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.
