”. It shows that the value of X is more than the value of Y.
- X < Y means “less than”. It shows that the value of X is smaller than the value of Y.
- X = Y means “equal to”. It shows that both X and Y have the same value.
- X ≤ Y means “less than or equal to”. It shows that X is either smaller than Y or exactly equal to Y.
- X ≥ Y means “greater than or equal to”. It shows that X is either greater than Y or exactly equal to Y.
- X ≠ Y means “not equal to”. It shows that X and Y do not have the same value.
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
1. 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)
2. 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)
3. 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 <)
4. Filler Inequality
In this type of question, the relationship between the elements is not directly provided. Instead of symbols such as <, >, =, ≤, ≥, and ≠, blanks or spaces are given. You are required to determine the appropriate symbol to fill in the blanks based on the conditions specified in the question.
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
5. 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:
Q. 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
Q. 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
6. 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’
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.