### Ques 1.

W ≥ D < M < P < A = F

II. P < W

I. F>D,

Consider the statement from D to F

D < M < P < A = F

Symbols between D and F are uniform i.e. < which implies D will be definitely lesser than F.

II. P < W

Consider the statement from P to W i.e. W ≥ D < M < P

Symbols between P and W are not uniform, mixer of lesser than and greater than symbol implies P can’t be definitely lesser than W

II. T> F

I. Q ≥ F

Consider the statement from Q to F

Q > R = F

Above statement implies that Q is definitely greater than F

II. T>F

Consider the statement from T to F i.e.

T>Q>R=F

Symbols between T and Fare uniform which consist of only > symbol which implies Twill be definitely greater than F

T $ J

II. T # M

M > J, consider statement from M to J

M < K ≥ T < J

Since it is the mixer of both < and > symbol

T % M

M # R

F @ M

F $ M

Statement: F = T ≤ M > R

Conclusion:

I. R < T

II. F = M

III. F < M

R < T, consider statement from R to T

T ≤ M > R

Since it is the mixer of both < and > symbol

F = M, consider statement from F to M

F = T ≤ M

From the above statement, It is possible that F can be equal to M

F < M, consider statement from F to M

F = T ≤ M

From the above statement, it is possible that F can be lesser than M

Ques 7.

H @ B,

B % N

II. N @ J

III. J & B

Statement: J ≥ H = B ≤ N

Conclusion:

I. N ≥ H

II. N = J

III. J ≥ B

N ≥ H, consider statement from H to N

H = B ≤ N

It clearly implies N ≥ H

N=J, consider statement from N to J

J ≥ H = B ≤ N

Since it is combination of <and > symbol we can’t predict N=J

J ≥ B, consider statement from J to B

J ≥ H = B

It clearly implies J ≥ B

Reasoning Ability: Concepts of Inequality with Examples: Part 1

Reasoning Ability: Concepts of Inequality with Examples: Part 2#### Conclusions:

I. F > DII. P < W

#### Solution:

__To solve Conclusion__I. F>D,

Consider the statement from D to F

D < M < P < A = F

Symbols between D and F are uniform i.e. < which implies D will be definitely lesser than F.

**Therefore conclusion I follows**__To solve conclusion__II. P < W

Consider the statement from P to W i.e. W ≥ D < M < P

Symbols between P and W are not uniform, mixer of lesser than and greater than symbol implies P can’t be definitely lesser than W

**Therefore Conclusion II doesn’t follow**### Ques 2.

H ≥ M > F <A = B> S

II. F < S

I. H > B

Consider the statement from H to B

H ≥ M > F <A=B

Symbols between H and B are mixer of both lesser than and greater than the symbol which implies H cannot be greater than B.

II. F<S

Consider the statement from F to S i.e. F <A=B> S

Symbols between F and S are mixer of lesser than and greater than symbol implies F can’t be definitely lesser than S

#### Conclusion:

I. H > BII. F < S

#### Solution:

__To solve Conclusion__I. H > B

Consider the statement from H to B

H ≥ M > F <A=B

Symbols between H and B are mixer of both lesser than and greater than the symbol which implies H cannot be greater than B.

**Therefore conclusion I doesn’t follow**__To solve conclusion__II. F<S

Consider the statement from F to S i.e. F <A=B> S

Symbols between F and S are mixer of lesser than and greater than symbol implies F can’t be definitely lesser than S

**Therefore Conclusion 2 doesn’t follow**### Ques 3.

B > T > Q > R = F

#### Conclusion:

I. Q ≥ FII. T> F

#### Solution:

To solve ConclusionI. Q ≥ F

Consider the statement from Q to F

Q > R = F

Above statement implies that Q is definitely greater than F

**Therefore conclusion I doesn’t follow**

__To solve conclusion__II. T>F

Consider the statement from T to F i.e.

T>Q>R=F

Symbols between T and Fare uniform which consist of only > symbol which implies Twill be definitely greater than F

**Therefore Conclusion 2 follows**

### Ques 4.

H < J, F < H, I ≤ J = K

II. I ≥ F

I. H>I

Since it is split statements combine statement with H and I variable

H < J ≥ I

Symbol between H and I are mixer of both > and < which implies H can’t be definitely greater than I.

II. I ≥ F

Combine the statement of I and F

F < H < J ≥ I

Symbols between T and Fare not uniform which consist of both < and > symbol which implies I can’t be ≥ F

#### Conclusion:

I. H > III. I ≥ F

#### Solution:

__To solve Conclusion__I. H>I

Since it is split statements combine statement with H and I variable

H < J ≥ I

Symbol between H and I are mixer of both > and < which implies H can’t be definitely greater than I.

**Therefore conclusion 1 doesn’t follow**__To solve conclusion__II. I ≥ F

Combine the statement of I and F

F < H < J ≥ I

Symbols between T and Fare not uniform which consist of both < and > symbol which implies I can’t be ≥ F

**Therefore Conclusion 2 doesn’t follow**__Direction (Q5-Q7): Read the information given below and solve the questions that follow.__% means not greater than (% ➔ ≤)

& means not smaller than (& ➔ ≥)

# means neither equal to nor smaller than (# ➔ >)

$ means neither equal to nor greater than ($ ➔ <)

@ means neither smaller than nor greater than (@ ➔ =)

From the above statements, we can conclude,

### Ques5.

#### Statements

M $ K,K & T,T $ J

#### Conclusions:

I. J # KII. T # M

III. M # J

Statement: M < K ≥ T < J

Conclusion:

I. J > K

II. T > M

III. M > J

J>K, consider statement from J to K

K ≥ T < J

Since it is the mixer of both < and > symbol

T > M, consider statement from T to M

M < K ≥ T

Since it is the mixer of both < and > symbol

#### Solution:

Convert the statement and conclusion from symbols to mathematical operation.Statement: M < K ≥ T < J

Conclusion:

I. J > K

II. T > M

III. M > J

__To solve Conclusion I__J>K, consider statement from J to K

K ≥ T < J

Since it is the mixer of both < and > symbol

**Conclusion 1 is false**__To solve Conclusion II__T > M, consider statement from T to M

M < K ≥ T

Since it is the mixer of both < and > symbol

**Conclusion 2 is false**

__To solve Conclusion III__M > J, consider statement from M to J

M < K ≥ T < J

Since it is the mixer of both < and > symbol

**Conclusion 3 is false**

**Therefore none of the three conclusions is true**

### Ques 6.

#### Statements:

F @ TT % M

M # R

#### Conclusion:

R $ TF @ M

F $ M

#### Solution:

Convert the statement and conclusion from symbols to mathematical operation.Statement: F = T ≤ M > R

Conclusion:

I. R < T

II. F = M

III. F < M

__To solve Conclusion I__R < T, consider statement from R to T

T ≤ M > R

Since it is the mixer of both < and > symbol

**Conclusion 1 is false**

__To solve Conclusion 2__F = M, consider statement from F to M

F = T ≤ M

From the above statement, It is possible that F can be equal to M

**Conclusion II may be True**

__To solve Conclusion 3__F < M, consider statement from F to M

F = T ≤ M

From the above statement, it is possible that F can be lesser than M

**Conclusion III may be True**

**Therefore Either Conclusion 2 or 3 can be true**

Ques 7.

#### Statements:

J & H,H @ B,

B % N

#### Conclusion:

I. N & HII. N @ J

III. J & B

#### Solution:

Convert the statement and conclusion from symbols to mathematical operation.Statement: J ≥ H = B ≤ N

Conclusion:

I. N ≥ H

II. N = J

III. J ≥ B

__To solve Conclusion I__N ≥ H, consider statement from H to N

H = B ≤ N

It clearly implies N ≥ H

**Conclusion I is True**

__To solve Conclusion II__N=J, consider statement from N to J

J ≥ H = B ≤ N

Since it is combination of <and > symbol we can’t predict N=J

**Conclusion II is False**

__To solve Conclusion III__J ≥ B, consider statement from J to B

J ≥ H = B

It clearly implies J ≥ B

**Conclusion III is True**

**Therefore Conclusion I and III are True**

**Must Read**

Reasoning Ability: Concepts of Inequality with Examples: Part 1

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