Inequalities Quiz Set 010

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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. Ω means X ≥ Y
  4. Ξ means X < Y
  5. @ means X > Y

Statements: M @ N; N @ O; O Ξ P; P Ξ Q;

Conclusions:

  1. O Ξ M
  2. Q Ξ O
  3. N Ξ Q

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 M > N > O < P < Q.

The conclusions translate to:

  1. O < M(True)
  2. Q < O(False)
  3. N < Q(False)
Solution | Discuss! | Chapters»

Question 2

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

  1. ∑ means X = Y
  2. Δ means X ≤ Y
  3. µ means X ≮ (not less than) Y
  4. √ means X < Y
  5. ¢ means X > Y

Statements: M ∑ N; N ¢ O; O µ P;

Conclusions:

  1. O ∑ P
  2. O ¢ 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 O = P. Conclusion II translates to O > 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 ≥.

Solution | Discuss! | Chapters»

Question 3

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

  1. µ means X = Y
  2. ⊕ means X ≤ Y
  3. Δ means X ≮ (not less than) Y
  4. λ means X < Y
  5. ρ means X > Y

Statements: N Δ O; O ρ P; P Δ Q;

Conclusions:

  1. O λ N
  2. N µ 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: d

The statements can be translated to N ≥ O > P ≥ Q. Conclusion I translates to O < N. Conclusion II translates to N = O. 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 ≥.

Solution | Discuss! | Chapters»

Question 4

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

  1. § means X = Y
  2. Ω means X ≤ Y
  3. λ means X ≥ Y
  4. √ means X < Y
  5. ⊗ means X > Y

Statements: L √ M; M § N; N § O; O ⊗ P;

Conclusions:

  1. O ⊗ L
  2. P ⊗ L
  3. L § N

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 L < M = N = O > P.

The conclusions translate to:

  1. O > L(True)
  2. P > L(False)
  3. L = N(False)
Solution | Discuss! | Chapters»

Question 5

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

  1. ∑ means X = Y
  2. Δ means X ≤ Y
  3. Γ means X ≥ Y
  4. Ξ means X < Y
  5. Ω means X > Y

Statements: T ∑ U; U ∑ V; V Ω W; W Ω X;

Conclusions:

  1. W Ξ T
  2. T Ω X
  3. V Ξ T

Which of the above conclusions is/are true?

 A

both I and III.

 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 < T(True)
  2. T > X(False)
  3. V < T(True)
Solution | Discuss! | Chapters»
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Updated on 2020-02-07. Published on: 2016-04-13

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