Inequalities Quiz Set 013

Question 1

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: K √ L; L √ M; M √ N;

Conclusions:

1. K ® M
2. L √ N
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 K > L > M > N. Conclusion I translates to K < M. Conclusion II translates to L > N. 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 2

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

1. ∀ means X = Y
2. Ω means X ≯ (not more than) Y
3. ⊕ means X ≮ (not less than) Y
4. ® means X < Y
5. Θ means X > Y

Statements: F ∀ G; G Θ H; H ∀ I;

Conclusions:

1. F Θ H
2. I ® G
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 F = G > H = I. Conclusion I translates to F > H. Conclusion II translates to I < G. 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 3

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. λ means X < Y
5. Δ means X > Y

Statements: T λ U; U λ V; V ω W; W ω X;

Conclusions:

1. U λ X
2. V ω X
3. T λ V

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 T < U < V = W = X.

The conclusions translate to:

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

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. £ means X ≥ 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: c

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 I 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. µ means X ≯ (not more than) Y
3. ® means X ≥ Y
4. Γ means X < Y
5. © means X > Y

Statements: L ® M; M Γ N; N µ O;

Conclusions:

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 L ≥ M < N ≤ O. Conclusion I translates to M > O. Conclusion II translates to L > O. 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 ≥.