Tips to Master Inequalities Concept with Practice Questions

With the SBI PO and RBI Assistant exams notifications aspirants must have started preparing for these. We advise the candidates to not wait for the last day of the online registrations and rather apply beforehand in order to avoid any last minute hassles. As far as RBI Assistant’s notification is concerned it is released featuring 450 vacancies and the last date for online application is 4th Oct 2023. As far as reasoning section is concerned, many people often find it difficult and time consuming. Thus, practice is the only key to crack the reasoning section and with this one must learn the technique of time management. Most of the reasoning ability section asks for a great speed and accuracy which is why practice is the key to success. In this article we are discussing about one yet another important concept which is tips to master inequalities concept with practice questions.

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Tips to Master Inequalities Concept with Practice Questions

Introduction to Inequalities

All major Banking and Government exams conducted in our country have questions based on reasoning inequality. At least 3-4 questions of 1 mark each, are asked and it is an easy to score topic from the reasoning ability section.

Basic concepts of reasoning Inequality:

In reasoning inequality, a group of elements are given, with a certain coded relationship denoted by <, >, = ≤ or ≥. Such type of questions falls under the category of reasoning Inequality.

The symbol used and their meaning are explained below.

1. P > Q means P is greater than Q.
2. P < Q means P is less than Q.
3. P = Q means P is equal to Q.
4. P ≥ Q means P is greater than or equal to Q.
5. P ≤ Q means P is less than or equal to Q.

In order to solve questions, understanding the order or the rank of these symbols is very important.

1. If A > B ≥ Cis given, then A > Cis true and not A ≥ C as, here the greater than sign is of higher order.
2. If A ≥ Bis given, then eitherA > B or A = B is true.
3. If A < B < Cis given, then A < C is true.
4. If A < B > C is given, then the relation between A and C cannot be determined.

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Types of Questions Asked in Inequalities

To solve the questions based on inequality, the relation between the given elements is to be determined.

The three patterns in which the Inequality questions in reasoning are asked is as follows:

1. Basic/Normal inequality:In these types of questions, the elements are given and the relationship between them is marked with the help of the signs (<, >, =, ≥ and ≤). These types of questions are frequently asked in the preliminary exam of all major government exams.

For example: P < Q ≤ R ≥ S

2. Coded Inequality:This is a new format of inequality questions. Here instead of direct symbols, each sign is coded using a symbol, a number or an alphabet.

For example, ‘A#B where ‘#’ means A is greater than or equal to B’. Here, the ‘≥’ sign has been denoted with the ‘#’ sign.

This pattern is being followed in particularly the mains exam of all major government exams to make the questions complex and confusing. The coded inequality questions take a bit more time than the direct inequality questions, as the codes are first to be replaced with the respective symbols. Thus, the code based inequality questions require continuous practice to improve speed.

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3. Missing symbol inequality:In these types of a question a statement is given with symbols missing. A relation, which needs to be satisfied, is given in the question and set of symbols which are to be placed in the blanks is given in option.

These questions can both be basic or coded.

For example:

Statements: A > B _ C _ D ≥ E

Which symbol are to be placed in the blanks so that A > C and C ≥ E?

(a) >, =

(b) <, =

(c) <, >

(d) <, =

(e) None of the above

Ans: a

Solution:

Here, when the symbols in option (a) are placed then, A > B > C = D ≥ E

Hence, option a.

Concept of complementary pairs:

‘Either’ and ‘or’ – This takes place only in complementary pairs. If the relationship between two elements with common elements is not established, then the element cannot be combined.

The example below can help illustrate the concept properly.

Example I:

Statement: X > Y > B, A > Z > X

On combining the given statements, we have, A > Z > X > Y > B

So, we can conclude that A > B.

Example II:

Statement: X > Y > B, L < X

On combining the given statements, we have L < X > Y > B.

Here the relation between L and Y cannot be determined. So, if in conclusion it is given that ‘L > Y’ and ‘L ≤ Y’, then they form complementary pair. Thus, either ‘L > Y’ or ‘L ≤ Y’.

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Question 1: In the following question the relationship between different elements are given in the statements followed by three conclusions I, II, and III. Read the statements carefully and mark your answer accordingly.

Statements: Q ≤ S, S ≥ P, P > M, M ≤ L, L = O, O < R

Conclusions:

1. M < R
2. S ≥ L

III. L > Q

1. A) Only Conclusion I and II are true
2. B) Only Conclusion III is true
3. C) Only Conclusion II is true
4. D) Only Conclusion I is true
5. E) Only Conclusion IIand II are true

Question 2: In the following question the relationship between different elements are given in the statements followed by three conclusions I, II, and III. Read the statements carefully and mark your answer accordingly.

Statements: M ≥ N, N > V, V > Z, Y = Z, Z ≤ L, L < O

Conclusions:

1. M > Z
2. Y < O

III. V > L

1. A) Only Conclusion I and III are true
2. B) Only Conclusion II is true
3. C) Only Conclusion I and II are true
4. D) Only Conclusion II and III are true
5. E) Only Conclusion I is true

Question 3: In the following question the relationship between different elements are given in the statements followed by three conclusions I, II, and III. Read the statements carefully and mark your answer accordingly.

Statements: T ≤ K, K > P, P ≥ M, M < N, N ≥ S, S > R

Conclusions:

1. P > R
2. K > R

III. R < N

1. M < T
2. A) Only Conclusion I and II are true
3. B) Only Conclusion III is true
4. C) Only Conclusion II is true
5. D) Only Conclusion IV is true
6. E) Only Conclusion I and III are true

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Question 4: In the following question the relationship between different elements are given in the statements followed by four conclusions I, II, III, and IV. Read the statements carefully and mark your answer accordingly.

Statements: Q > R, R = V, V ≥ Y, Y = K, K ≤ L, L < O

Conclusions:

1. Q > Y
2. R < K

III. R = Y

1. Y ≤ O
2. A) Only Conclusion I is true
3. B) Only Conclusion III is true
4. C) Only Conclusion II and III is true
5. D) Only Conclusion II is true
6. E) Only Conclusion IV is true

Question 5: In the question assuming the given statements to be true, find which of the conclusion(s) among given three conclusions is/are definitely follows and then give your answer accordingly.

Statements: R ≥ E ≥ D, D < A ≤ B = C, Q = P > R

Conclusions:

1. Q > D
2. D < C

III. R ≥ B

1. A) Only conclusion I is true
2. B) Only conclusion II is true
3. C) Only conclusion I and III is true
4. D) Only conclusion I and II is true
5. E) Only Conclusion III is true

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Question 6: In the question assuming the given statements to be true, find which of the conclusion(s) among given three conclusions is/are definitely follows and then give your answer accordingly.

Statements: V > Z < T, J < K < L, L = P > Q ≥ U = V

Conclusions:

1. L > Z
2. Q < J

III. Q > T

1. A) Only conclusion III is true
2. B) Only conclusion II is true
3. C) Only Conclusion I and III is true
4. D) Only conclusion I and II is true
5. E) Only Conclusion I is true

Question 7: In the question, assuming the given statements to be true, find which of the conclusion (s) among given two conclusions is /are definitely true and then give your answer accordingly.

Statements: Q > R ≥ S = T, T ≥ U = V > W < X

Conclusions:

1. X < S
2. R > V
3. A) Only Conclusion I is true
4. B) Only Conclusion II is true
5. C) Both Conclusions I and II are true
6. D) Either Conclusion I or II is true
7. E) Neither Conclusion I nor II is true

Question 8: In the question, assuming the given statements to be true, find which of the conclusion (s) among given two conclusions is /are definitely true and then give your answer accordingly.

Statements: A > C = D, D ≥ E = F, F > L = K

Conclusions:

1. L < A
2. C > K
3. A) Only Conclusion I is true
4. B) Only Conclusion II is true
5. C) Both Conclusions I and II are true
6. D) Either Conclusion I or II is true
7. E) Neither Conclusion I nor II is true

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Question 9: In the question, assuming the given statements to be true, find which of the conclusion (s) among given two conclusions is /are definitely true and then give your answer accordingly.

Statements: N ≥ P > D ≥ G < J ≤ B

Conclusions:

1. G < N
2. D < B
3. A) Only conclusion I is true
4. B) Only conclusion II is true
5. C) Either conclusion I or conclusion II is true
6. D) Neither conclusion I nor conclusion II is true
7. E) Both conclusions I and conclusion II are true

Question 10: In the question, assuming the given statements to be true, find which of the conclusion (s) among given two conclusions is /are definitely true and then give your answer accordingly.

Statements: A ≤ L = T < R ≤ H ≥ K

Conclusions:

1. H > A
2. R ≥ L
3. A) Only conclusion II is true
4. B) Only conclusion I is true
5. C) Either conclusion I or conclusion II is true
6. D) Neither conclusion I nor conclusion II is true
7. E) Both conclusions I and conclusion II are true

प्रश्न 1: निम्नलिखित प्रश्न में कुछ तत्वों के बीच के सम्बन्ध को कथन में दर्शाया गया है जिसके बाद तीन निष्कर्ष I, II और III हैं| कथन को ध्यान से पढ़ें और उसी अनुसार उत्तर दें|

कथन: Q ≤ S, S ≥ P, P > M, M ≤ L, L = O, O < R

निष्कर्ष:

1. M < R
2. S ≥ L

III. L > Q

1. A) केवलनिष्कर्षI और II सत्य है
2. B) केवलनिष्कर्षIII सत्य है
3. C) केवलनिष्कर्षII सत्य है
4. D) केवलनिष्कर्षI सत्य है
5. E) केवलनिष्कर्षII और III सत्य है

प्रश्न 2: निम्नलिखित प्रश्न में कुछ तत्वों के बीच के सम्बन्ध को कथन में दर्शाया गया है जिसके बाद तीन निष्कर्ष I, II और III हैं| कथन को ध्यान से पढ़ें और उसी अनुसार उत्तर दें|

कथन: M ≥ N, N > V, V > Z, Y = Z, Z ≤ L, L < O

निष्कर्ष:

1. M > Z
2. Y < O

III. V > L

1. A) केवलनिष्कर्षI और III सत्य है
2. B) केवलनिष्कर्षII सत्य है
3. C) केवलनिष्कर्षI और II सत्य है
4. D) केवलनिष्कर्षII और III सत्य है
5. E) केवलनिष्कर्षI सत्य है

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प्रश्न 3: निम्नलिखित प्रश्न में विभिन्न तत्वों के बीच के सम्बन्ध को कुछ कथन में दिया गया है जिसके बाद चार निष्कर्ष I, II, III, और IV दिए गए हैं| कथन को ध्यान से पढ़ें और उसी अनुसार अपना उत्तर दें|

कथन: T ≤ K, K > P, P ≥ M, M < N, N ≥ S, S > R

निष्कर्ष:

1. P > R
2. K > R

III. R < N

1. M < T
2. A) केवलनिष्कर्षI और II सत्य है
3. B) केवलनिष्कर्षIII सत्य है
4. C) केवलनिष्कर्षII सत्य है
5. D) केवलनिष्कर्षIV सत्य है
6. E) केवलनिष्कर्षI और III सत्य है

प्रश्न 4: निम्नलिखित प्रश्न में विभिन्न तत्वों के बीच के सम्बन्ध को कुछ कथन में दिया गया है जिसके बाद चार निष्कर्ष I, II, III, और IV दिए गए हैं| कथन को ध्यान से पढ़ें और उसी अनुसार अपना उत्तर दें|

कथन: Q > R, R = V, V ≥ Y, Y = K, K ≤ L, L < O

निष्कर्ष:

1. Q > Y
2. R < K

III. R = Y

1. Y ≤ O
2. A) केवलनिष्कर्षI सत्य है
3. B) केवलनिष्कर्षIII सत्य है
4. C) केवलनिष्कर्षII और III सत्य है
5. D) केवलनिष्कर्षII सत्य है
6. E) केवलनिष्कर्षIV सत्य है

प्रश्न 5: प्रश्न में दिए गए कथनों को सत्य मानते हुए, ज्ञात करें कि दिए गए तीन निष्कर्षों में से कौन-सा निष्कर्ष निश्चित रूप से अनुसरण करता है और फिर उसी के अनुसार अपना उत्तर दें।

कथन: R ≥ E ≥ D, D < A ≤ B = C, Q = P > R

निष्कर्ष:

1. Q > D
2. D < C

III. R ≥ B

1. A) केवलनिष्कर्षI सत्य है
2. B) केवलनिष्कर्षII सत्य है
3. C) केवलनिष्कर्षI और III सत्य है
4. D) केवलनिष्कर्षI और II सत्य है
5. E) केवलनिष्कर्षIII सत्य है

प्रश्न 6: प्रश्न में दिए गए कथनों को सत्य मानते हुए, ज्ञात करें कि दिए गए तीन निष्कर्षों में से कौन-सा निष्कर्ष निश्चित रूप से अनुसरण करता है और फिर उसी के अनुसार अपना उत्तर दें।

कथन: V > Z < T, J < K < L, L = P > Q ≥ U = V

निष्कर्ष:

1. L > Z
2. Q < J

III. Q > T

1. A) केवलनिष्कर्षIII सत्य है
2. B) केवलनिष्कर्षII सत्य है
3. C) केवलनिष्कर्षI और III सत्य है
4. D) केवलनिष्कर्षI और II सत्य है
5. E) केवलनिष्कर्षI सत्य है

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प्रश्न 7: निम्नलिखित प्रश्न में, दिए गए कथनों को सत्य मानकर, यह तय करें कि दिए गए दो निष्कर्षों में से कौन सा निष्कर्ष निश्चित रूप से सत्य है और उसी अनुसार अपना उत्तर दें|

कथन: Q > R ≥ S = T, T ≥ U = V > W < X

निष्कर्ष:

1. X < S
2. R > V
3. A) केवलनिष्कर्षI सत्य है
4. B) केवलनिष्कर्षII सत्य है
5. C) दोनोंनिष्कर्षI और II सत्य है
6. D) यानिष्कर्षI या II सत्य है
7. E) नाहीनिष्कर्ष I ना ही II सत्य है

प्रश्न 8: निम्नलिखित प्रश्न में, दिए गए कथनों को सत्य मानकर, यह तय करें कि दिए गए दो निष्कर्षों में से कौन सा निष्कर्ष निश्चित रूप से सत्य है और उसी अनुसार अपना उत्तर दें|

कथन: A > C = D, D ≥ E = F, F > L = K

निष्कर्ष:

1. L < A
2. C > K
3. A) केवलनिष्कर्षI सत्य है
4. B) केवलनिष्कर्षII सत्य है
5. C) दोनोंनिष्कर्षI और II सत्य है
6. D) यानिष्कर्षI या II सत्य है
7. E) नाहीनिष्कर्ष I ना ही II सत्य है

प्रश्न 9: प्रश्न में दिए गए कथनों को सत्य मानते हुए ज्ञात कीजिए कि दिए गए दो निष्कर्षों में से कौन सा/से निष्कर्ष निश्चित रूप से सत्य है/हैं और फिर उसी के अनुसार अपना उत्तर दें।

कथन: N ≥ P > D ≥ G < J ≤ B

निष्कर्ष:

1. G < N
2. D < B
3. A) केवलनिष्कर्षI सत्य है
4. B) केवलनिष्कर्षII सत्य है
5. C) यानिष्कर्षI या निष्कर्ष II सत्य है
6. D) नाहीनिष्कर्ष I ना ही निष्कर्ष II सत्य है
7. E) दोनोंनिष्कर्षI और निष्कर्ष II सत्य है

प्रश्न 10: प्रश्न में दिए गए कथनों को सत्य मानते हुए ज्ञात कीजिए कि दिए गए दो निष्कर्षों में से कौन सा/से निष्कर्ष निश्चित रूप से सत्य है/हैं और फिर उसी के अनुसार अपना उत्तर दें।

कथन: A ≤ L = T < R ≤ H ≥ K

निष्कर्ष:

1. H > A
2. R ≥ L
3. A) केवलनिष्कर्षII सत्य है
4. B) केवलनिष्कर्षI सत्य है
5. C) यातोनिष्कर्ष I या निष्कर्ष II सत्य है
6. D) नाहीनिष्कर्ष I ना ही निष्कर्ष II सत्य है
7. E) दोनोंनिष्कर्षI और निष्कर्ष II सत्य है

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Answer Keys and Solutions:

Solution 1: D)

Given statements: Q ≤ S, S ≥ P, P > M, M ≤ L, L = O, O < R

On combining the given statements, we get:

Q ≤ S ≥ P > M ≤ L = O < R

Conclusions:

1. M < R: True (As M ≤ L = O < R, so M < R).
2. S ≥ L: False (As S ≥ P > M ≤ L, so the relationship between S and L can’t be determined).

III. L > Q: False (As Q ≤ S ≥ P > M ≤ L, so the relationship between Q and L can’t be determined).

Only Conclusion I is true

Hence, option d.

Solution 2: C)

Given statements:M ≥ N, N > V, V > Z, Y = Z, Z ≤ L, L < O

On combining the given statements, we get:

M ≥ N > V > Y = Z ≤ L < O

Conclusions:

1. M > Z: True (As M ≥ N > V > Y = Z, so M > Z).
2. Y < O: True (As Y = Z ≤ L < O, so O<Y).

III. V > L: False (As V > Y = Z ≤ L, so the relationship between V and L can’t be determined).

Only Conclusion I and II are true.

Hence, option c.

Solution 3: B)

Given statements: T ≤ K, K > P, P ≥ M, M < N, N ≥ S, S > R

On combining the given statements, we get:

T ≤ K > P ≥ M < N ≥ S > R

Conclusions:

1. P > R: False (As P ≥ M < N ≥ S > R, so the relationship between P and R can’t be determined).
2. K > R: False (As K > P ≥ M < N ≥ S > R, so the relationship between K and R can’t be determined).

III. R < N: True (As N ≥ S > R, so R < N).

1. M < T: False (As T ≤ K > P ≥ M, so the relationship between T and M can’t be determined).

Only Conclusion III is true.

Hence, option b.

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Solution 4: A)

Given statements: Q > R, R = V, V ≥ Y, Y = K, K ≤ L, L < O

On combining the given statements, we get:

Q > R = V ≥ Y = K ≤ L < O

Conclusions:

1. Q > Y: True (As Q > R = V ≥ Y, so Q > Y).
2. R < K: False (As R = V ≥ Y = K, so R ≥ K).

III. R = Y: False (As R = V ≥ Y, so, R ≥ Y).

1. Y ≤ O: False (As Y = K ≤ L < O, so, Y < O).

Only Conclusion I is true.

Hence, option a.

Solution 5: D)

Given statements:

R ≥ E ≥ D, D < A ≤ B = C, Q = P > R

On combining the given statement, we get:

Q = P > R ≥ E ≥ D < A ≤ B = C

1. Q > D: True (As Q = P > R ≥ E ≥ D, so Q > D).
2. D < C: True (As D < A ≤ B = C, so D < C).

III. R ≥ B: False (As R ≥ E ≥ D < A ≤ B, so the relationship between R and B can’t be determined).

Only Conclusion I and II is true.

Hence, option d.

Solution 6: E)

Given statements:

V > Z < T, J < K < L, L = P > Q ≥ U = V

On combining the given statement, we get:

J < K < L = P > Q ≥ U = V > Z < T

1. L > Z: True (As L = P > Q ≥ U = V > Z, so L > Z).
2. Q < J: False (As J < K < L = P > Q, so the relationship between Q and J can’t be determined).

III. Q > T: False (As Q ≥ U = V > Z < T, so the relationship between Q and T can’t be determined).

Only Conclusion I is true.

Hence, option e.

Solution 7: E)

Given statements: Q > R ≥ S = T, T ≥ U = V > W < X

On combining the given statements, we get:

Q > R ≥ S = T ≥ U = V > W < X

Conclusions:

1. X < S: False (As S =T ≥ U = V > W < X, so, relationship between X and S cannot be determined).
2. R > V: False (As R ≥ S = T ≥ U = V, so, R ≥ V).

Neither Conclusion I nor II is true.

Hence, option e.

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Solution 8: C)

Given statements: A > C = D, D ≥ E = F, F > L = K

On combining the given statements, we get:

A > C = D ≥ E = F > L = K

Conclusions:

1. L < A: True (As A > C = D ≥ E = F > L, so L < A).
2. C > K: True (As C = D ≥ E = F > L = K, so C > K).

Both Conclusions I and II are true.

Hence, option c.

Solution 9: A)

Statement:

N ≥ P > D ≥ G < J ≤ B

Conclusions:

1. G < N: True (As N ≥ P > D ≥ G, so, G < N)
2. D < B: False (As D ≥ G < J ≤ B, so, the relation between D and B can’t be determined)

So, only conclusion I is true.

Hence, option a.

Solution 10: B)

Statement:

A ≤ L = T < R ≤ H ≥ K

Conclusion:

1. H > A: True (As A ≤ L = T <R ≤ H, so, H > A)
2. R ≥ L: False (As L = T < R, so, R > L)

Only conclusion I is true.

Hence, option b.

This brings us to the end of the article. Make sure you learn these Tips to Master Inequalities Concept with Practice Questions and try attempt these practice questions. Attempt RBI Assistant free mock test to get yours hands onto latest questions and their solutions. Check other related Reasoning Ability concept blogs along with practice questions.

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