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Inequalities - Advanced Level: direct inequalities ADVANCED

Master inequalities concepts through this hard problem set practice set. Worksheet 26 of 30 contains 20 advanced-level problems. Deep dive into direct inequalities while learning chain inequalities, inequality solving, comparison puzzles. Recommended for advanced learners aiming for complex scenarios and multi-step problems.

📝 Worksheet 26 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Inequalities
Worksheet 26 of 30 (86% complete)

Question 1

Statement: P = Q > R ≥ S > M Which conclusions are definitely true?
From P = Q > R ≥ S > M, we can derive: Q > S, R > M. These conclusions definitely follow.
multiple, evaluation, analysis

Question 2

Statements: E > F = G > D Conclusion: D > E Is the conclusion true?
From E > F = G > D, D > E contradicts the given inequalities, so it's false.
basic, comparison, transitive

Question 3

Statements: I. A ≥ F = G II. G > B ≥ E Which conclusions definitely follow?
Combining statements: A ≥ F = G > B ≥ E. Therefore, I, II, and III definitely follow(s).
compound, multiple, chain

Question 4

Statement: Y ≤ Z ≤ V Conclusions: I. Y < V II. Y = V Which follows?
From Y ≤ Z ≤ V, either Y < V or Y = V. Hence either I or II follows.
either-or, logical, possibility

Question 5

Statements: H > F ≥ C ≥ A Conclusion: F = A Is the conclusion true?
From H > F ≥ C ≥ A, we cannot determine the exact relationship between F and A.
basic, comparison, transitive

Question 6

Statements: V > Q; Q > P; Q > S; P = U; S ≥ R Which of the following is definitely true?
Analyzing the chain: V > Q; Q > P; Q > S; P = U; S ≥ R. Therefore, V > P is definitely true.
complex, chain, multi-step

Question 7

Statements: I. A < C > E II. C ≤ B < F Which conclusion is definitely false?
From the statements, A > F contradicts the established relationships and is definitely false.
reverse, mixed, direction

Question 8

Statements: U > P; P > Q; P > T; Q = S; T ≥ W Which of the following is definitely true?
Analyzing the chain: U > P; P > Q; P > T; Q = S; T ≥ W. Therefore, U > S is definitely true.
complex, chain, multi-step

Question 9

Statements: I. D > B < A II. B ≥ C > F Which conclusion is definitely false?
From the statements, F > B contradicts the established relationships and is definitely false.
reverse, mixed, direction

Question 10

Arrange the elements A, C, B, E, D based on these clues: - A > C - B > E - E > D - B < C Which element is the largest?
From the clues: A > C > B > E > D. Therefore, A is the largest.
puzzle, arrangement, ordering

Question 11

Arrange the elements B, A, C, D, E based on these clues: - D > E - B > A - C < A - C > D Which element is the largest?
From the clues: B > A > C > D > E. Therefore, B is the largest.
puzzle, arrangement, ordering

Question 12

Statement: P ≥ O > R = S ≥ M Which conclusions are definitely true?
From P ≥ O > R = S ≥ M, we can derive: P > R. These conclusions definitely follow.
multiple, evaluation, analysis

Question 13

Statements: W > Q; Q > P; Q > T; P = V; T ≥ R Which of the following is definitely true?
Analyzing the chain: W > Q; Q > P; Q > T; P = V; T ≥ R. Therefore, W > V is definitely true.
complex, chain, multi-step

Question 14

Statements: S > R; R > P; R > W; P = U; W ≥ V Which of the following is definitely true?
Analyzing the chain: S > R; R > P; R > W; P = U; W ≥ V. Therefore, S > P is definitely true.
complex, chain, multi-step

Question 15

Statements: I. G > D ≥ C II. C = A > B Which conclusions definitely follow?
Combining statements: G > D ≥ C = A > B. Therefore, I, II, and III definitely follow(s).
compound, multiple, chain

Question 16

Arrange the elements B, D, E, A, C based on these clues: - E > A - E < D - B > D - A > C Which element is the largest?
From the clues: B > D > E > A > C. Therefore, B is the largest.
puzzle, arrangement, ordering

Question 17

Statements: B ≥ D = E ≥ C Conclusion: C > B Is the conclusion true?
From B ≥ D = E ≥ C, C > B contradicts the given inequalities, so it's false.
basic, comparison, transitive

Question 18

Directions: * means ≥, ^ means ≤, ? means <, ~ means =, ! means > Statement: P ~ T ? Q ^ S Which conclusion follows?
Decoding: P = T → = T < Q → < Q ≤ S. Therefore, No definite conclusion.
coded, symbols, decoding

Question 19

Arrange the elements D, A, E, B, C based on these clues: - D > A - B > C - E > B - E < A Which element is the largest?
From the clues: D > A > E > B > C. Therefore, D is the largest.
puzzle, arrangement, ordering

Question 20

Statements: P > R ≥ W; S ≤ W < V; V = T; T ≥ Q Which of the following is definitely true?
Analyzing the chain: P > R ≥ W; S ≤ W < V; V = T; T ≥ Q. Therefore, V ≥ Q is definitely true.
complex, chain, multi-step
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