Inequality Reasoning: Direct and Coded Inequalities, Rules and Tricks for SSC
Rahul Kumar
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Inequality reasoning checks whether you can combine statements such as A > B ≥ C and decide which conclusions are definitely true. The topic is based on a small set of rules, so with a little practice you can solve each question in 20 to 30 seconds. This note explains the symbols, the combination rules, the coded form and the either-or case with solved examples, practice questions and FAQs.
Symbols and Meaning
| Symbol | Meaning |
|---|---|
| A > B | A is greater than B |
| A < B | A is smaller than B |
| A ≥ B | A is greater than or equal to B |
| A ≤ B | A is smaller than or equal to B |
| A = B | A is equal to B |
Rules for Combining Statements
| Statements | Result | Reason |
|---|---|---|
| A > B > C | A > C | Same direction, so the relation is passed on |
| A ≥ B ≥ C | A ≥ C | Same direction |
| A > B ≥ C | A > C | One strict sign makes the result strict |
| A ≥ B > C | A > C | One strict sign makes the result strict |
| A = B ≥ C | A ≥ C | Equal keeps the other sign |
| A > B < C | No relation | Opposite directions (B is the smallest) |
| A < B > C | No relation | Opposite directions (B is the largest) |
| A ≥ B ≤ C | No relation | Opposite directions |
- The relation is passed on only when both signs point the same way.
- If the signs point in opposite directions, the two end letters have no definite relation.
- A strict sign (> or <) anywhere in a same-direction chain makes the final result strict.
- A conclusion with ≥ or ≤ is true only if the chain gives that or something stronger. For example, A > C makes A ≥ C true.
Method to Solve
- Write all the statements in one chain, putting the common letters together.
- Mark the direction of each sign.
- Check each conclusion with the rules above.
- If a conclusion pairs two letters with no definite relation, it does not follow.
- If two conclusions are complementary, check for the either-or case.
Either-Or Case
When two conclusions involve the same pair of letters, neither is definitely true, but together they cover all the possibilities, then either I or II follows. Common complementary pairs are:
| Conclusion I | Conclusion II |
|---|---|
| A ≥ B | A < B |
| A ≤ B | A > B |
| A > B | A = B (together they give A ≥ B, so check the chain first) |
Coded Inequalities
Here symbols such as @, #, $, % and * stand for the usual signs. First decode, then solve exactly as in the direct type. A sample code is given below:
| Code | Meaning |
|---|---|
| A # B | A > B |
| A $ B | A < B |
| A @ B | A ≥ B |
| A % B | A ≤ B |
| A * B | A = B |
Solved Examples
| Statement and conclusions | Answer |
|---|---|
| Statements: A > B ≥ C = D. Conclusions: I. A > D, II. B ≥ D | Both follow. A > B ≥ C = D gives A > D, and B ≥ C = D gives B ≥ D. |
| Statements: P ≥ Q > R < S. Conclusions: I. P > R, II. Q > S | Only I follows. P ≥ Q > R gives P > R. Q and S have no relation because R is smaller than both. |
| Statements: M > N ≥ O. Conclusions: I. M > O, II. O ≥ M | Only I follows. II is the opposite of I and cannot be true. |
| Statements: X ≥ Y ≥ Z. Conclusions: I. X > Z, II. X = Z | Either I or II follows, because together they cover X ≥ Z. |
| Coded: P # Q, Q @ R, R $ S. Conclusions: I. P > R, II. S > Q | Decode: P > Q ≥ R < S. I follows (P > Q ≥ R). II does not follow because Q and S are not related. |
Common Mistakes
- Joining opposite signs, such as A > B < C, and concluding something about A and C.
- Treating a ≥ chain as strict: A ≥ B ≥ C does not give A > C.
- Not decoding the symbols correctly in the coded type. Write the table first.
- Missing the either-or case when both conclusions are about the same two letters.
Quick Tips
- Always write the combined chain on paper; do not keep it in your head.
- Check each conclusion against the chain from left to right.
- If the two end letters are separated by a sign pointing the other way, mark "no relation".
- Spend extra time on the either-or case only when both conclusions use the same pair.
Quick Revision Points
- Same direction signs pass the relation on; opposite directions give no relation.
- A strict sign in the chain makes the result strict.
- Complementary conclusions on the same pair give the either-or case.
- In coded questions, decode first and then solve.
- Equal (=) does not change the other sign.
Practice Questions With Answers
- If A > B and B > C, what is the relation of A and C?
Answer: A > C - If A ≥ B and B ≥ C, what is A and C?
Answer: A ≥ C - If A > B and B < C, what is A and C?
Answer: No definite relation - If P = Q and Q > R, then P ? R
Answer: P > R - In P ≥ Q > R, what is P and R?
Answer: P > R - If A < B < C, then C ? A
Answer: C > A - If X ≤ Y = Z, then X ? Z
Answer: X ≤ Z - In M > N ≥ O, which is definitely true: M > O or M = O?
Answer: M > O - Which pair makes an either-or case: "X > Y, X ≤ Y" or "X > Y, Y > X"?
Answer: X > Y and X ≤ Y - In A > B ≥ C, B ? A
Answer: B < A
How to Practise This Chapter
Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Inequality Reasoning notes page.
Frequently Asked Questions
What is inequality reasoning?
It is a reasoning topic where you combine statements with signs like >, <, ≥, ≤ and = and decide which conclusions are definitely true.
What is the basic rule of inequalities?
If both signs point the same way, the end letters are related. If the signs point in opposite directions, there is no definite relation.
What is a coded inequality?
A question in which symbols like @, #, $, % and * are given to stand for the usual signs. You decode them first.
What is the either-or case?
It is the case when two conclusions about the same pair of letters are complementary, so one of them must be true.
Does A ≥ B ≥ C give A > C?
No. It gives only A ≥ C, because both signs include equality.
Does A > B ≥ C give A > C?
Yes. One strict sign makes the result strict.
How much time should one inequality question take?
About 20 to 30 seconds with practice.
Is inequality asked in SSC exams?
It appears in some SSC and CPO papers and is a regular topic in bank exams. It is also a good scoring practice for logical thinking.
What if the two letters have no relation?
Then the conclusion about them does not follow.
Can I solve it with numbers?
You can try values to test a chain, but the sign rules are faster and safer.
What does A = B ≥ C give?
A ≥ C.
How can I improve my speed?
Learn the rules by heart, then practise 15 to 20 questions every day.
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Rahul Kumar
SSC Exam Expert & Content Editor
Rahul is a senior SSC exam strategist with 8+ years of experience helping aspirants crack CGL, CHSL and MTS exams. He writes in-depth notification breakdowns, exam pattern guides and preparation strategies.