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Inequalities - Expert Level: mixed inequalities EXPERT

Comprehensive self assessment worksheet covering 20 expert-level inequalities problems. Worksheet 28 of 30 emphasizes mixed inequalities. Master comparison puzzles, relational logic, inequality chains through detailed explanations. Difficulty: challenging problems and time-bound practice. Tailored for expert-level preparation.

📝 Worksheet 28 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Inequalities
Worksheet 28 of 30 (93% complete)

Question 1

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

Question 2

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

Question 3

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

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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

Question 10

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

Question 11

Statement: Z ≥ V ≥ X Conclusions: I. Z > X II. Z = X Which follows?
From Z ≥ V ≥ X, either Z > X or Z = X. Hence either I or II follows.
either-or, logical, possibility

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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