Read the given statement and conclusions carefully. Decide which of the given conclusions is/are definitely TRUE from the statement. Statement: F < B < E ≤ C = D ≥ A < G Conclusion I: G < F Conclusion II: C > G
Analyzing Inequality Statement
The given statement is:
$F < B < E ≤ C = D ≥ A < G$
Let's break down the relationships:
- From the statement, we can establish the following direct and indirect relationships:
- $F$ is less than $B$.
- $B$ is less than $E$.
- $E$ is less than or equal to $C$.
- $C$ is equal to $D$.
- $D$ is greater than or equal to $A$.
- $A$ is less than $G$.
- Combining these, we get a chain: $F < B < E ≤ C = D ≥ A < G$.
Evaluating Conclusion I
Conclusion I: $G < F$
From the combined chain $F < B < E ≤ C = D ≥ A < G$, we can clearly see that $F$ is less than $G$ ($F < G$). Therefore, the conclusion $G < F$ is definitely FALSE.
Evaluating Conclusion II
Conclusion II: $C > G$
We know that $C = D ≥ A < G$. This means $C$ is related to $G$ through $D$ and $A$.
- $C$ is equal to $D$.
- $D$ is greater than or equal to $A$.
- $A$ is strictly less than $G$.
Consider these scenarios:
- If $C = D = 10$, $A = 5$, and $G = 11$, then $C < G$.
- If $C = D = 10$, $A = 9$, and $G = 10$, then $C = G$.
- If $C = D = 10$, $A = 5$, and $G = 9$, then $C > G$.
Since there are possible scenarios where $C > G$ is not true ($C < G$ or $C = G$), Conclusion II is NOT definitely TRUE.
Final Determination
Conclusion I is FALSE. Conclusion II is not definitely TRUE.
Therefore, neither Conclusion I nor Conclusion II is definitely TRUE.
Similar Questions
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
The given statements are followed by two conclusions. Find out which conclusion is FALSE based on the given statements.
Statements:
J > K = L, M ≥ N < K, O < J < P, N > Q > R
Conclusions:
I. P > M
II. N < P
A statement is given followed by two conclusions. Find which conclusion is TRUE based on the given statement.
Statement:
$P \ge T; Q = R \ge U; V \ge R < S; T \ge Q$
Conclusions:
I: $T \ge U$
II: $V > T$
The given statements are followed by two conclusions. Find out which conclusion is TRUE based on the given statements.
Statements:
$J > K = L, M \geq N < K, O < J < P, N = Q \geq R$
Conclusions:
I. $M > R$
II. $M = R$- A statement is given followed by two conclusions. Find which conclusion is FALSE based on the given statement.
Statement:
$P \ge T ; Q = R \ge U ; V \ge R > S ; T \ge Q$
Conclusions:
I: $V \ge Q$
II: $P > S$
Important Questions from Mathematical Inequalities
Which figure should replace the question mark (?) in the following series to continue the pattern?
Select the option that is related to the third term in the same way as the second term is related to the first term and the sixth term is related to the fifth term.
400 : 200 :: 248 : ? :: 256 : 128
Which of the following option figures will complete the pattern in the figure given below?
A square sheet of paper is folded along the dotted line successively along the directions shown and is then punched in the last. How would the paper look when unfolded?
Select the correct combination of mathematical signs that can sequentially replace the * signs and balance the given expression.
23 * 9 * 13 * 96 * 2 * 92
