# Inequalities Quiz Set 046

### Question 1

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

1. ∑ means X = Y
2. Ω means X ≤ Y
3. ® means X ≮ (not less than) Y
4. Θ means X < Y
5. @ means X > Y

Statements: L Ω M; M Θ N; N Θ O;

Conclusions:

1. L Θ O
2. N ∑ 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: c

The statements can be translated to L ≤ M < N < O. Conclusion I translates to L < O. Conclusion II translates to N = L. 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. Θ means X = Y
2. Γ means X ≤ Y
3. ∇ means X ≮ (not less than) Y
4. « means X < Y
5. √ means X > Y

Statements: R Θ S; S « T; T √ U;

Conclusions:

1. R Θ U
2. T √ 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: b

The statements can be translated to R = S < T > U. Conclusion I translates to R = U. Conclusion II translates to T > R. 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 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. Ξ means X < Y
5. ∏ means X > Y

Statements: Q Ξ R; R Ξ S; S ⊕ T; T ∏ U;

Conclusions:

1. R Ξ U
2. R Ξ T
3. Q Ξ S

Which of the above conclusions is/are true?

A

both II and III.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to Q < R < S = T > U.

The conclusions translate to:

1. R < U(False)
2. R < T(True)
3. Q < S(True)

### 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. Ω means X < Y
5. \$ means X > Y

Statements: F ∑ G; G Ω H; H \$ I; I Ω J;

Conclusions:

1. F Ω J
2. I \$ F
3. J Ω H

Which of the above conclusions is/are true?

A

Neither of the three.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to F = G < H > I < J.

The conclusions translate to:

1. F < J(False)
2. I > F(False)
3. J < H(False)

### Question 5

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. § means X < Y
5. @ means X > Y

Statements: G @ H; H @ I; I § J; J § K;

Conclusions:

1. G @ K
2. H @ J
3. H @ K

Which of the above conclusions is/are true?

A

Neither of the three.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to G > H > I < J < K.

The conclusions translate to:

1. G > K(False)
2. H > J(False)
3. H > K(False)