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**Question 1:Â **In which of the given expressions $B>A$ is a definite true?

a)Â Aâ‰¥Dâ‰¥C>Eâ‰¥B

b)Â Â B<C>F=S>A

c)Â E<B=Câ‰¥F<A

d)Â A<Câ‰¤E=D<B

e)Â None of these

**Question 2:Â **Which of the following symbol will replace the question mark in the given expression$ P>Q; R?S; S>P; P>T$ in order to make the expression $R<T $definitely false?

a)Â >

b)Â <

c)Â â‰¥

d)Â â‰¤

e)Â =

**Question 3:Â **Which of the following symbol will replace the question mark in the given expression X>Yâ‰¥Z=A?B in order to make the expression X>B definitely true?

a)Â >

b)Â <

c)Â â‰¥

d)Â =

e)Â All except (b)

**Instructions**

In these questions, relationship between different elements is shown in the statements which are followed by conclusions. Study the conclusions based on the given statements and select the appropriate answer.

**Question 4:Â **Statement:

D < T = Y ; N > T â‰¥ X ; D â‰¥ A = B

Conclusions:

I: B < Y

II: X < Y

a)Â Only Conclusion I follows

b)Â Only Conclusion II follows

c)Â Either Conclusion I or Conclusion II follows

d)Â Both Conclusion I and Conclusion II follow

e)Â Neither Conclusion I nor Conclusion II follows

**Question 5:Â **Statement:

P < T > R ; S â‰¥ X = M ; X â‰¥ T â‰¤ N

Conclusions:

I: N < X

II: M â‰¤ N

a)Â Only Conclusion I follows

b)Â Only Conclusion II follows

c)Â Either Conclusion I or Conclusion II follows

d)Â Both Conclusion I and Conclusion II follow

e)Â Neither Conclusion I nor Conclusion II follows

**Question 6:Â **Statement:

A > L = P â‰¤ B ; L < C â‰¤ K ; P â‰¥ Q = M

Conclusions:

I: K > M

II: B < C

a)Â Only Conclusion I follows

b)Â Only Conclusion II follows

c)Â Either Conclusion I or Conclusion II follows

d)Â Both Conclusion I and Conclusion II follow

e)Â Neither Conclusion I nor Conclusion II follows

**Instructions**

The following statements and conclusions have been given.Based on the statements choose the correct option as per the data provided.

**Question 7:Â **Statements: (i)9>11>12>17; 12â‰¥10â‰¤8

Conclusions:(i) 11â‰¥8 (ii) 9>8

a)Â (i) follows

b)Â (ii) follows

c)Â Either (i) or (ii) follows

d)Â Both (ii) and (iii) follows

e)Â Neither(i) nor (ii) follows

**Question 8:Â **Statements: (i)F>D<A=E>Bâ‰¤Gâ‰¤C

Conclusions:(i) Aâ‰¥C (ii) E<C

a)Â (i) follows

b)Â (ii) follows

c)Â Either (i) or (ii) follows

d)Â Both (ii) and (iii) follows

e)Â Neither(i) nor (ii) follows

**Question 9:Â **Statements: (i)A=B>C<D; C<E<FConclusions:(i) A<E (ii) D<F

a)Â (i) follows

b)Â (ii) follows

c)Â Either (i) or (ii) follows

d)Â Both (ii) and (iii) follows

e)Â Neither(i) nor (ii) follows

**Question 10:Â **Statements: (i)Iâ‰¥Mâ‰¥N>Sâ‰¥P<Q=R

Conclusions:(i) Mâ‰¥P (ii) I>S

a)Â (i) follows

b)Â (ii) follows

c)Â Either (i) or (ii) follows

d)Â Both (ii) and (iii) follows

e)Â Neither(i) nor (ii) follows

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**Question 11:Â **Statements: (i)A>Râ‰¥Q=F<C>G=B

Conclusions:(i) A>F (ii) A>C

a)Â (i) follows

b)Â (ii) follows

c)Â Either (i) or (ii) follows

d)Â Both (ii) and (iii) follows

e)Â Neither(i) nor (ii) follows

**Instructions**

Study the following information and answer the questions that follow:

**Question 12:Â **Which of the following should replace the question mark (?) in the given expression in order to make G > T definitely true and Y â‰¤ U definitely false?

J > P = U ; W â‰¤ Y ? X = P ; X â‰¤ G ; W â‰¥ T

a)Â <

b)Â â‰¤

c)Â =

d)Â >

e)Â â‰¥

**Question 13:Â **Which of the following should replace the question mark (?) in the given expression in order to make both the expressions K < B and L < P definitely false?

A > N â‰¤ B ; K ? C = P ; C < R < N ; L â‰¤ K

a)Â <

b)Â â‰¤

c)Â =

d)Â >

e)Â More than one option

**Instructions**

In these questions, relationship between different elements is shown in the statements which are followed by conclusions. Study the conclusions based on the given statements and select the appropriate answer.

**Question 14:Â **Statement:

W = Z < D > T ; B â‰¥ Y > M ; N â‰¤ Y = D â‰¥ X

Conclusions:

I: W > N

II: Z < B

III: T < X

a)Â Only Conclusion II follows

b)Â Either Conclusion I or III follows

c)Â Both Conclusion II and III follow

d)Â Only Conclusion I follows

e)Â All the Conclusions follow

**Question 15:Â **Statement:

A â‰¤ H = C < M ; L > T â‰¥ H ; B = A â‰¥ N â‰¤ K

Conclusions:

I: L > K

II: A < T

III: B = T

a)Â Only Conclusion III follows

b)Â Only Conclusion I follows

c)Â Only Conclusion I and Either Conclusion II or III follow

d)Â Either Conclusion II or Conclusion III follows

e)Â None of the Conclusions follow

**Instructions**

In these questions, relationship between different elements is shown in the statements which are followed by conclusions. Study the conclusions based on the given statements and select the appropriate answer.

**Question 16:Â **Statement:

W â‰¥ T < Q = P ; T â‰¥ L = O ; Q < M â‰¤ N

Conclusions:

I: N > W

II: P > O

III: M > L

a)Â Only Conclusion II is true

b)Â Only Conclusion III is true

c)Â Both Conclusions II and III are true

d)Â Either Conclusion I or III is true

e)Â None of the Conclusions are true

**Question 17:Â **Statement:

L â‰¥ P â‰¤ Q ; R = S > Q ; J > T < L

Conclusions:

I: Q < T

II: R > P

II: T â‰¤ Q

a)Â Only Conclusion II is true

b)Â Either Conclusion I or Conclusion III is true

c)Â Both Conclusion I and II are true

d)Â Only Conclusion II and Either Conclusion I or III is true

e)Â None of the Conclusions are true

**Question 18:Â **Statement:

A > E â‰¥ G ; B = E < F â‰¤ T ; L â‰¤ B = S

Conclusions:

I: T > A

II: S â‰¤ T

III: F > G

a)Â Only Conclusion I is true

b)Â Only Conclusion III is true

c)Â Both Conclusions I and III are true

d)Â Either Conclusion I or II is true

e)Â None of the Conclusions are true

**Instructions**

**Question 19:Â **Statement:

$A < B \geq C , A = E , D \geq B , F \leq G > C$

Conclusions:

I: A > F

II: D > C

a)Â Only Conclusion I follows

b)Â Only Conclusion II follows

c)Â Either Conclusion I or Conclusion II follows

d)Â Both Conclusion I and Conclusion II follow

e)Â Neither Conclusion I nor Conclusion II follows

**Question 20:Â **Statement:

$L > M = N , M \leq P , R \geq L , N \geq Q$

Conclusions:

I: M > Q

II: Q = N

a)Â Only Conclusion I follows

b)Â Only Conclusion II follows

c)Â Either Conclusion I or Conclusion II follows

d)Â Both Conclusion I and Conclusion II follow

e)Â Neither Conclusion I nor Conclusion II follows

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**Answers & Solutions:**

**1)Â AnswerÂ (D)**

From the options, we get the option (d) to be correct for making $B>A$ to be true.

**2)Â AnswerÂ (B)**

Combining the expressions we get,

$R?S>P>T$

If we put < in the above expression we get

$R<S>P>T$ that will make the$ R<T $definitely false.

**3)Â AnswerÂ (E)**

We have, $X>A $

So, any sign except ‘<‘ will fit the expression to make it true.

**4)Â AnswerÂ (A)**

The relationship between B and Y can be written as

B = A â‰¤ D < T = Y

Here, B is definitely less than Y.

The relationship between X and Y can be written as

X â‰¤ T = Y

Here, X can be either less than Y or equal to Y.

Hence, Conclusion II cannot be concluded.

Therefore, Only Conclusion I follows.

**5)Â AnswerÂ (C)**

The relationship between N and X can be written as X â‰¥ T â‰¤ N

Here, The relation cannot be established.

Since X = M, replacing X by M in the above expression,

M â‰¥ T â‰¤ N.

Here, M can be either greater than or equal to or less than N.

If we replace X by M in Conclusion I, we get both the conclusions as

N < M (or) M > N

M â‰¤ N.

Therefore, Either Conclusion I or Conclusion II follows.

**6)Â AnswerÂ (A)**

The relationship between K and M can be written as,

K â‰¥ C > L = P â‰¥ Q = M

Here, We can say that K is definitely greater than M.

The relationship between B and C can be written as,

B â‰¥ P = L < C

Here, The relationship between B and C cannot be established.

Hence, Only Conclusion I follows.

**7)Â AnswerÂ (E)**

from the statements we have ;

9>11>12â‰¥10â‰¤8

We donâ€™t have the exact relation between 9 and 8 and 11 and 8 so both the statements will be false.

**8)Â AnswerÂ (C)**

from the statements we have ;

F>D<A=E>Bâ‰¤Gâ‰¤C

As A=E and we donâ€™t have the exact sign between E and C so either of the statements can be true.

**9)Â AnswerÂ (E)**

from the statements we have ;

A=B>C<E<F and D>C<E<F

We donâ€™t have the exact equality sign between A and E and D and F so both the conclusions will be false.

**10)Â AnswerÂ (B)**

from the statements we have ;

Iâ‰¥Mâ‰¥N>Sâ‰¥P<Q=R

M>P and I>S.

So, first conclusion will be false and second will be true.

**11)Â AnswerÂ (A)**

from the statements we have ;

A>Râ‰¥Q=F<C>G=B

From the conclusion we have A>F which is true.A>C is false as equality signs are opposite or no definite sign is there.

**12)Â AnswerÂ (A)**

If we replace ? with T â‰¤ W â‰¤ Y < X â‰¤ G

Y < X = P = U

Here, G > T is definitely true.

Y â‰¤ U is definitely false.

If we replace ? with â‰¤, the relationship between G and T and Y and U can be written as

T â‰¤ W â‰¤ Y â‰¤ X â‰¤ G

Y â‰¤ X = P = U

Here, G > T is not definitely true since G â‰¥ T from the above expression.

Y â‰¤ U is definitely true..

If we replace ? with =, the relationship between G and T and Y and U can be written as

T â‰¤ W â‰¤ Y = X â‰¤ G

Y = X = P = U

Here, G > T is not definitely true since G â‰¥ T from the above expression.

Y â‰¤ U is definitely false since Y = U from the above expression.

If we replace ? with > or â‰¥, the relationship between G and T and Y and U can be written as

T â‰¤ W â‰¤ Y > X â‰¤ G or T â‰¤ W â‰¤ Y â‰¥ X â‰¤ G

Y > X = P = U or Y â‰¥ X = P = U

Here, Both the expressions G > T and Y â‰¤ U will be definitely false.

Hence, ? can be replaced with only < to make G > T definitely true and Y â‰¤ U definitely false.

**13)Â AnswerÂ (D)**

The relationship between B and K can be written as

K ? C < R < N â‰¤ B

The relationship between P and L can be written as

L â‰¤ K ? C = P

Here, if we replace ? with K < C < R < N â‰¤ B

L â‰¤ K < C = P

Hence, Both the expressions are true.

If we replace ? with â‰¤, then we get

K â‰¤ C < R < N â‰¤ B

L â‰¤ K â‰¤ C = P

Here, K < B is definitely true and L < P is false.

If we replace ? with =, then we get

K = C < R < N â‰¤ B

L â‰¤ K = C = P

Here, K < B is definitely true and L < P is false.

If we replace ? with >, then we get

K > C < R < N â‰¤ B

L â‰¤ K > C = P

Here, Both the expressions K < B and L < P will be definitely false.

Hence, Option D is the correct answer.

**14)Â AnswerÂ (A)**

The relationship between W and N can be written from the statement as,

W = Z < D = Y â‰¥ N

Here, W < D â‰¥ N.

Hence, The relationship between W and N cannot be determined and Conclusion I does not follow.

The relationship between Z and B can be written as,

Z < D = Y â‰¤ B

Hence, Z < B is true.

The relationship between T and X can be written as,

T < D â‰¥ X.

Hence, The relation cannot be established and Conclusion III does not follow.

**15)Â AnswerÂ (D)**

The relationship between L and K from the given statement can be written as,

L > T â‰¥ H â‰¥ A â‰¥ N â‰¤ K

Here, L > K cannot be concluded since L > N â‰¤ K.

The relationship between T and A can be written as,

T â‰¥ H â‰¥ A

Here, T can be either greater than A or equal to A.

From the given statement, A = B.

Hence, Replacing A by B.

T â‰¥ H â‰¥ B

Hence, T can be either greater than B or equal to B.

Combining Conclusion II and Conclusion III,

Conclusion II says A < T

Conclusion III says B = T â‡’ A = T since A = B

Therefore, Either Conclusion II or Conclusion III follows.

**16)Â AnswerÂ (C)**

The relationship between N and W can be written from the statements as

N â‰¥ M > Q > T â‰¤ W

Hence, The relation cannot be established and Conclusion I will be false.

The relationship between P and O can be written as

P = Q > T â‰¥ L = O

Hence, we can say that P is greater than O.

The relationship between M and L can be written as

M > Q > T â‰¥ L

Hence, M is greater than L.

Therefore, Both II and III are true.

**17)Â AnswerÂ (D)**

The relationship between Q and T can be written from the statements as

Q â‰¥ P â‰¤ L > T

Therefore, The relation cannot be established between Q and T and hence Q can be either greater than or less than or equal to T.

Hence, Either I or III is true.

The relationship between R and P can be written as

R = S > Q â‰¥ P

Hence, R > P is true.

Therefore, Only Conclusion II and Either I or III is true.

**18)Â AnswerÂ (B)**

The relationship between T and A can be written from the statement as

T â‰¥ F > E < A

Hence, The relationship between T and A cannot be established and the Conclusion I cannot be true.

The relationship between S and T can be written as

T â‰¥ F > E = B = S

Here, S will be less than T but cannot be equal to T.

Hence, Conclusion II is false.

The relationship between F and G can be written as

F > E â‰¥ G

Hence, F > G is true.

Therefore, Only Conclusion III is true.

**19)Â AnswerÂ (E)**

The relationship between A and F from the statements can be written as

$A < B \geq C < G \geq F$

Here, We canâ€™t establish a relationship between A and F. A can be either greater than or less than or equal to F.

Hence, Conclusion I is false.

The relationship between D and C can be written as

$D \geq B \geq C$

Here, $D \geq C$

This can be written as

$D > C$ or $D = C$

The given conclusion D > C is false according to second case.

Hence, Conclusion II is false.

**20)Â AnswerÂ (C)**

From the statements, M = N.

Hence, Replacing N by M in Conclusion II.

Then, The two conclusions can be written as M > Q and M = Q

The relationship between M and Q can be written from the statements as

$M = N \geq Q$

The above statement can be split as

$M = N = Q$ or $M = N > Q$.

â‡’ $M = Q$ or $M > Q$

Hence, Either Conclusion I or Conclusion II follows.

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