# Inequalities Quiz Set 043

### 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. § means X ≥ Y
4. Γ means X < Y
5. ⊕ means X > Y

Statements: Q Γ R; R Γ S; S Γ T;

Conclusions:

1. Q Γ S
2. R § T
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 Q < S. 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 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. ⊕ means X < Y
5. ¥ means X > Y

Statements: B \$ C; C ⊕ D; D ¢ E;

Conclusions:

1. B ⊕ E
2. D ¥ B
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 B ≤ C < D = E. Conclusion I translates to B < E. Conclusion II translates to D > B. 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. ∑ means X = Y
2. ¥ means X ≤ Y
3. £ means X ≥ Y
4. ⊗ means X < Y
5. @ means X > Y

Statements: O ∑ P; P ⊗ Q; Q ∑ R; R ∑ S;

Conclusions:

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

### Question 4

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

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

Statements: C Ω D; D ∀ E; E Ω F;

Conclusions:

1. D ⊕ C
2. C ρ D
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 C ≥ D > E ≥ F. Conclusion I translates to D < C. Conclusion II translates to C = D. 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 5

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. µ means X > Y

Statements: I ¢ J; J µ K; K µ L;

Conclusions:

1. I ¢ L
2. J µ L
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 I < J > K > L. Conclusion I translates to I < L. Conclusion II translates to J > L. 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 ≥. 