Without further ado, lets dive into the basic concepts behind solving question in **Coded** **Inequalities**. As you are aware that this is a pretty common topic in most competitive exams we’ll see some of the most frequently asked coded inequality questions in banking and other government exams.

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Topics Covered

**Basic Coded Inequality Concepts**

- Questions consist of a couple of statements with some logical and arithmetic relationship (in terms of <, >, ≤, ≥, = & ≠) between them.
- This is followed by a couple of conclusions and aspirants need to find out which of the given conclusions follow from the given statements.

**Symbols used and their implications in Coded Inequality**

**u < v**means**u is lesser than v****u ≤ v**means**u is less than or equal to v****u = v**means**u is equal to v****u ≥ v**means**u is greater than or equal to v****u > v**means**u is greater than v****u ≠ v**means**u isn’t equal to v**

**Properties of Inequalities**

Property |
≥ |
≤ |

Addition |
If a ≥ b, then a + c ≥ b + c | If a ≤ b, then a + c ≤ b + c |

Subtraction |
If a ≥ b, then a – c ≥ b – c | If a ≤ b, then a – c ≤ b – c |

Multiplication |
If a ≥ b, then ac ≥ bc, where c>0 | If a ≤ b, then ac ≤ bc, where c>0 |

Division |
If a ≥ b, then a/c ≥ b/c, where c>0 | If a ≤ b, then a/c ≤ b/c, where c>0 |

Transitivity |
If a ≥ b and b ≥ c then, a ≥ c | If a ≤ b and b ≤ c then, a ≤ c |

Inverse Additive |
If a ≥ b, then -a ≤ -b, if a>0, b>0 | If a ≤ b, then -a ≥ -b, if a>0, b>0 |

Multiplicative |
If a ≥ b, then 1/a ≤ 1/b, if a>0, b>0 | If a ≤ b, then 1/a ≥ 1/b, if a>0, b>0 |

**Points to Remember**

- Only those conclusions will be true which are obviously true as per the given statements
- Use the common terms while combining statements
- Combining statements will help you in answering the questions quickly and easily

**Solved Coded Inequality Questions**

**Instructions**: Assume that the given statements are true. Find which of the conclusion is/are definitely true. Given answer based on the following options:

- If only conclusion I is true.
- Only conclusion II is true.
- If either I or II is true.
- Neither I nor II is true.

**In the following questions, the symbols %, ∆, #, &, ¢ are used. All the symbols define the following meanings.**

A % B means that ‘A is smaller than B’

A ∆ B means that ‘A is less than or equal to B’

A # B means that ‘A is equal to B’

A & B means that ‘A is greater than B’

A ¢ B means that ‘A is either greater than or equal to B’

**1. Statements: A % B, C ¢ D, B # D.**

**Conclusions: **

**I) B % C**

**II) B # C**

**Solution:**

**Step 1** – Draw a table with conventional signs for smaller and greater than signs used in the instructions as shown below –

Symbols % ∆ # & ¢

Meaning < ≤ = > ≥

**Step 2** – Start with the statements and decode them accordingly.

Once you replace the signs you’ll deduce that A < B, C ≥ D and B = D

**Step 3** – In the conclusion I, we can conclude that B < C, because the improved statement created help us establish that C ≤ B (as B=D and C ≤ D).

**Step 4** – We have B= C in the second conclusion, and since B = D and C ≥ D, we can conclude that it can be either C > B or C = B.

So the correct answer is C.

**2. Statement: A % B, B # C, C ¢ D**

**Conclusion: **

**I) A & D
II) B ∆ D**

Try it Yourself.

**Correct Answer – D**

**3. Answer the following questions based on the information given below:**

If ‘>’ is denoted as ‘#’

‘≥’ is denoted as ‘&’

‘=’ is denoted as ‘$’

‘≤’ is denoted as ‘%’

And ‘<’ is denoted as ‘@’

**Statements: **L % M @ N $ O # P; Q & R @ P $ S; A @ L % B

**Conclusions:**

**I. N # A**

**II. S $ B**

**III. R @ O**

- Only conclusion I is true.
- Only conclusion II is true
- Both conclusion I and III are true
- Both conclusion II and III are true.
- All the conclusions I, II and III are true.

**Solution:**

**Step 1** – Decode the signs of the statements to get

L ≤ M < N = O > P;

Q ≥ R < P = S;

A < L ≤ B

**Step 2** – Combine the equations to get

N > M ≥ L > A

R < P < O

B ≥ L ≤ M < N = O > P = S

**Step 3** – Cross Check with the Conclusions:

- N # A means N > A: True (As N > M ≥ L > A so N > A)
- S $ B means S = B: False (As B ≥ L ≤ M < N = O > P = S)
- R @ O means R < O: True (As R < P < O, so, R < O)

Hence **option C is the answer**.

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**Practice Questions for Coded Inequality**

**Direction (1-4): Study the following information to answer the given questions**

P$Q means P is not smaller than Q means P is neither smaller than nor equal to Q

P#Q means P is neither greater than nor equal to Q

P&Q means P is neither greater than nor smaller than Q

P*Q means P is not greater than Q

Choose correct option for each question –

A. None is true

B. Only I is true

C. Only II is true

D. Only III is true

E. Only IV is true

**1. Statements: A $ M, P @ L, K # P, A $ L**

**Conclusions:**

**I. K # L**

**II. A @ P**

**III.L*A**

**IV.M # P**

Answer – **D**

**2. Statements: W*N, K * V, Y @ V, W @ K**

**Conclusions:**

**I. Y @ K**

**II. W $ N**

**III.W @ Y**

**IV.W @ V**

Answer – **B**

**3. Statements: T * Y, S # M, Y $ S, M @ K**

**Conclusions:**

**I. K # S**

**II. Y @ M**

**III.T # M**

**IV.Y @ K**

Answer – **A**

**4. Statements: C # P, P * L, L @ E, E $ M**

**Conclusions:**

**I. M # P**

**II. M @ L**

**III.P # E**

**IV.L # C**

Answer – **A**

**Consider the following questions**

A α B means A is greater than B

A β B means A is either greater than or equal to B

A γ B means A is equal to B

A δ B means A is small than B.

A η B means A is either smaller than or equal to B

Now on the basis of the statement given below be true, find which of the following conclusion holds to be true?

**Statement: **E γ F, C δ D, F β G, D α E

**Conclusion 1: **E α G

**Conclusion 2: **C γ E

- If only conclusion 1 holds
- If only conclusion 2 holds
- If either 1 or 2 is true
- If neither 1 nor 2 is true
- If both 1 and 2 are true.

Correct Answer – 4

**In the following questions, the symbols @, CC, $, %, and # are used to illustrate the following meanings:**

P $ Q means that ‘P is not smaller than Q’

P # Q means ‘P is not greater than Q’

P @ Q means that ‘P is neither smaller than nor equal to Q’

P CC Q means that ‘P is neither greater than nor equal to Q’

P % Q means ‘P is neither greater than nor smaller than Q’

Now in each of the following questions, assuming the given statements to be true, find which of the three conclusions, I, II, III given below is/are definitely true.

**1. Statement: H % J, J CC N, N @ R**

**Conclusion: 1. R % J 2. H @ J**

A. Only I is true. B. Only III is true

C. Only II and III are true D. Only I and III are true

The correct answer is B.

**2. Statements: M @ j, J $ T, T CC N**

**Conclusions: 1. N # J 2. T CC N**

A. Only I and III are true B. Only II is true

C. Only II and III are true D. All I, II, and III are true

The correct answer is B.

**3. Statements: X $ Y, Y @ Z, W % Y**

**Conclusion: 1. X $ W 2. Z # W**

A. Only II is true B. Only I is true

C. Only III is true D. All I, II, and III are true

The correct answer is D.

Given the complexity of the topic, you might take some time initially but as you practice more and more of inequality sum, you’ll be in a better situation solving these questions during the actual exams. **Solve Free Mock Tests** and practice exam like question right before your exams.

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