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Inequalities - Expert Level: complex chains EXPERT

Strategic basic drills ★ for inequalities: 20 expert-level problems. Worksheet 29 of 30 - Focus: complex chains. Develop expertise in inequality logic, comparative reasoning, mathematical inequalities with step-by-step solutions. Ideal for expert-level learners targeting challenging problems and time-bound practice.

📝 Worksheet 29 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Inequalities
Worksheet 29 of 30 (96% complete)

Question 1

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

Question 2

Statements: C > G ≥ D > H Conclusion: C > H Is the conclusion true?
From C > G ≥ D > H, using transitivity, C > H is definitely true.
basic, comparison, transitive

Question 3

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

Question 4

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

Question 5

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

Question 6

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

Question 7

Statements: I. A ≥ C > E II. E < 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

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

Question 9

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

Question 10

Statement: V > Z > W Conclusions: I. V > W II. V < W Which follows?
From V > Z > W, V > W is definitely true. II does not follow.
either-or, logical, possibility

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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