Quantitative Logic — Trees in a Forest Facts: A forest has as many sandal trees as Ashoka trees. Three-fourths of all trees are old. One-half of all trees are at the flowering stage. Which statement must be true?

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:We are given totals and proportions for two equal groups of trees (sandal and Ashoka). The task is to infer a statement guaranteed by the data, regardless of how flowering trees are distributed. Given Data / Assumptions: Total trees = T. Sandal = T/2; Ashoka = T/2. Old trees = 3T/4. Flowering trees = T/2 (distribution unspecified). Concept / Approach: Use bounds: find the minimum number of old Ashoka trees consistent with the totals. Maximize old sandal trees to minimize old Ashoka trees, then compute the remainder of old trees that must belong to Ashoka. Step-by-Step Solution: Let old sandal = at most T/2 (all sandal trees old).Old total = 3T/4, so old Ashoka = 3T/4 − T/2 = T/4.Since Ashoka = T/2, old Ashoka proportion ≥ (T/4) / (T/2) = 1/2.Thus, at least one-half of the Ashoka trees are old, even in the extreme case. Verification / Alternative check: Any reduction in old sandal increases old Ashoka beyond T/4, so the one-half lower bound is safe. Why Other Options Are Wrong: a,b: “All” flowering is not guaranteed—flowering trees are T/2 and may be split in any way. d: “One-half of sandal are flowering” is also not forced by the data. Common Pitfalls: Assuming specific splits of flowering trees without evidence. Final Answer: At least one-half of the Ashoka trees are old.

Quantitative Logic — Trees in a Forest Facts: A forest has as many sandal trees as Ashoka trees. Three-fourths of all trees are old. One-half of all trees are at the flowering stage. Which statement must be true?

More Questions from Statement and Conclusion

Discussion & Comments