# Inequalities Quiz Set 036

### Question 1

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: K √ L; L √ M; M √ N;

Conclusions:

1. K ® M
2. L √ N
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 K > L > M > N. Conclusion I translates to K < M. Conclusion II translates to L > N. 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 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: L ∇ M; M ∇ N; N @ O; O @ P;

Conclusions:

1. M ∇ O
2. L ∇ O
3. P ∇ N

Which of the above conclusions is/are true?

A

III only.

B

both III and II.

C

II only.

D

I only.

Soln.
Ans: a

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

The conclusions translate to:

1. M > O(False)
2. L > O(False)
3. P > N(True)

### Question 3

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

1. Δ means X = Y
2. ¥ means X ≯ (not more than) Y
3. ® means X ≥ Y
4. ∏ means X < Y
5. £ means X > Y

Statements: G ® H; H £ I; I £ J;

Conclusions:

1. G Δ J
2. G £ I
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 G ≥ H > I > J. Conclusion I translates to G = J. Conclusion II translates to G > I. 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 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: S « T; T « U; U ∇ V; V ω W;

Conclusions:

1. S ∇ V
2. V ω T
3. S ∇ W

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 S = T = U > V < W.

The conclusions translate to:

1. S > V(True)
2. V < T(True)
3. S > W(True)

### 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. µ means X < Y
5. η means X > Y

Statements: M @ N; N @ O; O η P; P η Q;

Conclusions:

1. Q µ N
2. N η P
3. O µ M

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: b

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

The conclusions translate to:

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