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Inequalities - Intermediate-Advanced Level: inequality solving INTERMEDIATE-ADVANCED

This fundamentals focus worksheet contains 20 intermediate-advanced-level inequalities problems. Worksheet 21 of 30 focuses on inequality solving. Practice comparison puzzles, relational logic, inequality chains with our step-by-step solutions. Difficulty: advanced concepts with increasing complexity. Recommended for advanced developing learners.

📝 Worksheet 21 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate-advanced level

What you'll learn in this worksheet:
Your progress through Inequalities
Worksheet 21 of 30 (70% complete)

Question 1

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

Question 2

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

Question 3

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

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

Directions: % means ≤, @ means >, # means <, $ means ≥, & means = Statement: R $ S & Q Which conclusion follows?
Decoding: R ≥ S → ≥ S = Q. Therefore, No definite conclusion.
coded, symbols, decoding

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

Directions: © means >, £ means =, ™ means ≥, € means ≤, ® means < Statement: T ® R € P Which conclusion follows?
Decoding: T < R → < R ≤ P. Therefore, T ≤ U.
coded, symbols, decoding

Question 17

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

Question 18

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

Question 19

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

Question 20

Directions: £ means =, ™ means ≥, € means ≤, © means >, ® means < Statement: T © S £ Q ™ P Which conclusion follows?
Decoding: T > S → > S = Q → = Q ≥ P. Therefore, No definite conclusion.
coded, symbols, decoding
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