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
Only Conclusion II follows
Inequality Statement Analysis
The problem asks us to determine which of the given conclusions logically follow from the provided statement. We need to analyze the relationships between the variables based on the inequalities.
The given statement is:
E < U > L > K ≤ T = H ≤ Q
Let's break down the statement and analyze each conclusion:
Conclusion I Evaluation: U > H
From the statement, we can establish the following chains:
U > LL > KK ≤ TT = H
Combining these, we get:
U > L > K ≤ T = H
This means U is greater than L, which is greater than K. K is less than or equal to T, and T is equal to H. So, the chain looks like U > ... > K ≤ H.
We know U is greater than K (since U > L > K). We also know K ≤ H. However, we cannot definitively determine the relationship between U and H. For instance:
- If
U = 5andH = 4, thenU > H. - If
U = 5andH = 6, thenU < H.
Since both possibilities exist, Conclusion I (U > H) does not definitely follow from the statement.
Conclusion II Evaluation: T ≤ Q
From the statement, we have the following direct relationships:
T = HH ≤ Q
We can substitute H in the second inequality with T from the first equality.
This gives us: T = H ≤ Q.
Based on the transitivity property of inequalities, if T is equal to H and H is less than or equal to Q, then T must be less than or equal to Q.
Therefore, Conclusion II (T ≤ Q) definitely follows from the statement.
Final Determination
Based on the analysis:
- Conclusion I:
U > H- Does not necessarily follow. - Conclusion II:
T ≤ Q- Definitely follows.
Thus, only Conclusion II is definitely true.
Similar Questions
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 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
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 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
Each of A, B, C and D has Rs 100. A pays Rs 20 to B, who pays Rs 10 to C, who gets Rs 30 from D. In this context, which one of the following statements is not correct?
