# Inequalities Quiz Set 010

### 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)

### 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 ≥.

### 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 ≥.

### 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)

### 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) 