Inequality (Direct and Coded): Types, Methods and Examples
Inequality is a reasoning topic in which a set of statements shows the relation between quantities using the signs greater than, less than, equal to, greater than or equal to, and less than or equal to. From these statements one or more conclusions are given, and the candidate must decide which conclusion definitely follows from the statements. The method is to join the statements into a chain and then read the relation between the two quantities asked.
The special feature of this topic is that it is fully symbol based, so a well-practised candidate can solve it without any lengthy calculation. In the coded form, different symbols stand for the ordinary signs, so the candidate must first decode the symbols and then apply the same method. This article gives a complete deep-study revision of inequality. It explains the basic terms, the combination rules, the coded form, the order of solving, the common mistakes and a practical preparation plan so that the topic becomes a quick and reliable source of marks in APSC, ADRE, Assam Police, SSC and Railway examinations.
Basic Terms
- Inequality: a statement that two quantities are not necessarily equal.
- Greater than (>): the left quantity is larger than the right.
- Less than (<): the left quantity is smaller than the right.
- Greater than or equal to (≥): the left quantity is either larger than or equal to the right.
- Less than or equal to (≤): the left quantity is either smaller than or equal to the right.
- Equal to (=): both quantities are the same.
- Conclusion: a relation that is tested against the given statements.
- Common term: the quantity that appears in two statements and joins them.
- Chain: two or more statements joined through a common term.
- Coded inequality: a question in which special symbols are used in place of the ordinary signs.
Core Concepts and Combination Rules
- Two statements can be combined only when they share a common term.
- If A is greater than B and B is greater than C, then A is greater than C.
- If A is greater than B and B is equal to C, then A is greater than C.
- If A is greater than or equal to B and B is greater than C, then A is greater than C.
- If A is greater than B and B is less than C, no definite relation can be found between A and C.
- The direction of the signs must be the same while joining a chain; a change of direction stops the chain.
- Greater than or equal to combined with greater than gives greater than, and with equal to gives greater than or equal to.
- In coded inequality, first write the decoding table, then replace every symbol and solve as a direct question.
Types of Inequality Questions
The first type is direct inequality, in which the ordinary signs are given and conclusions must be tested. The second type is coded inequality, in which symbols stand for the signs and must be decoded first. The third type gives two or three conclusions and asks which of them follow. The fourth type is the either-or case, in which two conclusions together cover every possibility and therefore one of them must be true. A fifth type combines inequality with a coded or a word-based statement to make the decoding step the real challenge.
Steps to Solve an Inequality Question
First, if the question is coded, decode every symbol with the help of the given table. Second, identify the common terms that link the statements. Third, join the statements into a single chain, keeping the same direction of signs. Fourth, derive the relation between the two quantities named in the conclusion. Fifth, test each conclusion separately and mark it as follows or does not follow. Finally, in an either-or question, check whether the two conclusions together exhaust all the possibilities, because only then is the either-or answer correct.
Examination Trends
In competitive examinations inequality is a fast scoring topic and usually carries three to five marks. Coded inequality is asked more often than the direct form. The conclusions are usually two or three in number, and the either-or type appears regularly. Because the topic needs no calculation, it is among the first that a candidate should attempt, provided the combination rules are well memorised.
Common Mistakes to Avoid
- Do not reverse the direction of a sign while forming the chain.
- Do not combine two statements that do not share a common term.
- Do not treat a greater than or equal to sign as a strict greater than sign.
- Do not ignore the case where the two quantities may be equal.
- Do not mark either-or unless the two conclusions together cover all the possibilities.
- In a coded question, do not forget to decode before solving.
How to Prepare This Topic
Begin by memorising the five signs and the rules for combining them. Then practise direct inequality with two conclusions until the chain method becomes automatic. After that, move to coded inequality and practise writing the decoding table quickly. Then attempt the either-or questions and the three-conclusion questions. Since this topic is short and precise, daily practice of ten to fifteen questions for a few days is enough to make it a certain source of marks. Keep a note of every question in which you reversed a sign, because that is the most common error in this topic.
One more habit worth building is to rewrite each statement as a small arrow chain before looking at the conclusions. Turning the signs into a simple left-to-right order removes the confusion caused by the wording of the question, and it makes the either-or case easier to see. Remember also that a conclusion which is possibly true is not the same as a conclusion which definitely follows; only the definite relation counts. In the examination, inequality should be attempted early, because it needs no rough work and can often be finished in a few seconds. With the five signs and the combination rules clear in your mind, this topic becomes a source of guaranteed marks.
Frequently Asked Questions
What is inequality in reasoning?
Inequality is a reasoning topic in which statements with greater than, less than and equal to signs are given, and the candidate must decide which conclusion definitely follows.
When can two statements be combined?
Two statements can be combined only when they share a common term and the direction of the signs is the same.
What is coded inequality?
In coded inequality, special symbols stand for the ordinary greater than, less than and equal to signs. You first decode the symbols and then solve like a direct question.
What is the either-or case?
This is the case in which two conclusions together cover every possibility, so one of them must be true, and the answer is that either one or the other follows.
Why does no relation follow sometimes?
If the chain changes direction, for example A is greater than B and B is less than C, then no definite relation between A and C can be established, so no conclusion follows.