# Reasoning Ability (Inequalities) Practice Questions (28 – 09 – 2017)

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
III. M < N
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 isnt 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.