# Coded Inequalities Solved Questions for Government Exams

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A bank or any government job exam for that matter is not easy to crack particularly because of a large number of aspirants desperately vying for a government job to enjoy job security. This makes the competition extremely intense. To improve your chances to get a government job, you should have a strong grip over all the subjects that are a part of the syllabus for these exams.

A component that is common to all the government job exams is logical reasoning because every government job exam generally tests these four subjects – Quantitative Aptitude, Logical Reasoning, General Awareness and Verbal Ability or English Language.

## Logical Reasoning for Competitive Exams

Are you a bank or other government job aspirant who is slogging hard day and night to land a secured job in a government organization? Do you fear logical reasoning or are you the one who enjoys solving questions on logical reasoning especially puzzles? It doesn’t really matter whether you are the latter or the former because even if you are not the latter, you can easily become the latter with a little sincerity, hard work and dedication. Believe us, logical reasoning is an extremely interesting portion that a candidate can easily ace. All you require is a little hard work.

Let us leave all the worries concerning the exam aside and enjoy the process of solving the questions on logical reasoning. Let us explore the fun involved in solving logical reasoning questions.

We will take the topic “Coded Inequalities” and break down the entire topic in a manner that will make you wonder, what made you fear logical reasoning despite the fact that it is a very interesting topic.

## What are Coded Inequalities?

Breaking Down Coded Inequalities for your better understanding

Let us understand the concept of Coded Inequalities. What are coded inequalities?

We all have heard about or come across various forms of inequalities like social, economic and gender inequalities a number of times in our life but today we will not talk about these inequalities. Today we will talk about inequalities in the context of mathematical operations.

Coded Inequalities is a very common topic asked in almost every government job exam especially Bank exams, SSC, IBPS PO, IBPS clerk and more. Questions from this topic are asked frequently for various government job exams, which makes this chapter very important. So if you are thinking of skipping this chapter then we would like to caution you against doing it.

What do you mean by coded inequalities? Let us explain it to you in the simplest form.

Coded Inequalities may seem to be a little overwhelming and quite complex to you but believe us, all you need to solve the questions on coded inequalities is the knowledge of basic mathematical operations. So just be clear about the basic concepts of mathematical operations. You just need to be clear about the basic concepts like addition, subtraction, multiplication, division, lesser than, and greater than values. That’s all that you need for this topic.

The best way to ensure good marks in coded inequalities is to practice enough questions on this topic. After all we all have heard the famous saying “Practice makes a man perfect”

The only catch in coded inequalities is that the symbols like +, -, x, ÷, >, <, generally used in mathematical operations are represented by symbols different from them, which makes the topic a little complex. All you need to do is substitute the symbol that the given symbol in the question represents and then perform the mathematical operation. If you make a mistake in understanding what the symbols given in the question actually represent, then you will end up losing marks. This is why we would suggest that you practice a lot.

## What is BODMAS?

How many of you remember the term ‘BODMAS’? All of us have come across this term but most of us may not remember what it stands for. If you do not remember, then let us remind you what does BODMAS stand for

Source of the image – Google

The BODMAS rule is something that you will require to solve the questions on coding inequalities. The BODMAS rule is all about performing the mathematical operation as per the order prescribed by the BODMAS rule. To solve a question, you will have to first perform division, then multiplication, then addition and finally subtraction.

Following are the types of sub-topics on which you can expect questions for coded inequalities

–          Word Problems

–          Inequalities

## Coded Inequalities Solved Practice Questions

Here are some practice questions on Coded Inequalities

Directions (1–5): In each of the questions, relationships between some elements are shown in the statements(s). These statements are followed by conclusions numbered I and II. Read the statements and give the answer.

(a) If only conclusion I follows.

(b) If only conclusion II follows.

(c) If either conclusion I or II follows.

(d) If neither conclusion I nor II follows.

(e) If both conclusions I and II follow.

1. Statements: D ≤ F > Y, G > F, K < F

Conclusions:

I. K > Y

II. G > Y

Ans: 2

K < F > Y                 No relationship can be established between K and Y. Hence conclusion I is not true.

G > F > Y                 G > Y. Hence conclusion II is true.

2. Statements: X > N > K > F > P < I ≤ U

Conclusions:

I. X > U

II. I ≥ N

Ans: 4

X > N > K > F > P < I ≤ U                 No relationship can be established between X and U. Hence conclusion I is not true.

X > N > K > F > P < I ≤ U                 No relationship can be established between I and N. Hence conclusion II is not true.

3. Statements: Q < Z < T > S, E <T

Conclusions:

I. T > Q

II. E > Q

Ans: 1

Q < Z < T > S           T > Q. Hence conclusion I is true.

Q < Z < T > E           No relationship can be established between E and Q. Hence conclusion II is not true.

4. Statements: I ≥ K> S > F < M, Y < M, F > Y

Conclusions:

I. I > F

II. K > Y

Ans: 5

I ≥ K > S > F             I > F. Hence conclusion I is true.

I ≥ K> S > F > Y                   K > Y. Hence conclusion II is true.

5. Statements: A < B < C ≥ I > D, C > E

Conclusions:

I. B < D

II. C> A

Ans: 2

A < B < C ≥ I > D                 No relationship can be established between B and D. Hence conclusion I is not true.

A < B < C ≥ I > D                 C > A. Hence conclusion II is true.

Directions (6-8): In the following questions, the symbols @, #, %, \$ and © are used with the following meaning as illustrated below-

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

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

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

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

‘P @ Q’ means ‘P is not greater than Q’

Now in each of the following questions assuming the given statement to be true, find which of the conclusions given below them is/are definitely true and give your answer accordingly.

1) If only conclusion I is true

2) If only conclusion II is true

3) Either conclusion I or II is true

4) Neither conclusion I nor II is true

5) Both conclusion I and II are true

6. Statements: B # W © C, W % Y

Conclusions:

II. B # Y

Ans: 5

Decoded Statement: B < W > C, W = Y

Decoded conclusion: I. Y > C            II. B < Y

Combined Inequalities: B < W = Y > C

B < W = Y > C         Y > C. Hence conclusion I is true.

B < W = Y > C         B < Y. Hence conclusion II is true.

7. Statements: U \$ F, F % B, A © B

Conclusions:

II. B @ U

Ans: 5

Decoded Statement: U ≥ F, F = B, A > B

Decoded conclusion: I. A > F             II. B ≤ U

Combined Inequalities: U ≥ F = B < A

U ≥ F = B < A           A > F. Hence conclusion I is true.

U ≥ F = B < A           B ≤ U. Hence conclusion II is true.

8. Statements: D \$ Y, Y © J, J @ Z, Q © J

Conclusions:

II. J # D

Ans: 2

Decoded Statement: D ≥ Y, Y > J, J ≤ Z, Q > J

Decoded conclusion: I. D > Q            II. J < D

Combined Inequalities: D ≥ Y > J ≤ Z, Q > J

D ≥ Y > J < Q           No relationship can be established between D and Q. Hence conclusion I is not true.

D ≥ Y > J < Q           D > J. Hence conclusion II is true.

9. If the expressions, ‘M > K ≤ N < J,’L ≥ N’ and ‘N ≥ O’ are true then which of the following combinations will be definitely true?

(a) K ≥ O

(b) M < O

(c) L = O

(d) K ≤ L

(e) None of these

ANS: 4

K ≤ N ≥ O    No relationship can be established between K and O. Hence option 1 is incorrect.

M > K ≥ O    M > O. Hence option 2 is incorrect.

L ≥ N ≥ O     L ≥ O. Hence option 3 is incorrect.

K ≤ N ≤ L     K ≤ L. Hence option 4 is correct.

10. Which of the following symbols should replace the sign (#) and (&) respectively in the given expression in order to make the expression T < U and R ≥ S definitely true?

Q < T ≤ V = W < S # U ≤ P & R

(a) ≥, =

(b) ≥, ≤

(c) >, ≤

(d) =, ≤

(e) ≥, <

ANS: 4

Q < T ≤ V = W < S ≥ U ≤ P = R T < U and R ≥ S both are false.

Q < T ≤ V = W < S ≥ U ≤ P ≤ R T < U and R ≥ S both are false.

Q < T ≤ V = W < S > U ≤ P ≤ R T < U and R ≥ S both are false.

Q < T ≤ V = W < S = U ≤ P ≤ R T < U and R ≥ S both are true.

Q < T ≤ V = W < S ≥ U ≤ P < R         T < U and R ≥ S both are false.

Now there is an interesting challenge for you. Are You Ready For It? If yes, then go ahead and solve the following questions and test your proficiency in coded inequalities –

Directions (1-5): In the following questions, the symbols @, #, %, \$ and * are used with the following meaning as illustrated below.

‘A @ B’ means ‘A is not smaller than B’

‘A # B’ means ‘A is neither smaller than nor equal to B’

‘A % B’ means ‘A is neither smaller than nor greater than B’

‘A \$ B’ means ‘A is not greater than B’

‘A * B’ means ‘A is neither greater than nor equal to B’

1. Statements: N % O, O \$ P, P * Q, L \$ Q

Conclusion:  I. N % P   II. P # N            III. O @ L

1) Either conclusion I or II is true

2) Only conclusion II and III are true

3) Only conclusion III is true

4) Only conclusion I is true

5) None of these

2. Statements:  D % E, F * G, B # D, E @ F

Conclusion:  I. B # F     II. E @ B          III. G \$ E

1) Only conclusion I and II are true

2) Only conclusion II and III are true

3) Only conclusion III is true

4) Only conclusion I is true

5) None of these

3. Statements:  E @ F, C # D, D % E, B # C

Conclusion:  I. D # F     II. D % F           III.B # F

1) Only conclusion II is true

2) Only conclusion II and III are true

3) Only conclusion I is true

4) Either conclusion I or II and III are true

5) None is true

4. Statements:  Y @ Z, W \$ Y, V * W, X * Y

Conclusion:  I. V \$ Y     II. Y % W          III. X # W

1) Only conclusion II is true

2) Only conclusion II and III are true

3) Only conclusion I is true

4) Either conclusion I or II and III are true

5) None is true

5. Statements:  N % O, O \$ P, P @ Q, M * N

Conclusion:  I. N @ Q  II. P # M            III. Q # N

1) Only conclusion II is true

2) Only conclusion II and III are true

3) Only conclusion I is true

4) Either conclusion I or III and II are true

5) None is true

We hope that we have succeeded in removing your fear of coding inequalities and now that you know that solving questions on coded inequalities is not as difficult as you thought, just solve a good number of questions on coded inequalities and be prepared to take any competitive exam that comes your way

For more practice, you can refer to our mock tests

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