# Inequalities - 3

Directions (Qs. 1 - 5): Read the following information carefully and answer the questions given below.

C@D means C is not greater than D.

C ! D means C is greater than D.

C ∗ D means C is not less than D.

C % D means C is less than D.

C # D means C is neither greater nor less than D.

1. Statements: N ! I, L % N, H # I

Conclusions: I. I # L, II. N ∗ H

A) Only conclusion I follows

B) Only conclusion II follows

C) Either conclusion I or conclusion II follows

D) Both conclusion I and II follow

E) Neither conclusion I nor conclusion II follows

Explanation: As per the information given,

1. N ! I means N > I

2. L % N means L < N

3. H # I means H = I

So, the final equation will be,

L < N > I = H

Now the conclusion I. I # L means I = L

II. N ∗ H means N ≥ H

Let's check the Conclusions now, Here, we get the opposite signs between I and L, thus no relationship can be established between them. Hence conclusion I does not follows. Thus N ≥ H is not a true relationship from the above equation. Hence conclusion II does not follows.

Ans: E

2.Statements: F @ G, E % F, U ∗ G

Conclusions: I. E % G, II. U ∗ F

A) Only conclusion I follows

B) Only conclusion II follows

C) Either conclusion I or conclusion II follows

D) Both conclusion I and II follow

E) Neither conclusion I nor conclusion II  follows

Explanation: As per the information given,

1. F @ G means F ≤ G

2. E % F means E < F

3. U ∗ G means U ≥ G

So, the final equation will be

E < F ≤ G ≤ U

Now the conclusion I. E % G means E < G

II. U ∗ F means U ≥ F

Let's check the Conclusions now,  E < G is the true relation from the final equation.  Hence conclusion I follows.  U ≥ F is the true relation from the final equation. Hence conclusion II follows.

Ans: D

3. Statements: U # Z, Z % M, H ∗ M

Conclusions: I. M ! U, II. H ∗ U

A) Only conclusion I follows

B) Only conclusion II follows

C) Either conclusion I or conclusion II follows

D) Both conclusion I and II follows

E) Neither conclusion I nor conclusion II follows

Explanation: As per the information given,

1. U # Z means U = Z

2. Z % M means Z < M

3. H ∗ M means H ≥ M

So, the final equation will be,

U = Z < M ≤ H

Now the conclusion I. M ! U means M > U

II. H ∗ U means H ≥ U

Let's check the Conclusions now,  M > U is the true relation from the final equation. Hence conclusion I follows. H ≥ U is not a true relationship from the above equation. Hence conclusion II does not follows.

Ans: A

4. Statements: H ! V, M @ V, N ∗ H

Conclusions: I. N # V, II. N ! V

A) Only conclusion I follows

B) Only conclusion II follows

C) Either conclusion I or conclusion II follows

D) Both conclusion I and II follows

E) Neither conclusion I nor conclusion II follows

Explanation: As per the information given,

1. H ! V means H > V

2. M @ V means M ≤ V

3. N ∗ H means N ≥ H

So, the final equation will be,

N ≥ H > V ≥ M

Now the conclusion I. N # V means N = V

II. N ! V means N > V

Let's check the Conclusions now,  N = V is not a true relationship from the above equation. Hence conclusion I does not follows.  N > V is a true relationship from the above equation. Hence conclusion II follows.

Ans: B

5. Statements: A ! V, Q ∗ X, X @ V

Conclusions: I. A ! X, II. Q % V

A) Only conclusion I follows

B) Only conclusion II follows

C) Either conclusion I or conclusion II follows

D) Both conclusion I and II follows

E) Neither conclusion I nor conclusion II follows

Explanation: As per the information given,

1. A ! V means A > V

2. Q ∗ X means Q ≥ X

3. X @ V means X ≤ V

So, the final equation will be, Q ≥ X ≤ V < A

Now the conclusion I. A ! X means A > X

II. Q % V means Q < V  Let's check the Conclusions now, A > X is a true relationship from the above equation. Hence conclusion I follows.  Here, we get the opposite signs between Q and V, thus no relationship can be established between them. Hence conclusion II does not follows.

Ans: A

Directions (Qs. 6 - 10): In these questions, relationship between different elements is shown in the statement. The statement is followed by two conclusions. Choose the correct answer on the basis of information given below.

6. Statements: C > B ≥ U > G = Z ≤ T < E

Conclusions: I. G < E, II. B > T

A) Only conclusion I follows

B) Only conclusion II follows

C) Either conclusion I or conclusion II follows

D) Both conclusion I and II follows

E) Neither conclusion I nor conclusion II follows

Explanation:

For conclusion I: G < E

Here, the common sign between G and E is '<', hence G < E.  Thus conclusion I follows.

For conclusion II: B > T  Here, we can see the opposite sign between B and T, thus no relationship can be  established between them. Thus conclusion II does not follows. Therefore only conclusion I follows.

Ans: A

7. Statements: Z < P ≤ H ≤ L = V > M > Q

Conclusions: I. P = V, II. V > P

A) Only conclusion I follows

B) Only conclusion II follows

C) Either conclusion I or conclusion II follows

D) Both conclusion I and II follows

E) Neither conclusion I nor conclusion II  follows

Explanation: Here, the common sign between P and V is '≤', hence P ≤ V. Thus either P = V or V > P. Therefore either conclusion I or conclusion II follows.

Ans: C

8. Statements: N < U < H ≤ K = V > Z > S

Conclusions: I. H < V, II. K > S

A) Only conclusion I follows

B) Only conclusion II follows

C) Either conclusion I or conclusion II follows

D) Both conclusion I and II follows

E) Neither conclusion I nor conclusion II follows

Explanation: Here, the common sign between H and V is '≤', hence H < V does not follow. Therefore conclusion I does not follow.  And the common sign between K and S is '>', thus K > S follows. Therefore conclusion II follow.

Ans: B

9. Statement: 4 ≥ 10 < 8 ≤ 11 = 3 ≤ 7

Conclusions: I. 7 > 10 II. 10 ≤ 3

A) Only conclusion I follows

B) Only conclusion II follows

C) Either conclusion I or conclusion II follows

D) Both conclusion I and II follow

E) Neither conclusion I nor conclusion II follows

Explanation: Checking conclusion I: 7 > 10 From the given statement, we get:  While moving from 7 towards 10, the common sign of inequalities is '>' and the given conclusions is also '7 > 10'. Clearly, C1 follows. Checking conclusion II: 10 ≤ 3 In the statement 10 < 8 ≤ 11 = 3, the common sign of inequalities between 10 and 3 is '<' whereas the given conclusion is '10 ≤ 3'. Therefore, C2 doesn't follow.

Ans: A

10. Statement: Q ≤ S ≤ D = T > R > U

Conclusions: I. Q < R II. T ≥ Q

A) Only conclusion I follows

B) Only conclusion II follows

C) Either conclusion I or conclusion II follows

D) Both conclusion I and II follows

E) Neither conclusion I nor conclusion II follows

Explanation:

Checking conclusion I: Q < R

From the given statement, we get:

Q ≤ S ≤ D = T > R

The common sign of inequalities between Q and Rare reversed and therefore no definite conclusion can be withdrawn between these two elements. Hence, C1 doesn't follow.

Checking conclusion II: T ≥ Q

As we can see that in the given statement while moving from T towards Q, the common sign between these two elements is '≥' and the given conclusion is also T ≥ Q. Therefore, C2 follows here.

Ans: B

* Which of the following explanation is false, if the given expression is true?

F = G > H ≤ I = J

i. F > H ii. I ≥ H iii. I ≥ G iv. J ≥ H

A) Only i    B) Only ii   C) Only iii & iv   D) Only iii    E) None of these

Explanation: Given, F = G > H ≤ I = J  We can't compare I and G because between I & G opposite symbol used. We know that the inequalities does not works between opposite symbol.

Ans: D

* M ≤ P > W = F ≥ T

Which of the following ones is correct?

i. M ≤ W ii. P = F iii. P > T iv. T ≥ M

A) Only i     B) Only ii     C) Only iii      D) Only iii & iv     E) None of these

Explanation: Given, M ≤ P > W = F ≥ T

We can compare P and T. which shows that the option 3rd is correct because the common symbol between P and T is ‘>’.

Ans: C

Posted Date : 13-06-2023

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