Equality And InequalityPage 1
Section1
Direction:In these questions relationship between different elements is shown in statements. The statements are followed by conclusions. Study the conclusions based on the given statement and select the appropriate answer.
1.  Statements:
A ≥ B = C
B < D ≤ E
Conclusions:
D > A
E > C  (a)Only conclusion 1 is true  (b)Only conclusion 2 is true  (c)Neither conclusion 1 nor 2 is true  (d)Either conclusion 1 or 2 is true 

Answer is: BGiven statements
A ≥ B = C …………(1)
B < D ≤ E …………(2)
Combining both statements, we get A ≥ B < D ≤ E
Thus, we can’t compare A and D. Hence Conclusion 1 (D > A) is not true.
Again, B = C < D ≤ E. Thus C < E or E > C is true. Hence, conclusions 2 is true.
2.  Statements:
L > U ≥ K
Z < U < R
Conclusions:
L > Z
K < R  (a)Neither conclusion 1 nor 2 is true  (b)Only conclusion 1 is true  (c)Both conclusions 1 and 2 are true  (d)Only conclusion 2 is true 

Answer is: DL > U ≥ K …..(1)
Z < U < R ……(2)
Combining both statements, we get L > U > Z. Thus, L > Z is true. Hence conclusion 1 is true.
Again, K ≤ U < R. Thus K < R is true. Hence, conclusion 2 is true.
3.  Statements:
Y < J = P ≥ R > I
Conclusions:
J > I
Y < R  (a)Neither conclusion 1 nor 2 is true  (b)Either conclusion 1 or 2 is true  (c)Only conclusion 1 is true  (d)Only conclusion 2 is true 

Answer is: CGiven statements
Y < J = P ≥ R > I
Thus, J > I is true, Hence conclusion 1 is true.
Again, we can't compare Y and R. Hence, 2 is not true.
4.  Statements:
V ≥ K > M = N
M > S
T < K
Conclusions:
T < N
V = S  (a)Neither conclusion 1 nor 2 is true  (b)Either conclusion 1 or 2 is true  (c)Only conclusion 1 is true  (d)Only conclusion 2 is true 

Answer is: AGiven statements
V ≥ K > M = N ………….(1)
M > S ……………………..(2)
T < k …………………….(3)
Combining (1) and (3), we get
T < K > M = N
We can't compare T and N.
Hence conclusion 1 (T < N) is not true.
Again, combining (1) and (2),
V ≥ K > M > S
Thus, Conclusion (2) (V = S) is not true.
5.  Statements:
P < L ≤ A > M = K ≥ E
Conclusions:
K ≤ L
P < E  (a)Neither conclusion 1 nor 2 is true  (b)Either conclusion 1 or 2 is true  (c)Only conclusion 1 is true  (d)Only conclusion 2 is true 

Answer is: AGiven statements
P < L ≤ A > M = K ≥ E
Thus, we can't compare L and K. Hence 1 is not true,
Again, we can't compare P and E. Hence 2 is not true.
Hence, neither 1 nor 2 is true.
6.  Statements:
P > R = A < Y
D < A
Conclusions:
1. P > D
2. D < Y  (a)Neither conclusion 1 nor 2 is true  (b)Either conclusion 1 or 2 is true  (c)Both conclusions 1 and 2 are true  (d)Only conclusion 1 is true 

Answer is: CGiven statements 
P > R = A < Y ………(1)
D < A ……….(2)
Combining (1) and (2), we get
P > R = A > D
Thus, P > D is true. Hence 1 is true.
Again, D < A < Y
So, D < Y is true. Hence 2 is true.
7.  Statements:
P > R = A < Y
D < A
Conclusions:
P < Y
R ≤ D  (a)Neither conclusion 1 nor 2 is true  (b)Either conclusion 1 or 2 is true  (c)Only conclusion 1 is true  (d)Both conclusions 1 and 2 are true 

Answer is: AGiven statements 
P > R = A < Y ………(1)
D < A ……….(2)
Now, from (1), P > R = A < Y
We can't compare P and Y. Hence 1 is not true.
From (1) and (2), we get
P > R = A > D. Hence R > D is true. Hence (2) ( R ≤ D ) is not true.
8.  Statements:
C ≥ R > A = S ≤ H
R < P < Q
Conclusions:
C > S
P < C  (a)Neither conclusion 1 nor 2 is true  (b)Either conclusion 1 or 2 is true  (c)Only conclusion 1 is true  (d)Only conclusion 2 is true 

Answer is: CGiven statement –
C ≥ R > A = S ≤ H ……..(1)
R < P < Q …………(2)
Now, from equation 1
C ≥ R > A = S ≤ H
Thus, C > S is true. Hence 1 is true.
Again combining equation1 and 2, we get
C ≥ R < R < Q
So, we can't compare P and C. Hence, equation 2 is not true.
9.  Statements:
C ≥ R > A = S ≤ H
R < P < Q
Conclusions:
H ≥ R
R < Q  (a)Only conclusion 1 is true  (b)Only conclusion 2 is true  (c)Neither conclusion 1 nor 2 is true  (d)Either conclusion 1 or 2 is true 

Answer is: BGiven statement –
C ≥ R > A = S ≤ H ……..(1)
R < P < Q …………(2)
From equation (2)
R < P < Q
Hence, R < Q is true. Hence 2 is true.
Again, R > A = S ≤ H
We can't compare H and R. Hence, statement 1 is not true.
10.  Statements:
S > M ≥ D > H ≤ R ≤ T < W
Conclusions:
S > H
W > H
R < W
M > T  (a)Only 1 , 2 and 3 are true  (b)Only 1 and 2 are true  (c)Only 1 and Either 2 or 4 are true  (d)All 1, 2 3 and 4 are true 

Answer is: AS > M ≥ D > H ≤ R ≤ T < W
Thus, S > H is true. Hence 1 is true. Again,
H < W or W > H is true. Hence 2 is true.
R < W is true. Hence 3 is also true. But we can't compare M and T.
Hence 4 is not true. Hence only 1, 2 and 3 are true.