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Inequalities - Intermediate Level: mixed inequalities INTERMEDIATE

Exam-focused quick response training ★ worksheet: 20 intermediate-level inequalities questions. Worksheet 13 of 30 targets mixed inequalities. Build proficiency in inequality solving, comparison puzzles, relational logic with detailed solutions. Ideal for mid-level competitive exam preparation.

📝 Worksheet 13 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Inequalities
Worksheet 13 of 30 (43% complete)

Question 1

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

Question 2

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

Question 3

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

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

Statements: E ≥ A = F > D Conclusion: E > D Is the conclusion true?
From E ≥ A = F > D, using transitivity, E > D is definitely true.
basic, comparison, transitive

Question 17

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

Question 18

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 19

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

Question 20

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