MCQ Test: Inequalities - 1 - Bank Exams MCQ

Statements: R > I = N > P      Y ≥ R > K      N ≤ E < Z
Conclusions: K > I,         I < Z
For conclusion I: K > I
From the statements I and II, we get:
I < R > K
Here, the signs on inequalities between I and R are getting reversed. Conclusion I hence doesn't follow.

For conclusion II: I < Z
Combining statements I and III, we get:
I = N ≤ E < Z
Here, the common sign between I and Z is ‘<’ and the given conclusion is also I < Z. Hence, conclusion II follows.
Hence, the correct answer is would be ‘Only conclusion II follows’.

Statements:   B ≥ P = M ,    X > B < T,    Y = H ≤ X ,   R > Y > N
Conclusions:  P > H ,    P = H,     R > X
For Conclusion I: P > H
From statements I, II and III, we get:
H ≤ X > B ≥ P
Here, we can see the opposite sign between P and  H , thus no relationship can be established between them.
Hence conclusion I does not follow.
For Conclusion II: P = H
From statements I, II and III, we get:
H ≤ X > B ≥ P
Here, we can see the opposite sign between P and  H , thus no relationship can be established between them.
Hence conclusion II does not follow.
For Conclusion III: R > X
From statements II and III, we get:
R > Y = H ≤ X
Here, we can see the opposite sign between R and X, thus no relationship can be established between them.
Hence conclusion III does not follow.
Therefore none of the conclusions follows.
Hence option E is correct.

Statements:   C < H = J ,      X ≤ Y < J ,      N > X ≥ Z
Conclusions:  Y > Z ,      Y = Z
For conclusion I: Y > Z
From statements I and III, we get:
Y ≥ X ≥ Z
Here, the common sign between Y and Z is ‘≥’. Hence Y ≥ Z Thus conclusion I does not follow individually.
For conclusion II: Y = Z
From statements I and III, we get:
Y ≥ X ≥ Z
Here, the common sign between Y and Z is ‘≥’. Hence Y ≥ Z. Thus conclusion II also does not follow individually.
On combining conclusions I and II, we get: Y ≥ Z, which is the true relationship.
Thus either conclusion I or II follows.
Hence option B is correct.

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

Statements:   F < G < D ,      D < H > C ,      F = C < A
Conclusions:  G < C ,      H = A
For conclusion I: G < C
From statements I and III, we get:
C = F < G
Here, the common sign between C and G is ‘<’. Hence C < G. Thus conclusion I does not follow.
For conclusion I: H = A
From statements II and III, we get:
H > C < A
Here, we get opposite signs between H and A. Thus no relationship can be established between them.
Hence conclusion II does not follow.
Therefore neither conclusion I nor II follows.
Hence option E is correct.

Interpretation of the coded symbols:
A @ B means 'A is not less than B' i.e. A ≥ B
A $ B means 'A is not more than B' i.e. A ≤ B
A # B means 'A is neither less nor more than B' i.e. A = B
A * B means 'A is neither more than nor equal to B' i.e. A < B
A % B means 'A is neither less than nor equal to B' i.e. A > B
We will decode the given statements as per the above interpreted signs.

Statements: V ≥ I = E < D ;  N ≤ E > B = F
Conclusions: I. D > F  II. V ≥ B
For conclusion I: 
From both the statements we get:
F = B < E < D
The common sign between F and D is ‘<’, thus F < D or D > F is true.
Hence conclusion I follows.

For conclusion II:
From both the statements we get:
V ≥ I = E > B
The common sign between V and B is '>', thus V > B is the actual relationship.
Hence conclusion II does not follow.
Therefore only conclusion I follows.
Hence option A is correct.

Interpretation of the coded symbols:
A @ B means 'A is not less than B' i.e. A ≥ B
A $ B means 'A is not more than B' i.e. A ≤ B
A # B means 'A is neither less nor more than B' i.e. A = B
A * B means 'A is neither more than nor equal to B' i.e. A < B
A % B means 'A is neither less than nor equal to B' i.e. A > B
We will decode the given statements as per the above interpreted signs.

Statements: F < D ≤ E = R < S ≥ V > K
Conclusions: I. D < R  II. D = R

For conclusion I: 
D ≤ E = R
The common sign between D and R is ‘≤’, thus D ≤ R is the actual relationship.
So either D < R or D = R is true.
Therefore either conclusion I or II follows.
Hence option D is correct.

Interpretation of the coded symbols:
A @ B means 'A is not less than B' i.e. A ≥ B
A $ B means 'A is not more than B' i.e. A ≤ B
A # B means 'A is neither less nor more than B' i.e. A = B
A * B means 'A is neither more than nor equal to B' i.e. A < B
A % B means 'A is neither less than nor equal to B' i.e. A > B
We will decode the given statements as per the above interpreted signs.
Statements: V ≥ I = E < D ;  N ≤ E > B = F
Conclusions: I. V > F  II. V ≥ N
For conclusion I: 
From both the statements we get:
V ≥ I = E > B = F
The common sign between V and F is '>', thus V > F is true.
Hence conclusion I follows.

For conclusion II:
From both the statements we get:
V ≥ I = E ≥ N
The common sign between V and N is '≥', thus V ≥ N is the actual relationship.
Hence conclusion II follows.
Therefore both conclusions follow.
Hence option C is correct.

Statements: C > A ≥ T , S < E = T
Conclusions: A > E , C > S
After combining both the statements, we get:
C > A ≥ T = E > S
Thus A > E is false as the true relationship is A ≥ E.
C > S is true.
Hence only conclusion II follows.
Hence option B is correct.

Given statement: G ≤ L ≥ O ≥ W ≥ I < N
Thus, L ≥ I or I ≤ L is true.
It means either I < L or L = I is true.
Thus, Conclusion I and II make a complementary pair.
Hence, either conclusion I or II is true.
Hence, option C is correct.

Given statement:
R > M ≥ T ≤ Q = S
Thus, we can’t compare R and Q or Q and M.
Hence neither I (R > Q) nor II (Q ≥ M) is true.
Hence, option D is correct.

Statements: F < U ≤ N ,  D > H < U = B
Conclusions: H < N ,  H = N

From statements I and II , we get:
H < U ≤ N
Thus H < U is true whereas H = N is false.
Hence only conclusion I follows.
Hence option A is correct.

Given statement: G ≤ L ≥ O ≥ W ≥ I < N
Thus, we can’t compare G and O or W and N,
Hence neither conclusion I (O > G) nor II (W < N) is true.
Hence, option D is correct.

Statements: P ≤ Q ≤ R = S,        U ≥ V ≥ S
Conclusions: P < U,         P = U
For statements I and II:  P < U    and     P = U
Combining statements I and II, we get:
P ≤ Q ≤ R = S ≤ V ≤ U
Here, the common sign between P and U is ‘≤’ and the given conclusions are P < U and P = U. Hence, either P < U or P = U follows.
Hence, the correct answer would be Either conclusion I or conclusion II follows.

Statements: L > R,         R ≥ T,       T ≥ M
Conclusions: M ≥ R,        T < L
For conclusion I: M ≥ R
Combining statements II and III, we get:
R ≥ T ≥ M
Here, the common sign between R and M is ‘≥’ and the given conclusion is M ≥ R. Hence, conclusion I does not follow.
For conclusion II: T < L
Combining statements I and II, we get:
L > R ≥ T
Here, the common sign between L and T is ‘>’ and the given conclusion is T < L. Hence, conclusion II follows.
Hence, the correct answer would be ‘Only conclusion II follows’.