MCQ Test: Inequalities - 2 - Bank Exams MCQ

Statements:   B > A ≥ T > F = Y ≤ S < D
Conclusions:  F < D ,  A > S
For conclusion I: F < D
Here, the common sign between F and D is '<', hence F < D.
Thus conclusion I follows.
For conclusion II: A > S
Here, we can see the opposite sign between A and S, thus no relationship can be established between them.
Thus conclusion II does not follow.
Therefore only conclusion I follows.
Hence option A is correct.

Statements:   M < T < G ≤ J = U > Y > R
Conclusions:  G < U ,  J > R 
Here, the common sign between G and U is '≤', hence G < U does not follow.
Therefore conslusion I does not follow.
And, the common sign between J and R is '>', thus J > R follows.
Therefore conclusion II follows.
Hence option C is correct.

Statements:   M > H = A ,  X ≥ G < H ,  Y < M < P  ,  G > O > K
Conclusions:   P > X ,  G < P ,  Y < H
For conclusion I: P > X
From statements II and III, we get:
X ≥ G < H < M < P
Here, we can see the opposite sign between P and X, thus no relationship can be established between them.
Thus conclusion I does not follow.
For conclusion II: G < P
From statements I, II and III, we get:
G < H < M < P
Here, the common sign between G and P  is ‘< ’. Hence G < P.
Hence conclusion II follows.
For conclusion III: Y < H
From statements I and III, we get:
Y < M > H
Here, we can see the opposite sign between Y and H , thus no relationship can be established between them.
Thus conclusion III does not follow.
Therefore only conclusion II follows.
Hence option D is correct.

Statements:   Y < O ≤ G ≤ K = U > L > P
Conclusions:  O = U ,  U > O 
Here, the common sign between O and U is '≤', hence O ≤ U.
Thus, either O < U or O = U.
Therefore either conclusion I or II follows.
Hence option B is correct.

Statements: L ≥ A ≥ C ,  K = Y ≤ C ,  H > D ≤ K
Conclusions:  D < A  ,  A = D ,  L > Y
For conclusion I: D < A
From statements I, II and III, we get:
D ≤ K = Y ≤ C ≤ A
Here, the common sign between D and A is '≤', hence D ≤ A.
Thus conclusion I does not follow individually.
For conclusion II: A = D
From statements I, II and III, we get:
D ≤ K = Y ≤ C ≤ A
Here, the common sign between D and A is '≤', hence D ≤ A.
Thus conclusion II does not follow individually.
On combining conclusion I and II we get D ≤ A.
Therefore either conclusion I or II follows.
For conclusion III: L > Y
From statements I and II, we get:
Y ≤ C ≤ A ≤ L
Thus the common sign between Y and L is '≤', Therefore Y ≤ L is the true relationship
Hence conclusion III does not follow.
Therefore either conclusion I or II follows.
Hence option B is correct.

Statements:   W < K , Z < M ≤ W ,  B > Z ,  R ≤ K
Conclusions:  W < B ,      R > W
For conclusion I: W < B
From statements II and III, we get:
W ≥ M > Z < B
Here, we can see the sign of inequalities are getting opposite between W and B, thus no relationship can be established between them.
Thus conclusion I does not follow.
For conclusion II: R > W
From statements I and IV, we get:
R ≤ K > W
Here too, we can see the opposite sign between R and W, thus no relationship can be established between them either.
Thus conclusion II does not follow either.
Therefore neither conclusion I nor II follows.
Hence option E is correct.

Statements:   I ≥ H > A ,  Q < A = P , H ≥ B ,  I ≤ G
Conclusions:  P < I ,      G > B
For conclusion I: P < I
From statements I and II , we get:
I ≥ H > A = P 
Here, the common sign between I and P is '>', thus I > P or P < I.
Thus conclusion I follows.
For conclusion II: G > B
From statements III and IV, we get:
G ≥ I ≥ H ≥ B 
Here, the common sign between G and B is '≥', thus G ≥ B.
Thus conclusion II does not follow.
Therefore only conclusion I follows.
Hence option C is correct.

Statements:   X > Y ,  M =  X < Z ,  T < S ,  G ≥ T
Conclusions:  G > S ,      Y < Z
For conclusion I: G > S
From statements III and IV, we get:
G ≥ T < S
Here, we can see the opposite sign between G and S, thus no relationship can be established between them.
Thus conclusion I does not follow.
For conclusion II: Y < Z
From statements I and II, we get:
Z > M = X > Y
Here, the common sign between Z and Y is ‘>’. Hence Z > Y.
Thus conclusion II follows.
Therefore only conclusion II follows.
Hence option D is correct.

Statements:   I ≥ H > A ,  Q < A = P , H ≥ B ,  I ≤ G
Conclusions:  G = H ,      G > H
For conclusion I: G = H
From statements I and IV, we get:
G ≥ I ≥ H
Here, the common sign between G and H is '≥', thus G ≥ H.
Thus conclusion I does not follow individually.
For conclusion II: G > H
From statements I and IV, we get:
G ≥ I ≥ H
Here, the common sign between G and H is '≥', thus G ≥ H.
Thus conclusion II does not follow individually.
On combining both the conclusions we get , G ≥ H.
Therefore either conclusion I or II follows.
Hence option B is correct.

Statements:   L ≤ M , O ≥ H ,  F = M ,  K ≥ H ,  I < J > F
Conclusions:  L < J ,      O ≥ K
For conclusion I: L < J
From statements I, III and V, we get:
L ≤ M = F < J
Here, the common sign between L and J is '<', thus L < J.
Thus conclusion I follows.
For conclusion II: O ≥ K
From statements II and IV, we get:
O ≥ H ≤ K
Here, we can see the opposite sign between O and K, thus no relationship can be established between them.
Thus conclusion II does not follow.
Therefore only conclusion I follows.
Hence option C is correct.