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1.
Which of the following expressions makes "G > K" definitely true?
Correct Answer: A [G ≥ H > J = K]
Explanation:
G ≥ H > J = K: all signs open towards K with one strict sign → G > K.
2.
In which expression are both "A > D" and "C < E" definitely true?
Correct Answer: B [A > B ≥ C = D < E]
Explanation:
Only A > B ≥ C = D < E gives both A > D and C < E.
3.
Which pair of signs should replace the two question marks in B ? C ≥ D ? E so that both "B > E" and "C ≥ E" definitely follow?
Correct Answer: A [>, ≥]
Explanation:
B > C ≥ D ≥ E: one strict sign (B > C) gives B > E, and C ≥ D ≥ E gives C ≥ E.
4.
Statements (numbers are numbers): M ≥ 7 > N ≥ 4 ≥ P
Conclusions: I. M > P II. N > P
Conclusions: I. M > P II. N > P
Correct Answer: A [Only I follows]
Explanation:
I: M ≥ 7 > 4 ≥ P – true; II: N ≥ 4 ≥ P gives N ≥ P only – N > P not certain
5.
Statements (numbers are numbers): X ≥ 9, Y < 5, Y ≥ Z
Conclusions: I. X > Y II. Z ≥ 9
Conclusions: I. X > Y II. Z ≥ 9
Correct Answer: A [Only I follows]
Explanation:
I: X ≥ 9 > 5 > Y – true; II: Z ≤ Y < 5 < 9 gives Z < 9, so Z ≥ 9 is false
6.
Statements: P > Q, Q ≥ R, R = S, S < T, T ≤ U. Which conclusions definitely follow?
I. P > S II. U > R III. Q ≥ T
I. P > S II. U > R III. Q ≥ T
Correct Answer: C [Only I and II]
Explanation:
I: P > Q ≥ R = S true; II: U ≥ T > S = R true; III: Q ≥ R = S < T – opposite signs, so not definitely true.
7.
Statements: A ≥ B, C < B. Which extra statement makes "A > D" definitely true?
Correct Answer: D [D < C]
Explanation:
With D < C: A ≥ B > C > D, so A > D.
8.
Statements: W ≤ X, X = Y, Y < Z, Z ≥ Q, Q > R
Conclusions: I. W ≥ Q II. W < Q
Conclusions: I. W ≥ Q II. W < Q
Correct Answer: C [Either I or II follows]
Explanation:
I: W ≤ X = Y < Z ≥ Q – opposite signs, no definite relation; II: W ≤ X = Y < Z ≥ Q – opposite signs, no definite relation; I and II are complementary and one must be true → Either
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