Directions: In the following question, assuming the given statements to be…
2025
Directions: In the following question, assuming the given statements to be true, find which of the given conclusions is/are definitely true, and then answer accordingly.
- A.
Only II is true
- B.
Only I is true
- C.
Both I and II are true
- D.
Either I or II is true
- E.
None is true
Attempted by 7 students.
Show answer & explanation
Correct answer: C
Concept: In a combined inequality/equality chain, relations propagate transitively: if a ≤ b and b < c, then a < c, since the overall relation between the two ends is strict whenever any single link along the path is strict. If a = b, every relation stated for b transfers directly to a, and two separate statements that share a common term can be merged exactly at that term using this substitution.
Application:
Since B = F, substitute one for the other wherever it appears in either statement, as the two terms denote the same value.
Combine the first statement, B = F ≤ J < V ≤ W: from B ≤ J and J < V, the link between B and V is strict (B < V); extending through V ≤ W gives B < W directly from this one statement.
In the second statement, B < U: substituting F for B (from B = F) gives F < U, which is the same relation as U > F, obtained directly from the same substitution.
Both required relations come out of the given statements without needing any further assumption, so both listed conclusions are established.
Cross-check: Assigning values that satisfy every symbol in both statements — for instance F = B = 1, J = 2, V = 3, W = 4, U = 5, P = 0 — confirms B = 1 ≤ J = 2 < V = 3 ≤ W = 4 and B = 1 < U = 5 > P = 0 hold together; for this assignment, B = 1 < W = 4 while U = 5 > F = 1, matching the result above, and any other assignment consistent with the stated symbols reproduces the same pair of outcomes.
Result: Both of the listed conclusions are definitely true.