Inequalities Quiz Set 047

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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. Ξ means X ≥ Y
  4. ⊕ means X < Y
  5. λ means X > Y

Statements: L ⊕ M; M ≅ N; N λ O; O λ P;

Conclusions:

  1. P λ L
  2. N λ P
  3. L λ N

Which of the above conclusions is/are true?

 A

II only.

 B

both I and II.

 C

I only.

 D

III only.

Soln.
Ans: a

The statements can be translated to L < M = N > O > P.

The conclusions translate to:

  1. P > L(False)
  2. N > P(True)
  3. L > N(False)

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. ω means X ≥ Y
  4. ∑ means X < Y
  5. ∂ means X > Y

Statements: B ∑ C; C ∑ D; D ∂ E;

Conclusions:

  1. B ∑ E
  2. D ∂ B
 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 B < C < D > E. Conclusion I translates to B < E. Conclusion II translates to D > B. 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. ∩ means X ≤ Y
  3. ® means X ≮ (not less than) Y
  4. ¥ means X < Y
  5. ¢ means X > Y

Statements: H ∩ I; I ¢ J; J ® K;

Conclusions:

  1. J ¥ H
  2. H ¢ 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: d

The statements can be translated to H ≤ I > J ≥ K. Conclusion I translates to J < H. Conclusion II translates to H > J. 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 4

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

  1. ∧ means X = Y
  2. ∃ 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 ∩ N
  2. N § 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: a

The statements can be translated to M > N < O = P. Conclusion I translates to M > N. Conclusion II translates to N < P. 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. ⊗ means X = Y
  2. Ξ means X ≤ Y
  3. ∏ means X ≮ (not less than) Y
  4. ∃ means X < Y
  5. µ means X > Y

Statements: B Ξ C; C ∃ D; D ∃ E;

Conclusions:

  1. B ∃ E
  2. D ⊗ B
 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 < E. Conclusion II translates to D = B. 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 047" 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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