Inequalities Quiz Set 001

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Question 1

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

  1. Θ means X = Y
  2. η means X ≯ (not more than) Y
  3. ∏ means X ≥ Y
  4. « means X < Y
  5. ⊕ means X > Y

Statements: G ∏ H; H ⊕ I; I Θ J;

Conclusions:

  1. G « J
  2. H Θ J
 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 G ≥ H > I = J. Conclusion I translates to G < J. Conclusion II translates to H = J. 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 2

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. Ξ means X < Y
  5. ∃ means X > Y

Statements: F Ξ G; G ∏ H; H © I;

Conclusions:

  1. G ∃ I
  2. G ∏ I
 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 F < G = H ≥ I. Conclusion I translates to G > I. Conclusion II translates to G = I. 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 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: N ⊗ O; O ≅ P; P ≅ Q;

Conclusions:

  1. N ⊗ Q
  2. O ≅ Q
 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 N < O > P > Q. Conclusion I translates to N < Q. Conclusion II translates to O > Q. 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 4

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

  1. ∀ means X = Y
  2. ∧ means X ≤ Y
  3. © means X ≥ Y
  4. Δ means X < Y
  5. Γ means X > Y

Statements: B ∀ C; C ∀ D; D ∧ E;

Conclusions:

  1. B Γ E
  2. D Γ B
 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 B = C = D ≤ E. Conclusion I translates to B > E. Conclusion II translates to D > B. 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 5

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

  1. λ means X = Y
  2. ∃ means X ≤ Y
  3. ∩ means X ≥ Y
  4. ¢ means X < Y
  5. ∅ means X > Y

Statements: T ¢ U; U ¢ V; V ∅ W; W ¢ X;

Conclusions:

  1. W ∅ U
  2. V ∅ X
  3. X ∅ T

Which of the above conclusions is/are true?

 A

Neither of the three.

 B

I only.

 C

II only.

 D

III only.

Soln.
Ans: a

The statements can be translated to T < U < V > W < X.

The conclusions translate to:

  1. W > U(False)
  2. V > X(False)
  3. X > T(False)

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This Blog Post/Article "Inequalities Quiz Set 001" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-06-24.

Posted by Parveen(Hoven),
Aptitude Trainer


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