# Inequalities Quiz Set 006

### Question 1

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

1. @ means X = Y
2. ∂ means X ≯ (not more than) Y
3. Γ means X ≥ Y
4. ⊕ means X < Y
5. ∑ means X > Y

Statements: G ∑ H; H ⊕ I; I ⊕ J;

Conclusions:

1. H ⊕ J
2. H Γ 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: c

The statements can be translated to G > H < I < J. Conclusion I translates to H < J. Conclusion II translates to H ≥ J. 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 2

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

1. ω means X = Y
2. Δ means X ≤ Y
3. @ means X ≮ (not less than) Y
4. ∅ means X < Y
5. Ω means X > Y

Statements: K Ω L; L Ω M; M @ N;

Conclusions:

1. M Ω N
2. M ω 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: d

The statements can be translated to K > L > M ≥ N. Conclusion I translates to M > N. Conclusion II translates to M = N. 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. ω means X ≯ (not more than) Y
3. Δ means X ≥ Y
4. µ means X < Y
5. « means X > Y

Statements: M « N; N µ O; O Δ 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 ≥.

### Question 4

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

1. µ means X = Y
2. ∧ means X ≤ Y
3. ∀ means X ≮ (not less than) Y
4. Ξ means X < Y
5. § means X > Y

Statements: N ∀ O; O § P; P § Q;

Conclusions:

1. N µ Q
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: b

The statements can be translated to N ≥ O > P > Q. Conclusion I translates to N = Q. Conclusion II translates to N > P. 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. Γ means X ≤ Y
3. η means X ≥ Y
4. ∇ means X < Y
5. µ means X > Y

Statements: T µ U; U µ V; V Γ W;

Conclusions:

1. T ∇ W
2. V µ T
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 T > U > V ≤ W. Conclusion I translates to T < W. Conclusion II translates to V > T. 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 ≥.