# Inequalities Quiz Set 045

### 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. ρ means X < Y
5. µ means X > Y

Statements: O µ P; P µ Q; Q « R; R « S;

Conclusions:

1. S ρ P
2. O ρ Q
3. O µ S

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 O > P > Q = R = S.

The conclusions translate to:

1. S < P(True)
2. O < Q(False)
3. O > S(True)

### Question 2

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. ρ means X < Y
5. Ω means X > Y

Statements: Q © R; R ρ S; S ρ T;

Conclusions:

1. T Ω R
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 Q ≥ R < S < T. Conclusion I translates to T > R. Conclusion II translates to R ≥ T. 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 3

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

1. ¥ means X = Y
2. ρ means X ≤ Y
3. \$ means X ≮ (not less than) Y
4. η means X < Y
5. © means X > Y

Statements: R ¥ S; S © T; T η U;

Conclusions:

2. T η U
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 R = S > T < U. Conclusion I translates to R > T. Conclusion II translates to T < U. 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 4

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: M ω N; N ω O; O √ P; P √ Q;

Conclusions:

1. N √ Q
2. Q ω O
3. O ω M

Which of the above conclusions is/are true?

A

II only.

B

both I and II.

C

I only.

D

III only.

Soln.
Ans: a

The statements can be translated to M > N > O < P < Q.

The conclusions translate to:

1. N < Q(False)
2. Q > O(True)
3. O > M(False)

### Question 5

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

1. √ means X = Y
2. λ means X ≤ Y
3. \$ means X ≮ (not less than) Y
4. ∇ means X < Y
5. ⊕ means X > Y

Statements: M √ N; N ⊕ O; O λ P;

Conclusions:

1. M ⊕ P
2. O ∇ M
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 M = N > O ≤ P. Conclusion I translates to M > P. Conclusion II translates to O < M. 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 ≥. 