Discussion
STATEMENT :
B ≥ A < K < F ; F < B = D
CONCLUSION I : B < K
CONCLUSION II : A > D
CONCLUSION III : D < F
CONCLUSION IV : F ≤ B
Answer: B
Correct answer: Only IV is true
Two statements are given: \( B \ge A < K < F \) and \( F < B = D \). The second is what makes the question tractable, because it feeds F back into B - and B into D.
Combining them gives \[ K < F < B = D, \] which settles three of the four conclusions outright.
I. \( B < K \): we have just shown \( K < F < B \), so \( B > K \). Definitely false.
II. \( A > D \): from \( B \ge A \) and \( B = D \) we get \( D \ge A \). Definitely false.
III. \( D < F \): from \( F < B = D \) we get \( D > F \). Definitely false.
IV. \( F \le B \): \( F < B \) is given, and a strict inequality satisfies the weak one. True.
Only IV holds. Conclusion IV is the one candidates most often reject, on the grounds that the statements say less than rather than at most; but \( \le \) asks only that F is not greater than B, which \( F < B \) guarantees.
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