A statement is given followed by two conclusions. Find which conclusion is TRUE based on the given statement. Statement: C < A ≤ T = D ≥ O; G ≥ D < S; T ≥ A Conclusions: I: A ≤ O II: C < G
Statement Analysis
The given statement provides a series of relationships between different variables:
- $C < A ≤ T = D ≥ O$
- $G ≥ D < S$
- $T ≥ A$ (This is consistent with $A ≤ T$ from the first part)
Let's combine these to understand the overall structure:
- From $C < A ≤ T$ and $T = D$, we establish $C < A ≤ T = D$.
- Adding $D ≥ O$ gives $C < A ≤ T = D ≥ O$.
- Adding $G ≥ D$ gives $C < A ≤ T = D ≤ G$.
- The relation $D < S$ is also given but does not influence the conclusions regarding C, A, O, and G.
Conclusion I Evaluation: A ≤ O
From the analysis, we have $A ≤ T = D$ and $D ≥ O$.
This means A is less than or equal to D, and D is greater than or equal to O. However, there's no fixed relationship between A and O based on these inequalities alone. A could be less than, equal to, or greater than O.
For instance:
- If T=D=5, A=3, and O=7, then $A < O$.
- If T=D=5, A=6, and O=3, then $A > O$.
Since $A > O$ is possible, Conclusion I ($A ≤ O$) is not necessarily true.
Conclusion II Evaluation: C < G
The combined chain of inequalities derived from the statement is $C < A ≤ T = D ≤ G$.
This chain directly shows that C is strictly less than A, which is less than or equal to T, which equals D, which is less than or equal to G.
Therefore, it logically follows that $C < G$.
Conclusion II is true.
Final Determination
Based on the analysis:
- Conclusion I ($A ≤ O$) is not necessarily true.
- Conclusion II ($C < G$) is necessarily true.
Hence, only Conclusion II follows from the given statement.
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Important Questions from Mathematical Inequalities
Directions: In the following question assuming the given statements to be true, find which of the conclusion(s) among given conclusions is/are definitely true and then give your answers accordingly.
Statement:
Y ≥ C < O ≥ F < R = B
Conclusions:
I. B > F
II. R > C
Directions: In each of the following questions assuming the given statement to be true, find which of the conclusions among given conclusions is / are definitely true and then give your answers accordingly.
Statement: E < U > L > K ≤ T = H ≤ Q
Conclusions:
I. U > H
II. T ≤ Q
Directions: In the following question assuming the given statements to be True, find which of the conclusion among given conclusions is/are definitely true and then give your answers accordingly.
Statements: Y > U ≥ Z ≥ K = X ≤ B ≤ A
Conclusions:
I. U = X
II. U > X
Directions: In each of the following questions assuming the given statement to be true, find which of the conclusions among given conclusions is/are definitely true and then give your answers accordingly.
Statement: S > L < P = T ≥ V > R
Conclusions:
I. P > R
II. S > V
In the question given, relations between different elements are shown in the statements. These statements are followed by two conclusions. Find out which of the given conclusions follow(s) the given statements and select the correct alternative from the given choices.
Statement:
L ≥ M = N < O, P < Q ≥ R = S ≥ L
Conclusion:
I. Q > M
II. N = Q
