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Inequalities - Intermediate-Advanced Level: chain inequalities INTERMEDIATE-ADVANCED

Intensive strategic solving 🎯 drill: 20 intermediate-advanced-level inequalities questions. Worksheet 20 of 30 hones your chain inequalities abilities. Practice inequality solving, comparison puzzles, relational logic under timed conditions. Best for advanced developing students seeking advanced concepts with increasing complexity.

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

What you'll learn in this worksheet:
Your progress through Inequalities
Worksheet 20 of 30 (66% complete)

Question 1

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

Question 2

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

Question 3

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

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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

Question 10

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

Question 11

Statements: I. F = E < B II. B ≤ D = A Which conclusions definitely follow?
Combining statements: F = E < B ≤ D = A. Therefore, Only I definitely follow(s).
compound, multiple, chain

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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