Coded Inequalities MCQ - 1 - Bank Exams MCQ

Explanation:
To understand the answer, let's analyze each conclusion separately:
Conclusion I: C > H
- We have A ≥ H and B ≥ C.
- Since A ≥ B, we can deduce that B ≥ H.
- Therefore, we cannot conclude that C > H.
Conclusion II: H > B
- We have A ≥ B and A ≥ H.
- However, we cannot determine the relationship between H and B based on the given information.
Conclusion III: B > G
- We have C > G and B ≥ C.
- Since B ≥ C and C > G, we can conclude that B > G.
Conclusion IV: I > A
- We have I = B and A ≥ B.
- Therefore, we cannot conclude that I > A.
Based on the analysis, only Conclusion III (B > G) is true. Therefore, the correct answer is E.

Explanation:
Let's analyze each conclusion one by one:
Conclusion I: F < B
- We have A = B, and B < F. Therefore, F > A, and since A = B, F > B. So, conclusion I is not true.
Conclusion II: F > G
- We have G > C, and C ≤ F. We cannot definitely conclude F > G because there might be a case where G = F. So, conclusion II is not true.
Conclusion III: A > G
- We have A = B, and G > C, and C ≤ F, and B < F. We cannot definitely conclude A > G because there might be a case where A = G. So, conclusion III is not true.
Conclusion IV: A > C
- We have A = B, and C ≤ F, and B < F. We cannot definitely conclude A > C because there might be a case where A = C. So, conclusion IV is not true.
Since none of the conclusions are true, the correct answer is:
E: None is true

Given statements: - A ≥B>C = D>E; F>B; Z<D; M>A

M > Z- True (As Per M>A ≥B>C=D>Z)

M = Z- False (because when we moving from M to Z we see > Sign as M>A so we give priority to > Sign)

Z > C- False (Because we can see that Z<D and D = C. Therefore, Z>D holds Definitely False)

B = D- False (Because B > C = D. So B=D holds definitely False)

Hence, the correct answer is M>Z.

Explanation:
Let's analyze each conclusion one by one:
Conclusion I: T > R**
- Given: R < S ≤ T
- Since R < S and S ≤ T, we can conclude that T > R.
- So, Conclusion I is true.
Conclusion II: T > Q
- Given: P ≥ Q > R < S ≤ T
- We cannot directly conclude that T > Q from the given information. There is no specific relationship given between T and Q that allows us to determine their order.
- So, Conclusion II is not true.
Conclusion III: R < P
- Given: P ≥ Q > R < S ≤ T
- Since P ≥ Q and Q > R, we can conclude that P > R.
- So, Conclusion III is true.
Conclusion IV: Q > P
- Given: P ≥ Q > R < S ≤ T
- The given information states that P ≥ Q, which means P can be greater than or equal to Q, but not necessarily less than Q.
- So, Conclusion IV is not true.
Based on the analysis, only Conclusions I and III are true. Therefore, the correct answer is:
C: Only I and III are true.Only I and III are true

The correct answer is E.

Given:

P < Q ≥ R > S ≤ T

Conclusions:

I. T ≥ R

This is true. Since R > S ≤ T, then T ≥ R.

II. P < R

This is true. Since P < Q ≥ R, then P < R.

III. Q > S

This is not necessarily true. We know that Q ≥ R > S, but we do not know the relationship between Q and S.

IV. S < P

This is not necessarily true. We know that P < Q ≥ R > S, but we do not know the relationship between P and S.

Therefore, only conclusions I and II are true.

The correct answer is E.

Given:

• M<N<O=P
• N = Q

Conclusions:

I. P>M

This is true. Since M<N<O=P, then P>M.

II. Q<O

This is true. Since N = Q and N<O, then Q<O.

Therefore, both conclusions I and II are true.

Explanation of the answer:
Given Statements:
- A > N = I > W < O < P
- O > S
- T < N
We need to find the validity of the given conclusions:
1. P > S
2. A < W
Conclusion 1: P > S
- From the first statement, we have O < P
- From the second statement, we have O > S
- Combining these two, we get: S < O < P, which implies P > S
- Therefore, Conclusion 1 is true.
Conclusion 2: A < W
- From the first statement, we have A > N = I > W
- This implies A > W, which is opposite to the given conclusion (A < W)
- Therefore, Conclusion 2 is false.
Based on the above analysis, the correct answer is **A: Only I is true**.Only I is true

Explanation:
Given statements:
- M≥N≥O
- P≤Q≤R
We need to analyze the given conclusions:
i. M>Q
ii. N≤R
Let's analyze each conclusion:
Conclusion i. M>Q
- We know M≥N≥O, but we have no information about the relationship between O and Q. Hence, we cannot conclude anything about the relationship between M and Q. So, conclusion i is not necessarily true.
Conclusion ii. N≤R
- We know N≥O and P≤Q≤R, but we have no information about the relationship between O and P. Hence, we cannot conclude anything about the relationship between N and R. So, conclusion ii is not necessarily true.
Since neither conclusion i nor conclusion ii is necessarily true, the answer is:
D: Neither I nor II is true

Explanation:
Given Statements:
- M- H≥F- J≥P
Let's analyze the given conclusions:
Conclusion I: P≤B
- From the first statement, we have P≤G = F≥B.
- We can infer that P≤G and G=F≥B.
- However, we cannot directly conclude that P≤B from the given information.
Conclusion II: M- From the first statement, we have M- From the second statement, we have H≥F.
- From the third statement, we have J≥P.
- Since M- We are also given H≥F- Since H≥F and G=F, we can infer that H≥G.
- Since M
Answer: B (Only II is true)

1. Decode Symbols:

   • O & A → O = A

   • A $ R → A ≥ R → O ≥ R (since O = A)

   • R # S → R < S

   • S * Q → S ≤ Q → Q ≥ S

2. Derive Relationships:

   • From R < S ≤ Q, conclude Q > R (Conclusion I: True).

   • From O ≥ R, two possibilities:

     • O = R (Conclusion III: True).

     • O > R (Conclusion IV: True).

3. Evaluate Conclusions:

   • Conclusion I (Q @ R): Always true (Q > R).

   • Conclusions III (R & O) and IV (R # O): Mutually exclusive and dependent on whether O = R or O > R. Exactly one must be true.

E is correct because Conclusion I is always true, and either III or IV is true based on the given constraints.

Key Validation:

• Example 1: O > R → I and IV true.

• Example 2: O = R → I and III true.

• Conclusion II (S @ O): Not necessarily true (depends on specific values).

E: Either III or IV and I are true is the correct choice.

1. Decode Symbols:

   • A * E → A ≤ E

   • E $ F → E ≥ F

   • F # O → F < O

   • O @ L → O > L

2. Combine Relationships:

   • From the statements:

     • A ≤ E

     • E ≥ F

     • F < O

     • O > L

3. Analyze Conclusions:

   • I. L # F (L < F):

     • O > L and F < O. L and F are independent; L can be < or > F. Not always true.

   • II. E @ O (E > O):

     • E ≥ F < O. E can be <, =, or > O. Not always true.

   • III. A # O (A < O):

     • A ≤ E ≥ F < O. If E > O, A could be > O (e.g., A=6 ≤ E=6, O=5). Not always true.

   • IV. E @ L (E > L):

     • O > L and E ≥ F < O. E can be < or > L (e.g., E=3, L=4). Not always true.

None of the conclusions (I–IV) are necessarily true based on the given statements.
E: None is true

I, II and IV are true

$ → < 
# → = 
% → > 
Statements: T%I, I#L, L%U 
T> I=L>U 
Conclusions:
 I. T$L → T < L(False) 
II. U$T → U < T(True)

1. Decode Symbols:

   • A $ E → A ≥ E

   • E @ F → E > F

   • F * G → F ≤ G

   • G # H → G < H

2. Derive Relationships:

   • From A ≥ E > F → A > F (Conclusion IV: True).

   • H > G ≥ F < E: H and E are independent; H can be > or < E (Conclusion I: Not always true).

   • A ≥ E > F ≤ G: A and G are independent; A can be ≥ or < G (Conclusion II: Not always true).

   • E > F ≤ G < H: E and H are independent; E can be > or < H (Conclusion III: Not always true).

3. Conclusion Validation:

   • Conclusion IV (A @ F) is always true because A≥E>F  ⟹  A>FA≥E>F⟹A>F.

   • Conclusions I, II, and III are not necessarily true due to variable relationships.

E: Only IV is true

If only Conclusion I follows

If neither Conclusion I nor II follows

If only Conclusion II follow

If only Conclusion II follows

Option 2 : Only I is True

P<A≤U≤T;W≥O>T

≥, =, ≥,<

V ≥ E = G ≥ W = Y ≥ D

A < B

P<A≤S≤T;V≥O>T<B