DeduceEXAM-GRADE DAILY REASONING

Inequality reasoning questions with answers

These inequality reasoning questions give you a coded chain and ask which conclusions definitely follow. The whole family is mechanical: decode the symbols, read the chain, and accept a conclusion only where every link points the same way. Each walkthrough writes the decoded chain out in full, because the marks are lost in the translation far more often than in the logic.

Download the PDF — 15 questions with answers

Free, ungated, no email. This is the inequality reasoning questions with answers PDF — the same 15 questions as below, with every worked solution at the back, ready to print.

How to use this set

The 15 questions below are ordered the way an exam block is rather than easiest-first: two gentle openers, then a run of medium, and a hard one every sixth question — 2 of the 15 sit in the hard band. Every question is a coded inequality.

Work each question on paper before you open its solution. The walkthrough is the method itself, step for step, so reading it first turns a practice set into a reading exercise and teaches nothing. If you are stuck on the method rather than on one question, the method guide is a better place to start than the next question: Inequality: when a chain proves nothing.

15 inequality reasoning questions with answers

Every question below was generated by the same engine that mints the Deduce daily puzzle round, and machine-checked before it reached this page — a multiple-choice question validates its own answer against its own options at generation, and ships only with a walkthrough attached. The walkthrough is the engine's own.

Question 1

Which of the following conclusions is DEFINITELY true from the given expression?

Code: * = >, $ = >=, # = <, @ = <=, % = =

Expression: F * D, D * C

  1. D > F
  2. F = D
  3. D <= C
  4. C > D
  5. F > C
Show the worked solution
  1. First decode each symbol: * means >, $ means >=, # means <, @ means <=, % means =.
  2. So the expression reads: F > D, D > C.
  3. Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
  4. From the closure, F > C is the only option that must hold — the others are either false or can't be concluded.

Question 2

Which of the following conclusions is DEFINITELY true from the given expression?

Code: $ = >, % = >=, * = <, # = <=, @ = =

Expression: C $ E, E $ A

  1. E = C
  2. E >= C
  3. E = A
  4. C > A
  5. A > E
Show the worked solution
  1. First decode each symbol: $ means >, % means >=, * means <, # means <=, @ means =.
  2. So the expression reads: C > E, E > A.
  3. Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
  4. From the closure, C > A is the only option that must hold — the others are either false or can't be concluded.

Question 3

Which of the following conclusions is DEFINITELY true from the given expression?

Code: * = >, % = >=, @ = <, $ = <=, # = =

Expression: E * F, F * B, B * D

  1. F >= E
  2. D = B
  3. F > E
  4. E > D
  5. E = B
Show the worked solution
  1. First decode each symbol: * means >, % means >=, @ means <, $ means <=, # means =.
  2. So the expression reads: E > F, F > B, B > D.
  3. Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
  4. From the closure, E > D is the only option that must hold — the others are either false or can't be concluded.

Question 4

Which of the following conclusions is DEFINITELY true from the given expression?

Code: $ = >, @ = >=, % = <, * = <=, # = =

Expression: E @ C, C # B, B @ F, E $ B

  1. C >= E
  2. B < F
  3. B >= E
  4. E > F
  5. B > F
Show the worked solution
  1. First decode each symbol: $ means >, @ means >=, % means <, * means <=, # means =.
  2. So the expression reads: E >= C, C = B, B >= F, E > B.
  3. Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
  4. From the closure, E > F is the only option that must hold — the others are either false or can't be concluded.

Question 5

Which of the following conclusions is DEFINITELY true from the given expression?

Code: % = >, # = >=, $ = <, * = <=, @ = =

Expression: B % D, D % F, F % A

  1. F >= D
  2. B > F
  3. F = B
  4. F > D
  5. B <= D
Show the worked solution
  1. First decode each symbol: % means >, # means >=, $ means <, * means <=, @ means =.
  2. So the expression reads: B > D, D > F, F > A.
  3. Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
  4. From the closure, B > F is the only option that must hold — the others are either false or can't be concluded.

Question 6

Which of the following conclusions is DEFINITELY true from the given expression?

Code: @ = >, $ = >=, # = <, * = <=, % = =

Expression: A % E, E $ D, D $ C, C $ F, A @ D

  1. E > D
  2. A < F
  3. A < D
  4. D = E
  5. D = F
Show the worked solution
  1. First decode each symbol: @ means >, $ means >=, # means <, * means <=, % means =.
  2. So the expression reads: A = E, E >= D, D >= C, C >= F, A > D.
  3. Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
  4. From the closure, E > D is the only option that must hold — the others are either false or can't be concluded.

Question 7

Which of the following conclusions is DEFINITELY true from the given expression?

Code: @ = >, % = >=, $ = <, * = <=, # = =

Expression: E % B, B % A

  1. A < B
  2. B < E
  3. E > A
  4. B = A
  5. E >= A
Show the worked solution
  1. First decode each symbol: @ means >, % means >=, $ means <, * means <=, # means =.
  2. So the expression reads: E >= B, B >= A.
  3. Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
  4. From the closure, E >= A is the only option that must hold — the others are either false or can't be concluded.

Question 8

Which of the following conclusions is DEFINITELY true from the given expression?

Code: * = >, % = >=, @ = <, $ = <=, # = =

Expression: A * B, B * E

  1. A <= B
  2. B <= E
  3. A > E
  4. A = B
  5. B < E
Show the worked solution
  1. First decode each symbol: * means >, % means >=, @ means <, $ means <=, # means =.
  2. So the expression reads: A > B, B > E.
  3. Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
  4. From the closure, A > E is the only option that must hold — the others are either false or can't be concluded.

Question 9

Which of the following conclusions is DEFINITELY true from the given expression?

Code: % = >, $ = >=, * = <, # = <=, @ = =

Expression: F % A, A % E, E % D

  1. D = A
  2. E <= D
  3. E > A
  4. F <= A
  5. F > E
Show the worked solution
  1. First decode each symbol: % means >, $ means >=, * means <, # means <=, @ means =.
  2. So the expression reads: F > A, A > E, E > D.
  3. Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
  4. From the closure, F > E is the only option that must hold — the others are either false or can't be concluded.

Question 10

Which of the following conclusions is DEFINITELY true from the given expression?

Code: * = >, # = >=, @ = <, $ = <=, % = =

Expression: C * D, D * B, B * F

  1. C < B
  2. F >= D
  3. B < F
  4. B = F
  5. C > F
Show the worked solution
  1. First decode each symbol: * means >, # means >=, @ means <, $ means <=, % means =.
  2. So the expression reads: C > D, D > B, B > F.
  3. Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
  4. From the closure, C > F is the only option that must hold — the others are either false or can't be concluded.

Question 11

Which of the following conclusions is DEFINITELY true from the given expression?

Code: # = >, % = >=, * = <, $ = <=, @ = =

Expression: E # A, A # C, C # D

  1. C > A
  2. A = D
  3. A > D
  4. E <= A
  5. C < D
Show the worked solution
  1. First decode each symbol: # means >, % means >=, * means <, $ means <=, @ means =.
  2. So the expression reads: E > A, A > C, C > D.
  3. Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
  4. From the closure, A > D is the only option that must hold — the others are either false or can't be concluded.

Question 12

Which of the following conclusions is DEFINITELY true from the given expression?

Code: @ = >, $ = >=, * = <, % = <=, # = =

Expression: C @ F, F @ D, D @ E, E @ A

  1. C < A
  2. E = C
  3. C > D
  4. F = C
  5. F < D
Show the worked solution
  1. First decode each symbol: @ means >, $ means >=, * means <, % means <=, # means =.
  2. So the expression reads: C > F, F > D, D > E, E > A.
  3. Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
  4. From the closure, C > D is the only option that must hold — the others are either false or can't be concluded.

Question 13

Which of the following conclusions is DEFINITELY true from the given expression?

Code: # = >, $ = >=, % = <, @ = <=, * = =

Expression: B # E, E # F

  1. E = B
  2. F = E
  3. F > E
  4. B > F
  5. E <= F
Show the worked solution
  1. First decode each symbol: # means >, $ means >=, % means <, @ means <=, * means =.
  2. So the expression reads: B > E, E > F.
  3. Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
  4. From the closure, B > F is the only option that must hold — the others are either false or can't be concluded.

Question 14

Which of the following conclusions is DEFINITELY true from the given expression?

Code: @ = >, # = >=, * = <, % = <=, $ = =

Expression: B @ E, E @ A

  1. E <= A
  2. B > A
  3. B <= E
  4. E = A
  5. A > E
Show the worked solution
  1. First decode each symbol: @ means >, # means >=, * means <, % means <=, $ means =.
  2. So the expression reads: B > E, E > A.
  3. Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
  4. From the closure, B > A is the only option that must hold — the others are either false or can't be concluded.

Question 15

Which of the following conclusions is DEFINITELY true from the given expression?

Code: * = >, # = >=, $ = <, @ = <=, % = =

Expression: E # F, F % A, A # C, F * C

  1. F >= E
  2. A > C
  3. A = E
  4. F <= C
  5. F > E
Show the worked solution
  1. First decode each symbol: * means >, # means >=, $ means <, @ means <=, % means =.
  2. So the expression reads: E >= F, F = A, A >= C, F > C.
  3. Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
  4. From the closure, A > C is the only option that must hold — the others are either false or can't be concluded.
Play today's puzzle free — no sign-up →

Where these questions come from

Most free practice for this topic is a scanned upload or a blog quiz, and neither can tell you a question has exactly one answer. That is the one thing this set can promise: it is minted, not typed. The engine behind it serves Deduce's daily puzzle round, so the questions here are the same shape as the ones a live round would give you — and there is an unlimited supply of them, which is why this page can be regenerated rather than padded.

If you want the method rather than more questions, Inequality: when a chain proves nothing covers the approach, the traps and a worked table. This page and that one deliberately answer different questions: that one is how do I solve these, this one is give me inequality reasoning questions with the answers.

FAQ

When does a chain fail to prove a relation?

When the links change direction. From A > B and C > B nothing follows about A versus C, because B is the smaller element in both and the two larger ones are never compared. A chain proves a relation only when every link points the same way from one end to the other.

What is an 'either-or' conclusion?

When two conclusions about the same pair are individually uncertain but together cover every case — typically A ≥ B and A < B — the pair follows as an either-or. It is worth recognising on sight, because candidates who mark both as 'does not follow' lose a mark that was free.

Are coded and plain inequality questions solved differently?

No. A coded question adds one translation step at the start; after the symbols are rewritten as ordinary signs the reasoning is identical. Write the decoded chain on paper rather than holding it in your head — that is where coded sets actually go wrong.

More question banks

Play today's puzzle free — no sign-up →

Deduce is not affiliated with IBPS, SBI, SSC or RBI.