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# Inequalities Questions for IBPS PO Prelims

Instructions

In the following questions, the relationship between different elements is shown in the statements. These statements are followed by conclusions. Identify which conclusion is true as per the statements.

Question 1: Statements :: Tarun>Varun=Vinay≥Tushar≤Vijay=Vikash
Conclusion (i) :: Varun ≥ Vikash
Conclusion (ii) :: Vinay < Vijay

a) Neither conclusion (i) nor conclusion (ii) is true.

b) Both conclusion (i) and conclusion (ii) are true.

c) Only conclusion (ii) is true.

d) Only conclusion (i) is true.

e) Either conclusion (i) or conclusion (ii) is true.

Solution:

Here individually both of the given conclusions are false because of reverse signs. But as we can see that Varun=Vinay and Vikash=Vijay. So these can form either or case. Because all the three relation between them are possible.
Hence, option e is the correct answer.

Question 2: Statements :: Yr>Sr≥Lr>Qr, Jr<Nr≤Sr≤Fr=Vr
Conclusion (i) :: Vr≥Lr
Conclusion (ii) :: Jr<Yr

a) Neither conclusion (i) nor conclusion (ii) is true.

b) Both conclusion (i) and conclusion (ii) are true.

c) Only conclusion (ii) is true.

d) Only conclusion (i) is true.

e) Either conclusion (i) or conclusion (ii) is true.

Solution:

Conclusion (i) :: Vr≥Lr
To obtain the relationship between Vr and Lr, we need to combine the given statements.
Vr=Fr≥Sr≥Lr>Qr
As per the given statements, the given conclusion follows.
Conclusion (ii) :: Jr<Yr
To obtain the relationship between Jr and Yr, we need to combine the given statements.
Jr<Nr≤Sr<Yr
As per the given statements, the given conclusion follows.
Hence, option b is the correct answer.

Question 3: Statements :: Fc≥Tc>Rc≥Vc=Lc<Mc≤Pc≤Jc
Conclusion (i) :: Lc≤Fc
Conclusion (ii) :: Pc≥Rc

a) Both conclusion (i) and conclusion (ii) are true.

b) Neither conclusion (i) nor conclusion (ii) is true.

c) Only conclusion (ii) is true.

d) Only conclusion (i) is true.

e) Either conclusion (i) or conclusion (ii) is true.

Solution:

Conclusion (i) :: Lc≤Fc
From the given statements, the relationship between Lc and Fc is Lc<Fc. So the given conclusion is not true.
Conclusion (ii) :: Pc≥Rc
Here between Pc and Rc reverse signs are given in the statements. So we cannot get the definite relation between them and the given conclusion is not true.
Hence, option b is the correct answer.

Question 4: Which of the following conclusions is definitely false for the expression Gs>Ns=Cs≥Zs>Rs≥Es<Vs=Ts≤Ws?

a) Rs≥Vs

b) Zs≤Ts

c) Ws<Es

d) Gs>Rs

e) Es<Ns

Solution:

Option (a) Rs≥Vs
Because of reverse signs, we cannot say the given conclusion is definitely false.
Option (b) Zs≤Ts
Because of reverse signs, we cannot say the given conclusion is definitely false.
Option (c) Ws<Es
The given conclusion is definitely false. Because the relationship between Ws and Es is Ws>Es.
Option (d) Gs>Rs
The given conclusion is definitely true.
Option (e) Es<Ns
The given conclusion is definitely true.
Hence, option c is the correct answer.

Question 5: What will come in place of the question mark in the expression U≤P=V(?)M<S≤D=H and G=T≥Y≥M to make conclusions G≥U and V<H definitely true?

a) =

b) <

c) ≤

d) >

e) More than one option is true

Solution:

Option (a) =
If we replace the given symbol in place of question mark, then both the given conclusions will be definitely true.
Option (b) <
If we replace the given symbol in place of question mark, then conclusion G≥U will not be true.
Option (c) ≤
If we replace the given symbol in place of question mark, then both the given conclusions will be definitely true.
Option (d) >
If we replace the given symbol in place of question mark, then none of the given conclusions will be true because of reverse signs.
Hence, option e is the correct answer.

Instructions

In the following questions, the relationship between different elements is shown in the statements. These statements are followed by conclusions. Identify which conclusion is true as per the statements. The different symbols are represented as shown below

A & B means ‘A is not greater than B’
A @ B means ‘A is neither greater than nor equal to B’
A # B means ‘A is not less than B’
A % B means ‘A is neither less than nor equal to B’
A $B means ‘A is neither less than nor greater than B’ Question 6: Statement : D & Q, Q$ P, P # V, V $Y, Y @ H Conclusion (I) : Q % Y Conclusion (II) : H @ P Conclusion (III) : P # D a) Only I and III are true b) Only III is true c) Only II and III are true d) Only II is true e) All I, II, III are true 6) Answer (B) Solution: The given symbols represent the respective symbols are shown in below table The given statements are D & Q, Q$ P, P # V, V $Y, Y @ H By Combining all the statements, D ≤ Q = P ≥ V = Y < H Conclusion (I) : Q > Y The relation between Q and Y is Q ≥ Y. So conclusion (I) is not true. Conclusion (II) : H < P Opposite signs are between H and P. So we cannot say the relation between H and P. So conclusion (II) is not true. Conclusion (III) : P ≥ D The relation between P and D is D ≤ P. So conclusion (III) is true. Hence, the correct answer is Option B Question 7: Statement : S # X, X # G, G$ T, T @ J, J $O Conclusion (I) : T @ S Conclusion (II) : X % O Conclusion (III) : S$ G

a) Either II or III is true

b) Either II or III is true and I is true

c) Either I or III is true and II is true

d) Either I or III is true

e) Only I is true

Solution:

The given symbols represent the respective symbols are shown in below table

The given statements are S ≥ X, X ≥ G, G = T, T < J, J ≤ O
By Combining all the statements,
S ≥ X ≥ G = T < J ≤ O

Conclusion (I) : T < S
Conclusion (III) : S = G
Here G = T ≤ S
Hence both conclusions form either or condition.

Conclusion (II) : X > O
Opposite signs are between X and O. So we cannot say the relation between X and O. So conclusion (II) is not true.
Hence, the correct answer is Option D

Question 8: Statement : E @ R, R % L, L & Z, Z @ W, W $B Conclusion (I) : R @ W Conclusion (II) : B # L Conclusion (III) : W % E a) Only I is true b) Only II is true c) Only III is true d) None of them are true e) All I, II, III are true 8) Answer (D) Solution: The given symbols represent the respective symbols are shown in below table The given statements are E < R, R > L, L ≤ Z, Z < W, W = B By Combining all the statements, E < R > L ≤ Z < W = B Conclusion (I) : R < W Opposite signs are between R and W. So we cannot say the relation between R and W. So conclusion (I) is not true. Conclusion (II) : B ≥ L The relation between L and B is L < B. So conclusion (II) is not true. Conclusion (III) : W > E Opposite signs are between W and E. So we cannot say the relation between W and E. So conclusion (III) is not true. Hence, the correct answer is Option D Question 9: Statement : P @ F, F & Y, Y$ K, K # C
Conclusion (I) : Y % P
Conclusion (II) : C & Y
Conclusion (III) : P & K

a) Only I and II are true

b) Only I and III are true

c) Only II and III are true

d) Only II is true

e) All I, II, III are true

Solution:

The given symbols represent the respective symbols are shown in below table

The given statements are P < F, F ≤ Y, Y = K, K ≥ C
By Combining all the statements,
P < F ≤ Y = K ≥ C

Conclusion (I) : Y > P
The relation between P and Y is P < Y. So conclusion (I) is true.

Conclusion (II) : C ≤ Y
The relation between Y and C is Y ≥ C. So conclusion (II) is true.

Conclusion (III) : P ≤ K
The relation between P and K is P < K. So conclusion (III) is not true.
Hence, the correct answer is Option A

Question 10: What will come in place of the question mark in the below given expression to make the expression K > I definitely true?
V = K ≥ Q (?) G ≥ I ≤ L > S ≥ Y

a) >

b) ≤

c) <

d) =

e) None of the above

Solution:

If we place > in place of question mark, then the expression K > I is definitely true.
For other options, K > I is not definitely true.
So > will come in place of question mark.
Hence, the correct answer is Option A

Instructions

In the following questions, the relationship between different elements is shown in the statements. These statements are followed by conclusions. Identify which conclusion is true as per the statements. The different symbols are represented as shown below

A % B means ‘A is not greater than B’
A $B means ‘A is neither greater than nor equal to B’ A # B means ‘A is not less than B’ A & B means ‘A is neither less than nor equal to B’ A @ B means ‘A is neither less than nor greater than B’ Question 11: Statement : O % J, R # T, G @ O, J % R, T & S Conclusion (I) : J & S Conclusion (II) : O$ R
Conclusion (III) : R @ G

a) Either I or II is true

b) Only II is true

c) Only III is true

d) Either II or III is true

e) Only I is true

Solution:

The given symbols represent the respective symbols are shown in below table

The given statements are O ≤ J, R ≥ T, G = O, J ≤ R, T > S
By Combining all the statements
G = O ≤ J ≤ R ≥ T > S

Conclusion (I) : J > S
Opposite signs are between J and S. So we cannot say the relation between J and S. So conclusion (I) is not true.

Conclusion (II) : O < R
Conclusion (III) : R = G
Here G = O ≤ R . Hence both conclusions form either or condition.
Hence, the correct answer is Option D

Question 12: Statement : C @ Z, C # D, D % F, F % X
Conclusion (I) : C % X
Conclusion (II) : Z # D
Conclusion (III) : X @ D

a) Only II is true

b) Only I is true

c) Only III is true

d) None of them are true

e) All I, II, III are true

Solution:

The given symbols represent the respective symbols which are shown in the below table

The given statements are C = Z, C ≥ D, D ≤ F, F ≤ X
By Combining all the statements,
Z = C ≥ D ≤ F ≤ X

Conclusion (I) : C ≤ X
Opposite signs are between C and X. So we cannot say the relation between C and X. So conclusion (I) is not true.

Conclusion (II) : Z ≥ D
The relation between Z and D is Z ≥ D. So conclusion (II) is true.

Conclusion (III) : X = D
The relation between X and D is X ≥ D Q. So conclusion (III) is not true.
Hence, the correct answer is Option A

Question 13: Statement : Y # A, B \$ A, B # Q, Q @ I
Conclusion (I) : A & I
Conclusion (II) : Y @ Q
Conclusion (III) : Y & Q

a) Only I and either II or III are true

b) Only I and III are true

c) Only II and III are true

d) Only I is true

e) All I, II, III are true

Solution:

The given symbols represent the respective symbols which are shown in the below table

The given statements are Y ≥ A, B < A, B ≥ Q, Q = I
By Combining all the statements,
Y ≥ A > B ≥ Q = I

Conclusion (I) : A > I
The relation between A and I is A > I. So conclusion (I) is true.

Conclusion (II) : Y = Q
The relation between Y and Q is Y > Q. So conclusion (II) is not true.

Conclusion (III) : Y > Q
The relation between Y and Q is Y > Q. So conclusion (III) is true.
Hence, the correct answer is Option B

Instructions

In each of the following questions given below are some conclusions followed by some statements. You have to choose the correct set of statements that logically satisfies the given conclusions.

Question 14: Conclusion (i): E < Q
Conclusion (ii): Z ≥ C
Statements (i): E<Z≥K≥Y<Q≤F, Y≥C<M
Statements (ii): O<Z≥E>L=X≤W, C≤X>Q
Statements (iii): S≥Z=A≥T≤B<Q, C≤T≥E

a) Only statement (i)

b) Statements (ii) and (iii)

c) Only statement (iii)

d) Statements (i) and (ii)

e) None of the above

Solution:

i) E<Z≥K≥Y<Q≤F, Y≥C<M
From given statements, E<Z≥K≥Y<Q. Opposite signs are between E and Q. So we cannot say the relation between E and Q. So conclusion (i) is not true.
By combining both statements, Z≥K≥Y≥C. The relationship between Z and C is Z≥C. So conclusion (ii) is true.

ii) O<Z≥E>L=X≤W, C≤X>Q
By combining both statements, E>L=X>Q. The relationship between E and Q is E>Q. So conclusion (i) is not true.
By combining both statements, Z≥E>L=X≥C. The relationship between Z and C is Z>C. So conclusion (ii) is not true.

iii) S≥Z=A≥T≤B<Q, C≤T≥E
By combining both statements, E≤T≤B<Q. The relationship between E and Q is E<Q. So conclusion (i) is true.
By combining both statements, Z=A≥T≥C. The relationship between Z and C is Z≥C. So conclusion (ii) is true.

Hence, the correct answer is Option C

Question 15: Conclusion (i): R > Y
Conclusion (ii): J > I
Statements (i): B<C<R≤J<L, E>Y<C≥I
Statements (ii): B<C≤R≤J<L, E>Y<C>I
Statements (iii): B<C<R≤J<L, E<Y>C≥I

a) Only statement (i)

b) Statements (ii) and (iii)

c) Only statement (iii)

d) Statements (i) and (ii)

e) Only statement (ii)

Solution:

i) B<C<R≤J<L, E>Y<C≥I
By combining both statements, Y<C<R. The relationship between Y and R is Y<R. So
conclusion (i) is true.
By combining both statements, I≤C<R≤J. The relationship between I and J is I<J. So conclusion (ii) is true.

ii) B<C≤R≤J<L, E>Y<C>I
By combining both statements, Y<C≤R. The relationship between Y and R is Y<R. So conclusion (i) is true.
By combining both statements, I<C<R≤J. The relationship between I and J is I<J. So conclusion (ii) is true.

iii) B<C<R≤J<L, E<Y>C≥I
By combining both statements, Y>C<R. Opposite signs are between Y and R. So we cannot say the relation between Y and R. So conclusion (i) is not true.
By combining both statements, I≤C<R≤J. The relationship between I and J is I<J. So conclusion (ii) is true.

Hence, the correct answer is Option D

Instructions

In the following questions, the relationship between different elements is shown in the statements. These statements are followed by conclusions. Identify which conclusion is true as per the statements.

Question 16: Statement : R≤T=B>C≥A, K>F≥B
Conclusion (i) A>K
Conclusion (ii) F≥A

a) Both conclusion (i) and conclusion (ii) are true.

b) Only conclusion (ii) is true.

c) Either conclusion (i) or conclusion (ii) is true.

d) Neither conclusion (i) nor conclusion (ii) is true.

e) Only conclusion (i) is true.

Solution:

Conclusion (i) A>K
After combining both the statements, the expression will be K>F≥B>C≥A. As per the given statement the relationship between A and K is K>A. So the given conclusion is not true.
Conclusion (ii) F≥A
After combining both the statements, the expression will be K>F≥B>C≥A. As per the given statement the relationship between A and F is F>A. So the given conclusion is not true.
Hence, option d is the correct answer.

Question 17: Statement : T≥N=L>C<P, N≥E=W
Conclusion (i)T>W
Conclusion (ii) E≤L

a) Both conclusion (i) and conclusion (ii) are true.

b) Only conclusion (ii) is true.

c) Either conclusion (i) or conclusion (ii) is true.

d) Neither conclusion (i) nor conclusion (ii) is true.

e) Only conclusion (i) is true.

Solution:

T≥N=L>C<P, N≥E=W
Conclusion (i)T>W
After combining both the statements, the expression will be T≥N≥E=W. So here the relationship between T and W is T≥W. So the given conclusion is not true.
Conclusion (ii) E≤L
After combining both the statements, the expression will be L=N≥E. So here the relationship between E and L is E≤L. So the given conclusion is true.
Hence, option b is the correct answer.

Question 18: Statement : Y<U=E≤W=F≤K=C
Conclusion (i) C>E
Conclusion (ii) K=U

a) Both conclusion (i) and conclusion (ii) are true.

b) Only conclusion (ii) is true.

c) Either conclusion (i) or conclusion (ii) is true.

d) Neither conclusion (i) nor conclusion (ii) is true.

e) Only conclusion (i) is true.

Solution:

From the given statement, individually both the conclusions are not true. But these are making either or case where either of the conclusions is true.
Hence, option c is the correct answer.

Question 19: Statement : J=L≥M>H<R=W<Q≤P
Conclusion (i) P>R
Conclusion (ii) J≤Q

a) Both conclusion (i) and conclusion (ii) are true.

b) Only conclusion (ii) is true.

c) Either conclusion (i) or conclusion (ii) is true.

d) Neither conclusion (i) nor conclusion (ii) is true.

e) Only conclusion (i) is true.

Solution:

Conclusion (i) P>R
From the given statement, the relationship between P and R is P>R. So the given conclusion is true.
Conclusion (ii) J≤Q
From the given statement, the relationship between J and Q can be anything because of reverse signs. So the given conclusion is not true.
Hence, option e is the correct answer.

Instructions

In the following questions, the relationship between different elements is shown in the statements. These statements are followed by conclusions. Identify which conclusion is true as per the statements.

Question 20: Statement : W≤B=J≤F=R<P≤N=Q
Conclusion (i) N≥B
Conclusion (ii) R≥W

a) Neither conclusion (i) nor conclusion (ii) is true.

b) Only conclusion (i) is true.

c) Both conclusion (i) and conclusion (ii) are true.

d) Only conclusion (ii) is true.

e) Either conclusion (i) or conclusion (ii) is true.