What Inequality Questions Test
- Direct inequality chains (A > B ≥ C)
- Coded inequalities (symbols standing for >, <, =)
- Certain vs possible conclusions
- Either-or cases on complementary conclusions
Question bank coverage by sub-pattern
How Inequality Appears in IBPS PO
Inequality is part of the Reasoning Ability section (20% of the IBPS PO syllabus). See the full IBPS PO Prelims breakdown.
Inequality Solved Examples for IBPS PO
12 exam-pattern inequality questions from the practice bank, each with a full solution.
Statements: A ≥ B > C, D = C, E < D. Conclusions: I. A > E. II. B > E.
- A.Only conclusion I follows
- B.Only conclusion II follows
- C.Both I and II followCorrect
- D.Neither I nor II follows
Solution
A ≥ B > C = D > E. So A ≥ B > C = D > E. A > E (I follows). B > C = D > E, so B > E (II follows). Both follow.
Statements: P ≤ Q = R, R > S, S ≥ T. Conclusions: I. Q > T. II. P ≤ R.
- A.Only conclusion I follows
- B.Only conclusion II follows
- C.Both I and II followCorrect
- D.Neither I nor II follows
Solution
Q = R > S ≥ T, so Q > T (I follows). P ≤ Q = R, so P ≤ R (II follows). Both follow.
Statements: G > H ≥ I = J < K ≤ L. Conclusions: I. G > J II. L > I. Which of the following is true?
- A.Only conclusion I is true
- B.Only conclusion II is true
- C.Both conclusions I and II are trueCorrect
- D.Neither conclusion I nor II is true
Solution
For conclusion I: G > H ≥ I = J implies G > J. For conclusion II: L ≥ K > J = I implies L > I. Therefore, both conclusions are true.
Statements: A@V&U&B; K#C%B@P Conclusions:
- A.A^C
- B.V&CCorrect
- C.P@U
- D.K&P
- E.A&P
Solution
Given A>V>=U>=B>=C and P<B, then V>=C is true. Thus, V&C is the correct answer.
Statements: A#C%B^O; Y@S&N^E^O Conclusions:
- A.C@N
- B.A%S
- C.S@O
- D.C#E
- E.C%SCorrect
Solution
Given A<C<=B=O=E=N<=S, then C<=S is true. Thus, C%S is the correct answer.
Solve the linear inequality for x: 2x - 5 < 23.
- A.x > 14
- B.x ≥ 14
- C.x ≤ 14
- D.x < 16
- E.x < 14Correct
Solution
2x - 5 < 23 => 2x < 23 + 5 = 28 => x < 28 / 2 = 14.
Solve the linear inequality for x: 2x - 7 < 185.
- A.x < 96Correct
- B.x ≤ 96
- C.x > 96
- D.x ≥ 96
- E.x < 98
Solution
2x - 7 < 185 => 2x < 185 + 7 = 192 => x < 192 / 2 = 96.
If x @ y means x is not greater than y; x # y means x is not smaller than y. Now assuming the given statements to be true, find which of the following conclusions is definitely true given the statements: Statements: A @ B, B # C Conclusions: I. A @ C II. A # C III. A = C
- A.Only I is true
- B.Only II is true
- C.Only III is true
- D.Either I or III is trueCorrect
Solution
Decoding: x @ y means x <= y x # y means x >= y Given: A <= B, B >= C I. A @ C means A <= C. This is not necessarily true. A could be greater than C, equal to C, or less than C. II. A # C means A >= C. This is not necessarily true. A could be greater than C, equal to C, or less than C. III. A = C. This is not necessarily true. A could be greater than C, equal to C, or less than C. However, if B = A and B = C, then A = C. Also, if A <= B and B >= C, it is possible that A <= C. Thus, either A <= C or A = C could be true, but we cannot say for sure. Given that B is between A and C, A <= B >= C. This means it is possible for A <= C, and if A = B and B = C, then A = C. Thus, either I or III could be true.
For what values of x is x² + 1 > 0?
- A.All real numbersCorrect
- B.x > 1 or x < -1
- C.-1 < x < 1
- D.No real numbers
Solution
Since x² is always non-negative (x² ≥ 0), x² + 1 is always greater than 0 for any real number x. Therefore, the solution is all real numbers.
If A © B means A is greater than B; A £ B means A is either greater than or equal to B; A µ B means A is smaller than B; A ª B means A is either smaller than or equal to B; A ® B means A is equal to B. Now assuming the given statements to be true, which of the following conclusions is definitely true? Statements: M £ N, N ® O, O © P Conclusions: I. M £ O II. P µ N III. M © P
- A.Only I is true
- B.Only II is true
- C.Only III is trueCorrect
- D.Only I and III are true
Solution
Decoding: A © B means A > B A £ B means A >= B A µ B means A < B A ª B means A <= B A ® B means A = B Given: M >= N, N = O, O > P I. M £ O means M >= O. Since M >= N and N = O, then M >= O. This is true. II. P µ N means P < N. We have O > P and N = O, then N > P or P < N. So, II is true. III. M © P means M > P. We have M >= N = O > P. So, M > P. Thus, III is true. The question asks for which conclusion is *definitely* true. M >= O is true, but not strictly M > O. P < N is true, but M > P is also true. Since M > P, M >= O and P < N are also true. Since M > P, it implies that M is greater than P, so only III is true.
Solve the linear inequality for x: 2x - 7 < 133.
- A.x < 70Correct
- B.x ≥ 70
- C.x < 72
- D.x > 70
- E.x ≤ 70
Solution
2x - 7 < 133 => 2x < 133 + 7 = 140 => x < 140 / 2 = 70.
Solve the linear inequality for x: 2x - 5 < 31.
- A.x ≥ 18
- B.x ≤ 18
- C.x < 18Correct
- D.x < 20
- E.x > 18
Solution
2x - 5 < 31 => 2x < 31 + 5 = 36 => x < 36 / 2 = 18.
Inequality — Frequently Asked Questions
What is the key rule for combining inequalities?
A definite relation between two elements needs an unbroken chain of same-direction inequalities between them. If the chain changes direction (A > B < C), the relation between A and C cannot be determined.
How do coded inequalities differ?
Only in translation — first rewrite the coded symbols as standard ones, then solve normally. Writing the decoded chain down eliminates the memory errors the coding is designed to cause.
How many Inequality practice questions does Parikshala have for IBPS PO?
44 exam-pattern Inequality questions for IBPS PO Reasoning Ability, each with a step-by-step solution. Practice is free — no sign-up needed to start.