# Inequalities Quiz Set 042

### Question 1

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

1. £ means X = Y
2. ∏ means X ≤ Y
3. ρ means X ≮ (not less than) Y
4. ∅ means X < Y
5. Θ means X > Y

Statements: H ∏ I; I Θ J; J ∏ K;

Conclusions:

1. H ∅ K
2. I ∅ J
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 H ≤ I > J ≤ K. Conclusion I translates to H < K. Conclusion II translates to I < J. 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 ≥.

### Question 2

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: N % O; O % P; P ¥ Q; Q § R;

Conclusions:

1. Q ¥ O
2. P ¥ R
3. R ¥ N

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 N > O > P < Q = R.

The conclusions translate to:

1. Q < O(False)
2. P < R(True)
3. R < N(False)

### 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: B © C; C © D; D ⊕ E; E ⊕ F;

Conclusions:

1. F ∏ C

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 B < C < D = E = F.

The conclusions translate to:

1. F > C(True)
2. B < D(True)
3. B < F(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. η means X ≮ (not less than) Y
4. ∇ means X < Y
5. ∀ means X > Y

Statements: J η K; K £ L; L ∂ M;

Conclusions:

1. J ∇ L
2. J ∀ 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 J ≥ K = L ≤ M. Conclusion I translates to J < L. Conclusion II translates to J > 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 ≥.

### Question 5

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

1. ¢ means X = Y
2. ⊗ means X ≯ (not more than) Y
3. η means X ≥ Y
4. « means X < Y
5. Θ means X > Y

Statements: M ⊗ N; N Θ O; O η P;

Conclusions:

1. O « M
2. M Θ 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 M ≤ N > O ≥ P. Conclusion I translates to O < M. Conclusion II translates to M > 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 ≥. 