__Reasoning Ability (Inequalities) Practice Questions (28 – 09 – 2017)__**Directions (1 – 3): In this question, the relationship between different elements is shown in the statements. These statements are followed by three conclusions. Mark your answer from the given options.**

**1. Statements:**

R
≤ J > M, J ≥ L = S < N, S ≥ P

**Conclusions:**

I.
P ≤ J

II.
R = L

a)
Only I is true

b)
Only II is true

c)
Only I and III are true

d)
All are true

e)
None of these

**2. Statements:**

S
< P = Z ≤ M, Z ≥ K ≥ R, S ≥ J

**Conclusions:**

I.
M ≥ R

II.
Z > J

III.
S < Z ≥ R

a)
Only I is true

b)
Only II is true

c)
Only I and II are true

d)
All I, II and III are true

e)
Only II and III are true

**3. Statements:**E ≥ C = B; D = C ≥ M > N

**Conclusions:**

I.
D = B

II.
N ≤ E

III.
N > E

a)
Only (I)

b)
Only (I) and either (II) or (III)

c)
Both (I) and (III)

d)
Both (I) and (II)

e)
None of these

**4. Which of the following expression will not be true if the expression**

**U < V < W < X < Y = Z ≥ A = B > C**

**is definitely true?**

a)
Z > C

b)
U < Y

c)
Y > C

d)
Z < U

e)
B < Y

**5. Which of the following symbols should replace the question mark in the given expression in order to make the expressions ‘A > D’ as well as ‘F ≥ C’ definitely true?**

**A > B ≥ C ? D ≤ E = F**

a)
>

b)
<

c)
≤

d)
=

e)
Either = or ≥

**6. Statements:**K ≥ J; L = M; O < N; K <L; K < P; M ≥ N

**Conclusions:**

I.
M < O

II.
J < L

III.
J > L

IV.
N < P

a)
None is true

b)
Only II and IV are true

c)
Only I and IV are true

d)
Only II is true

e)
Only III is true

**7. Statements:**

B
> D; D ≥ H; E ≥ A; C < B; B = A

**Conclusions:**

I.
A > H

II.
H < B

III.
E > D

IV.
H < E

a)
None is true

b)
Only I is true

c)
Only II and III are true

d)
Only IV is true

e)
All are true

**8. Statements:**A = Z; B ≥ Y; Y > D; A < F; Z < D

**Conclusions:**

I.
B < F

II.
B > Z

III.
A ≠ Y

IV.
B ≥ D

a)
None is true

b)
Only IV is true

c)
Only II and III are true

d)
Only II, III and IV are tre

e)
Only II is true

**9. Statements:**A < S < Z; Z ≥ B; Z < Y > X; B > A

**Conclusions:**

I.
Y > S

II.
B = S

III.
S < X

IV.
A > Y

a)
None is true

b)
Only I is true

c)
Only I and II are true

d)
Only III and IV are true

e)
All are true

**10. Which of the following expressions will be true if the given expression**

**‘P ≥ Q < R > S = T’**

**is definitely true?**

a)
Q > T

b)
P > S

c)
P < R

d)
R < T

e)
None of these

**11. Statements:**A > X; B ≤ Q; P = M; M ≥ A; A ≤ B

**Conclusions:**

I.
P ≤ X

II.
B ≤ X

III.
A ≥ Q

IV.
Q > X

a)
None is true

b)
Only I is true

c)
Only II is true

d)
Only III is true

e)
Only IV is true

**12. Statements:**Q < A < P, T < B > C, S ≥ R, R ≤ S > T

**Conclusions:**

I.
A = B

II.
S is the largest

III.
P is the largest

a)
None is true

b)
Only I is true

c)
Only III is true

d)
Only II is true

e)
Either II or III are true

**13. Statements:**

A
≤ B < C > D ≥ E; B ≤ F < H; I ≤ K ≤ E

**Conclusions:**

I.
A ≤ C

II.
C < F

III.
B <
H

IV.
D ≥ K

V.
B <
K

a)
Only III and IV are true

b)
I, III and IV are true

c)
II and IV are true

d)
II and either I or III are true

e)
Only II is true

**14. Statements:**

Y>X;
X ≤ S; W ≤ X; R > V; V = X; S < T; R ≤ U

**Conclusions:**

I.
X< U

II.
Y> T

III.
W < U

a)
All are true

b)
Only I and II are true

c)
Either II or III are true

d)
Only I and III are true

e)
None is true

**15. Statements:**

L
= M; M > N; L < H; G > I; G ≤ N; J < N; J ≤ K

**Conclusions:**

I.
M > K

II.
I < L

III.
H = J

a)
None is true

b)
Only I is true

c)
Only II is true

d)
Only III is true

e)
All are true

**Solutions:**

**1. A)**Given statements:

R
≤ J > M, J ≥ L = S < N, S ≥ P

On
simplifying:

R
≤ J, J > M, J ≥ L = S ≥ P, L = S < N

Conclusions:

I.
P ≤ J → Clearly True (as J ≥ L = S ≥ P → J ≥ P)

II.
R = L → False (as R ≤ J and J ≥ L → R ≤ J ≥ L → clear relationship between R
and L cannot be determined)

III.
M < N → False (as J > M, J ≥ L and L = S < N, so we get, M < J ≥ L
= S < N → M < J ≥ L < N → clear relationship between M and N cannot be
determined)

Hence
only conclusion I is true.

**2. D)**Given statements:

S
< P = Z ≤ M, Z ≥ K ≥ R, S ≥ J

On
combining:

J
≤ S < P = Z ≤ M,

M
≥ Z ≥ K ≥ R

Conclusions:

I.
M ≥ R → Clearly True (as M ≥ Z ≥ K ≥ R → M ≥ R)

II.
Z > J → Clearly True (as J ≤ S < P = Z → J < Z)

III.
S < Z ≥ R → Clearly True (as S < P = Z and Z ≥ K ≥ R, so we get, S < P
= Z ≥ K ≥ R → S < Z ≥ R)

Hence
all the conclusions are true.

**3. A)**Statement: E ≥ C = B; D = C ≥ M > N

→
E ≥ C ≥ M > N, C = B = D

Let
us check each conclusion one by one.

I)
D = B → True

II)
N ≤ E → False (E ≥ C ≥ M > N → E ≥ M > N → E > N)

III)
N > E → False (E ≥ C ≥ M > N → E ≥ M > N → E > N)

Hence,
only conclusion I is true.

**4. D)**Given expression: U < V < W < X < Y = Z ≥ A = B > C.

Let’s
check validity of all options:

a)
Z > C ⇒ True as Z ≥ B and B > C.

b)
U < Y ⇒ True as Y > V and V > U.

c)
Y > C⇒ Tue as Y ≥ B and B > C.

d)

**Z < U****⇒****Not true as Z > V and V > U**.
e)
B < Y ⇒ Probably True as Y ≥ B

Hence,
only option Z < U isn’t true.

**5. D)**A > B ≥ C ? D ≤ E = F

__For A > D__→ C can be equal to D or greater than D or both because A > C → C = D; C > D or C ≥ D.

__For F ≥ C__→ Since F ≥ D that means we have to make no further change in relationship of D and C. All we have to do is make them equal. → C = D ≤ F.

Hence,
‘=’ sign is common in both conditions.

→
A > B >

**C = D**≤ E = F
Here,
A > D and F ≥ C are definitely true.

**6. D)**

**Given statements:**K ≥ J; L = M; O < N; K < L; K < P ; M ≥ N

On
combining: J ≤ K < L = M ≥ N > O; K < P

**Conclusions:**

I.
M < O → False (as M ≥ N > O)

II.
J < L → True (as J ≤ K < L)

III.
J > L → False (as J ≤ K < L)

IV.
N < P → False (No relation between N and P)

Therefore,
conclusion II is true.

**7. E)**Given statements: B > D; D ≥ H; E ≥ A; C < B; B = A

On
combining: E ≥ A = B > D ≥ H; C < B

**Conclusions:**

I.
A > H → True (as A = B > D ≥ H → A > H)

II.
H < B → True (as H ≤ D < B → H <B)

III.
E > D → True (as E ≥ A = B > D → E > D)

IV.
H < E → True (as E ≥ A > D ≥ H → E > H)

Therefore,
all the given conclusions are true.

**8. C)**Given statements: A = Z; B ≥ Y; Y > D; A < F; Z < D

On
combining: F > A = Z < D < Y ≤ B

**Conclusions:**

I.
B < F → False (F > A = Z < D < Y ≤ B → thus we cannot determine the
relation between B and F)

II.
B > Z → True (Z < D < Y ≤ B → Z < B)

III.
A ≠ Y → True (A = Z < D < Y → A < Y)

IV.
B ≥ D → False (D < Y ≤ B → D < B)

Hence,
conclusion II and III follows.

**9. B)**Given statements: A < S < Z; Z ≥ B; Z < Y > X; B > A

On
combining: B > A < S < Z < Y > X; Z ≥ B

**Conclusions:**

I.
Y > S → True (as S < Z and Z < Y → S < Y)

II.
B = S → False (as B > A and S > A → thus clear relation between B and S
cannot be determined)

III.
S < X → False (as S < Y and X < Y → thus clear relation between S and
X cannot be determined)

IV.
A > Y → False (as A < S < Z < Y → A < Y)

Therefore,
only conclusion I is true.

**10. E)**Given, P ≥ Q < R > S = T

Now
we will check each relation:

1)
Q > T, not true as no relation between Q and T can be established.

2)P
> S, not true as no relation between P and S can be established.

3)
P < R, is possibly true if P = Q as P ≥ Q and R > Q are true, but it is
not definitely true.

4)
R < T, not true as R > T.

Thus
the only possible expression which can true is P < R.

**11. E)**Given statements: A > X; B ≤ Q; P = M; M ≥ A; A ≤ B

Combining
statements: P = M ≥ A > X; X < A ≤ B ≤ Q; P = M

Conclusions:

I.
P ≤ X → False (as P = M, M ≥ A, A > X, thus P > X)

II.
B ≤ X → False (as X < A, A ≤ B, thus X < B)

III.
A ≥ Q → False (as Q ≥ B, B ≥ A, thus Q ≥ A)

IV.
Q > X →True (as Q ≥ B ≥ A > X, thus Q > X)

**Therefore, only conclusion IV is true.**

**12. A)**Given statements areQ < A < P, T < B > C, S ≥ R, R ≤ S > T

Combining
all the statements we get, R ≤ S > T < B > C and R ≤ S > Q < A
< P

Conclusions:

I.
A = B→ False (as S > Q < A and S > T < B → So no clear relation
between A and B is provided)

II.
S is the largest → False (as R ≤ S > T < B > C and S > Q < A
< P →So, Either S, P or B can be the largest)

III.P
is the largest → False (as R ≤ S > T < B > C and S > Q < A <
P →So, Either S, P or B can be the largest)

Hence,
none of conclusion is true.

**13. A)**Given statement:A ≤ B < C > D ≥ E; B ≤ F < H; I ≤ K ≤ E

On
combining: A ≤ B < C > D ≥ E ≥ K ≥ I; B ≤ F < H

Conclusion:

I.
A ≤ C → False as A ≤ B < C, thus A < C.

II.
C < F → False as F ≥ B < C, therefore there is no definite relation
between them.

III.
B < H → True as B ≤ F < H, thus B < H.

IV.
D ≥ K → True as D ≥ E ≥ K, thus D ≥ K.

V.
B < K → False as B < C > D ≥ E ≥ K, there is no definite relation
between them.

Hence
only conclusion III and IV follows.

**14. D)**Given statements: Y>X; X ≤ S; W ≤ X; R > V; V = X; S < T; R ≤ U

On
combining: Y>X = V < R ≤ U; W ≤ X ≤ S < T

Conclusions:

I.
X< U → True (as X = V < R ≤ U → X< U)

II.
Y> T→ False (as Y>X and X ≤ S < T → Y>X ≤ S < T → thus clear
relation between Y and T cannot be determined)

III.
W < U → True (as X = V < R ≤ U and W ≤ X → W ≤ X = V < R ≤ U → W <
U)

Therefore,
conclusions I and III are true.

**15. C)**Given statements: L = M; M > N; L < H; G > I; G ≤ N; J < N; J ≤ K

On
combining: H > L = M > N ≥ G > I; N > J ≤ K

Conclusions:

I.
M > K → False (as M > N and N > J ≤ K → M > N > J ≤ K → thus
clear relation between M and K cannot be determined)

II.
I < L→ True (as L = M > N ≥ G > I → L > I)

III.
H = J→ False (as H > L = M > N and N > J → H > L = M > N > J
→ H > J)

Therefore,
only conclusion II follows.