Inequalities Quiz Set 044

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Question 1

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: S § T; T ω U; U ω V; V ω W;

Conclusions:

  1. T ω V
  2. W © T
  3. U © S

Which of the above conclusions is/are true?

 A

All.

 B

both I and II.

 C

II only.

 D

both II and III.

Soln.
Ans: a

The statements can be translated to S > T = U = V = W.

The conclusions translate to:

  1. T = V(True)
  2. W < T(True)
  3. U < S(True)

Question 2

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

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

Statements: B ∃ C; C ∃ D; D ⊗ E; E ∃ F;

Conclusions:

  1. D ⊗ B
  2. E ⊗ C
  3. D ⊗ F

Which of the above conclusions is/are true?

 A

I only.

 B

both I and II.

 C

II only.

 D

III only.

Soln.
Ans: a

The statements can be translated to B < C < D > E < F.

The conclusions translate to:

  1. D > B(True)
  2. E > C(False)
  3. D > F(False)

Question 3

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

  1. ∩ means X = Y
  2. ¢ means X ≯ (not more than) Y
  3. @ means X ≮ (not less than) Y
  4. £ means X < Y
  5. $ means X > Y

Statements: F £ G; G ∩ H; H ¢ I;

Conclusions:

  1. F $ I
  2. G $ I
 A

both I and II are true.

 B

only conclusion II is true.

 C

only conclusion I is true.

 D

neither I nor II is true.

Soln.
Ans: d

The statements can be translated to F < G = H ≤ I. Conclusion I translates to F > I. Conclusion II translates to G > I. So we can see that neither I nor II is true.

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


Question 4

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

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

Statements: M % N; N Γ O; O η P;

Conclusions:

  1. N % P
  2. N Γ P
 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: d

The statements can be translated to M > N = O ≥ P. Conclusion I translates to N > P. Conclusion II translates to N = P. So we can see that either I or II can be 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. © means X = Y
  2. ∅ means X ≯ (not more than) Y
  3. ⊕ means X ≮ (not less than) Y
  4. ∀ means X < Y
  5. § means X > Y

Statements: D ∅ E; E © F; F § G;

Conclusions:

  1. D © G
  2. D ∀ F
 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 D ≤ E = F > G. Conclusion I translates to D = G. Conclusion II translates to D < F. 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 ≥.


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This Blog Post/Article "Inequalities Quiz Set 044" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-04-07.

Posted by Parveen(Hoven),
Aptitude Trainer


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