Inequalities Quiz Set 027

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Question 1

In a certain language different symbols represent different operators as follows.

  1. ∂ means X = Y
  2. ∧ means X ≤ Y
  3. ∀ means X ≥ Y
  4. ∃ means X < Y
  5. Ξ means X > Y

Statements: F ∃ G; G ∃ H; H Ξ I; I Ξ J;

Conclusions:

  1. H ∃ F
  2. I Ξ G
  3. J ∃ H

Which of the above conclusions is/are true?

 A

III only.

 B

both III and II.

 C

II only.

 D

I only.

Soln.
Ans: a

The statements can be translated to F < G < H > I > J.

The conclusions translate to:

  1. H < F(False)
  2. I > G(False)
  3. J < H(True)

Question 2

In a certain language different symbols represent different operators as follows.

  1. ∅ means X = Y
  2. Γ means X ≯ (not more than) Y
  3. Ω means X ≥ Y
  4. « means X < Y
  5. ∩ means X > Y

Statements: M ∩ N; N « O; O ∩ P;

Conclusions:

  1. M ∅ P
  2. N « O
 A

both I and II are true.

 B

only conclusion II is true.

 C

only conclusion I is true.

 D

either I or II can be true.

Soln.
Ans: b

The statements can be translated to M > N < O > P. Conclusion I translates to M = P. Conclusion II translates to N < O. So we can see that only conclusion II is true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.


Question 3

In a certain language different symbols represent different operators as follows.

  1. ≅ means X = Y
  2. Ξ means X ≤ Y
  3. λ means X ≥ Y
  4. ∑ means X < Y
  5. ⊗ means X > Y

Statements: P ∑ Q; Q ∑ R; R ≅ S; S ≅ T;

Conclusions:

  1. R ⊗ T
  2. T ⊗ Q
  3. P ∑ S

Which of the above conclusions is/are true?

 A

both II and III.

 B

I only.

 C

II only.

 D

III only.

Soln.
Ans: a

The statements can be translated to P < Q < R = S = T.

The conclusions translate to:

  1. R > T(False)
  2. T > Q(True)
  3. P < S(True)

Question 4

In a certain language different symbols represent different operators as follows.

  1. ω means X = Y
  2. ∏ means X ≤ Y
  3. ∑ means X ≥ Y
  4. % means X < Y
  5. ⊗ means X > Y

Statements: B ω C; C % D; D ω E;

Conclusions:

  1. B % E
  2. C % D
 A

both I and II are true.

 B

only conclusion II is true.

 C

only conclusion I is true.

 D

either I or II can be true.

Soln.
Ans: a

The statements can be translated to B = C < D = E. Conclusion I translates to B < E. Conclusion II translates to C < D. So we can see that both I and II are true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.


Question 5

In a certain language different symbols represent different operators as follows.

  1. Δ means X = Y
  2. ∇ means X ≯ (not more than) Y
  3. λ means X ≥ Y
  4. £ means X < Y
  5. ∂ means X > Y

Statements: B £ C; C £ D; D £ E;

Conclusions:

  1. B £ D
  2. C λ E
 A

both I and II are true.

 B

only conclusion II is true.

 C

only conclusion I is true.

 D

either I or II can be true.

Soln.
Ans: c

The statements can be translated to B < C < D < E. Conclusion I translates to B < D. Conclusion II translates to C ≥ E. So we can see that only conclusion I is true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.


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This Blog Post/Article "Inequalities Quiz Set 027" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.

Posted by Parveen(Hoven),
Aptitude Trainer


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