OU All In One

Inequalities questions

Conclusions from coded inequality chains.

1. Statement: T = S < V < U = P Conclusions: I. T < V II. V ≤ U

  1. Both I and II follow
  2. Neither I nor II follows
  3. Only I follows
  4. Only II follows
Answer

A. Both I and II follow A relation is certain only if every sign between the two letters points the same way. I is certain; II is certain.

2. Statement: Q ≥ S > P ≥ V = U Conclusions: I. V ≤ U II. P ≥ V

  1. Both I and II follow
  2. Only I follows
  3. Neither I nor II follows
  4. Only II follows
Answer

A. Both I and II follow A relation is certain only if every sign between the two letters points the same way. I is certain; II is certain.

3. Statement: V = R ≤ W < U ≤ S Conclusions: I. R ≥ W II. U ≤ S

  1. Only I follows
  2. Both I and II follow
  3. Only II follows
  4. Neither I nor II follows
Answer

C. Only II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is certain.

4. Statement: Q < T ≤ W = P = S Conclusions: I. Q < T II. P = S

  1. Only II follows
  2. Neither I nor II follows
  3. Both I and II follow
  4. Only I follows
Answer

C. Both I and II follow A relation is certain only if every sign between the two letters points the same way. I is certain; II is certain.

5. Statement: U ≤ V < R ≥ Q > P Conclusions: I. Q ≤ P II. R ≥ P

  1. Neither I nor II follows
  2. Both I and II follow
  3. Only I follows
  4. Only II follows
Answer

D. Only II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is certain.

6. Statement: W = R ≤ T > S < U Conclusions: I. S ≤ U II. T > S

  1. Neither I nor II follows
  2. Only I follows
  3. Both I and II follow
  4. Only II follows
Answer

C. Both I and II follow A relation is certain only if every sign between the two letters points the same way. I is certain; II is certain.

7. Statement: S < P > T = W < U Conclusions: I. P > U II. S > U

  1. Both I and II follow
  2. Only II follows
  3. Only I follows
  4. Neither I nor II follows
Answer

D. Neither I nor II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is not certain.

8. Statement: P > Q > V = U = W Conclusions: I. P > W II. U ≤ W

  1. Neither I nor II follows
  2. Only I follows
  3. Both I and II follow
  4. Only II follows
Answer

C. Both I and II follow A relation is certain only if every sign between the two letters points the same way. I is certain; II is certain.

9. Statement: S < W ≥ P < R = T Conclusions: I. P > R II. P ≤ T

  1. Only I follows
  2. Only II follows
  3. Neither I nor II follows
  4. Both I and II follow
Answer

B. Only II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is certain.

10. Statement: P = U < V ≥ W ≤ R Conclusions: I. V > R II. U > V

  1. Neither I nor II follows
  2. Both I and II follow
  3. Only II follows
  4. Only I follows
Answer

A. Neither I nor II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is not certain.

11. Statement: Q < T > W > P = V Conclusions: I. P > V II. Q ≥ V

  1. Only II follows
  2. Neither I nor II follows
  3. Both I and II follow
  4. Only I follows
Answer

B. Neither I nor II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is not certain.

12. Statement: V > Q < T ≥ S = W Conclusions: I. T ≥ S II. T > W

  1. Both I and II follow
  2. Only II follows
  3. Neither I nor II follows
  4. Only I follows
Answer

D. Only I follows A relation is certain only if every sign between the two letters points the same way. I is certain; II is not certain.

13. Statement: T ≤ P ≥ W < R ≥ Q Conclusions: I. P ≥ W II. T > W

  1. Neither I nor II follows
  2. Only I follows
  3. Only II follows
  4. Both I and II follow
Answer

B. Only I follows A relation is certain only if every sign between the two letters points the same way. I is certain; II is not certain.

14. Statement: T ≤ R < V ≤ P ≥ S Conclusions: I. R < S II. P ≥ S

  1. Both I and II follow
  2. Only II follows
  3. Only I follows
  4. Neither I nor II follows
Answer

B. Only II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is certain.

15. Statement: T > R > W > P < V Conclusions: I. P > V II. W ≥ P

  1. Only I follows
  2. Neither I nor II follows
  3. Only II follows
  4. Both I and II follow
Answer

C. Only II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is certain.

16. Statement: V = T = U ≥ P > R Conclusions: I. T ≥ U II. P ≤ R

  1. Only I follows
  2. Both I and II follow
  3. Only II follows
  4. Neither I nor II follows
Answer

A. Only I follows A relation is certain only if every sign between the two letters points the same way. I is certain; II is not certain.

17. Statement: R = V ≥ Q < T = W Conclusions: I. V < T II. R ≤ W

  1. Only II follows
  2. Neither I nor II follows
  3. Only I follows
  4. Both I and II follow
Answer

B. Neither I nor II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is not certain.

18. Statement: W > U ≤ P ≥ R > T Conclusions: I. U ≤ T II. R < T

  1. Only II follows
  2. Only I follows
  3. Both I and II follow
  4. Neither I nor II follows
Answer

D. Neither I nor II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is not certain.

19. Statement: U ≤ S < P < R ≥ Q Conclusions: I. R > Q II. R = Q

  1. Only II follows
  2. Only I follows
  3. Either I or II follows
  4. Both I and II follow
Answer

C. Either I or II follows Along the chain R ≥ Q. Neither conclusion is certain alone, but one of them must be true, so either I or II follows.

20. Statement: S = T = U ≤ V > W Conclusions: I. T ≤ V II. T < W

  1. Only I follows
  2. Both I and II follow
  3. Only II follows
  4. Neither I nor II follows
Answer

A. Only I follows A relation is certain only if every sign between the two letters points the same way. I is certain; II is not certain.

21. Statement: T ≥ W ≤ Q ≤ S = R Conclusions: I. S = R II. Q ≤ S

  1. Neither I nor II follows
  2. Only II follows
  3. Both I and II follow
  4. Only I follows
Answer

C. Both I and II follow A relation is certain only if every sign between the two letters points the same way. I is certain; II is certain.

22. Statement: Q > P < T = U < S Conclusions: I. P ≤ T II. P ≤ U

  1. Both I and II follow
  2. Only II follows
  3. Only I follows
  4. Neither I nor II follows
Answer

A. Both I and II follow A relation is certain only if every sign between the two letters points the same way. I is certain; II is certain.

23. Statement: P ≥ S ≤ T ≥ Q ≤ V Conclusions: I. P ≤ Q II. Q ≤ V

  1. Both I and II follow
  2. Only II follows
  3. Neither I nor II follows
  4. Only I follows
Answer

B. Only II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is certain.

24. Statement: V = P ≥ U ≥ Q = W Conclusions: I. V < P II. P ≥ U

  1. Both I and II follow
  2. Only II follows
  3. Only I follows
  4. Neither I nor II follows
Answer

B. Only II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is certain.

25. Statement: T < V > W ≥ S > P Conclusions: I. S > P II. V ≥ S

  1. Only I follows
  2. Both I and II follow
  3. Neither I nor II follows
  4. Only II follows
Answer

B. Both I and II follow A relation is certain only if every sign between the two letters points the same way. I is certain; II is certain.

26. Statement: P ≤ U ≤ V < S ≤ T Conclusions: I. S < T II. S = T

  1. Both I and II follow
  2. Only II follows
  3. Only I follows
  4. Either I or II follows
Answer

D. Either I or II follows Along the chain S ≤ T. Neither conclusion is certain alone, but one of them must be true, so either I or II follows.

27. Statement: P = V ≥ S ≥ R ≥ U Conclusions: I. P > U II. P = U

  1. Both I and II follow
  2. Either I or II follows
  3. Only II follows
  4. Only I follows
Answer

B. Either I or II follows Along the chain P ≥ U. Neither conclusion is certain alone, but one of them must be true, so either I or II follows.

28. Statement: T ≤ P = Q ≥ R = U Conclusions: I. T < P II. T = P

  1. Only I follows
  2. Only II follows
  3. Either I or II follows
  4. Both I and II follow
Answer

C. Either I or II follows Along the chain T ≤ P. Neither conclusion is certain alone, but one of them must be true, so either I or II follows.

29. Statement: W = P < S = R < U Conclusions: I. R > U II. P < R

  1. Both I and II follow
  2. Neither I nor II follows
  3. Only II follows
  4. Only I follows
Answer

C. Only II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is certain.

30. Statement: T = Q < R > V > S Conclusions: I. T > R II. V ≥ S

  1. Both I and II follow
  2. Only I follows
  3. Neither I nor II follows
  4. Only II follows
Answer

D. Only II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is certain.

31. Statement: P ≥ R ≤ W < U < S Conclusions: I. P < W II. R ≤ S

  1. Neither I nor II follows
  2. Only II follows
  3. Only I follows
  4. Both I and II follow
Answer

B. Only II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is certain.

32. Statement: W > P ≥ R < Q = U Conclusions: I. W < Q II. P ≥ R

  1. Neither I nor II follows
  2. Only I follows
  3. Only II follows
  4. Both I and II follow
Answer

C. Only II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is certain.

33. Statement: T < W ≤ R = P ≥ U Conclusions: I. P > U II. P = U

  1. Only II follows
  2. Both I and II follow
  3. Either I or II follows
  4. Only I follows
Answer

C. Either I or II follows Along the chain P ≥ U. Neither conclusion is certain alone, but one of them must be true, so either I or II follows.

34. Statement: Q ≤ V ≤ W < S ≥ T Conclusions: I. Q ≤ S II. S > T

  1. Neither I nor II follows
  2. Only II follows
  3. Both I and II follow
  4. Only I follows
Answer

D. Only I follows A relation is certain only if every sign between the two letters points the same way. I is certain; II is not certain.

35. Statement: U < W ≥ T ≥ S > Q Conclusions: I. T ≥ Q II. S > Q

  1. Only I follows
  2. Neither I nor II follows
  3. Only II follows
  4. Both I and II follow
Answer

D. Both I and II follow A relation is certain only if every sign between the two letters points the same way. I is certain; II is certain.

36. Statement: T < U ≤ W < R ≥ P Conclusions: I. U < W II. U = W

  1. Both I and II follow
  2. Either I or II follows
  3. Only I follows
  4. Only II follows
Answer

B. Either I or II follows Along the chain U ≤ W. Neither conclusion is certain alone, but one of them must be true, so either I or II follows.

37. Statement: W = V ≤ Q > S > R Conclusions: I. W ≥ S II. S > R

  1. Only II follows
  2. Both I and II follow
  3. Only I follows
  4. Neither I nor II follows
Answer

A. Only II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is certain.

38. Statement: R < P < S > U ≥ V Conclusions: I. R ≤ S II. P ≤ S

  1. Both I and II follow
  2. Neither I nor II follows
  3. Only I follows
  4. Only II follows
Answer

A. Both I and II follow A relation is certain only if every sign between the two letters points the same way. I is certain; II is certain.

39. Statement: W > U ≥ V ≥ Q = T Conclusions: I. Q ≤ T II. U ≥ T

  1. Neither I nor II follows
  2. Only II follows
  3. Only I follows
  4. Both I and II follow
Answer

D. Both I and II follow A relation is certain only if every sign between the two letters points the same way. I is certain; II is certain.

40. Statement: R < W ≤ U ≤ Q < T Conclusions: I. U < T II. W ≤ Q

  1. Only II follows
  2. Only I follows
  3. Both I and II follow
  4. Neither I nor II follows
Answer

C. Both I and II follow A relation is certain only if every sign between the two letters points the same way. I is certain; II is certain.

41. Statement: P > T ≥ U > V = W Conclusions: I. V ≤ W II. U ≥ W

  1. Only II follows
  2. Only I follows
  3. Neither I nor II follows
  4. Both I and II follow
Answer

D. Both I and II follow A relation is certain only if every sign between the two letters points the same way. I is certain; II is certain.

42. Statement: P > Q ≤ W < T ≤ R Conclusions: I. Q < T II. W ≤ R

  1. Neither I nor II follows
  2. Only I follows
  3. Only II follows
  4. Both I and II follow
Answer

D. Both I and II follow A relation is certain only if every sign between the two letters points the same way. I is certain; II is certain.

43. Statement: Q > R ≥ W ≤ S ≥ V Conclusions: I. S > V II. S = V

  1. Either I or II follows
  2. Only II follows
  3. Only I follows
  4. Both I and II follow
Answer

A. Either I or II follows Along the chain S ≥ V. Neither conclusion is certain alone, but one of them must be true, so either I or II follows.

44. Statement: P = V ≤ U > S = T Conclusions: I. V ≤ T II. P ≥ T

  1. Both I and II follow
  2. Only I follows
  3. Only II follows
  4. Neither I nor II follows
Answer

D. Neither I nor II follows A relation is certain only if every sign between the two letters points the same way. I is not certain; II is not certain.

45. Statement: S < Q ≥ V = R = P Conclusions: I. R ≥ P II. S < R

  1. Only I follows
  2. Neither I nor II follows
  3. Both I and II follow
  4. Only II follows
Answer

A. Only I follows A relation is certain only if every sign between the two letters points the same way. I is certain; II is not certain.

46. Statement: S < R ≥ V = W > P Conclusions: I. R > P II. R ≥ W

  1. Neither I nor II follows
  2. Only I follows
  3. Only II follows
  4. Both I and II follow
Answer

D. Both I and II follow A relation is certain only if every sign between the two letters points the same way. I is certain; II is certain.

47. Statement: P ≤ T = W ≥ U = S Conclusions: I. W > S II. W = S

  1. Either I or II follows
  2. Only II follows
  3. Both I and II follow
  4. Only I follows
Answer

A. Either I or II follows Along the chain W ≥ S. Neither conclusion is certain alone, but one of them must be true, so either I or II follows.

48. Statement: P = S > V > Q < U Conclusions: I. Q < U II. V < U

  1. Only I follows
  2. Both I and II follow
  3. Neither I nor II follows
  4. Only II follows
Answer

A. Only I follows A relation is certain only if every sign between the two letters points the same way. I is certain; II is not certain.

49. Statement: T < V ≤ P ≥ R = W Conclusions: I. T < P II. V < R

  1. Only II follows
  2. Both I and II follow
  3. Only I follows
  4. Neither I nor II follows
Answer

C. Only I follows A relation is certain only if every sign between the two letters points the same way. I is certain; II is not certain.

50. Statement: V ≥ U ≥ Q ≥ T < S Conclusions: I. T < S II. Q > S

  1. Only I follows
  2. Both I and II follow
  3. Only II follows
  4. Neither I nor II follows
Answer

A. Only I follows A relation is certain only if every sign between the two letters points the same way. I is certain; II is not certain.

Mock test

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