Inequalities Quiz Set 005

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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. ω means X > Y

Statements: C ω D; D ∏ E; E ∏ F;

Conclusions:

  1. C ω F
  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: a

The statements can be translated to C > D = E = F. Conclusion I translates to C > F. Conclusion II translates to D = F. 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. µ means X = Y
  2. $ means X ≤ Y
  3. ® means X ≥ Y
  4. % means X < Y
  5. ∀ means X > Y

Statements: R µ S; S µ T; T ∀ U; U ∀ V;

Conclusions:

  1. R µ T
  2. U % S
  3. R ∀ V

Which of the above conclusions is/are true?

 A

both I and II.

 B

I only.

 C

II only.

 D

III only.

Soln.
Ans: a

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

The conclusions translate to:

  1. R = T(True)
  2. U < S(True)
  3. R > V(False)

Question 3

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

  1. Ω means X = Y
  2. ∑ means X ≯ (not more than) Y
  3. ⊕ means X ≮ (not less than) Y
  4. ∇ means X < Y
  5. Δ means X > Y

Statements: F Ω G; G Δ H; H ∑ I;

Conclusions:

  1. F Δ I
  2. H ∇ F
 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 H < F. 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. Δ means X = Y
  2. ∧ means X ≤ Y
  3. £ means X ≮ (not less than) Y
  4. Ξ means X < Y
  5. Ω means X > Y

Statements: H ∧ I; I Ω J; J Ω K;

Conclusions:

  1. H Δ K
  2. I Ω K
 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 H ≤ I > J > K. Conclusion I translates to H = K. Conclusion II translates to I > K. 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 5

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

  1. § means X = Y
  2. ® means X ≤ Y
  3. λ means X ≥ Y
  4. η means X < Y
  5. % means X > Y

Statements: I § J; J % K; K % L; L § M;

Conclusions:

  1. M η I
  2. J % M
  3. L η I

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 I = J > K > L = M.

The conclusions translate to:

  1. M < I(True)
  2. J > M(True)
  3. L < I(True)

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This Blog Post/Article "Inequalities Quiz Set 005" 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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