Quantitative logic — Compare item costs from linked equivalences Premise 1: Three pencils cost the same as two erasers. Premise 2: Four erasers cost the same as one ruler. Claim (to evaluate): Pencils are more expensive than rulers.

Question

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

Accepted Answer

Introduction / Context:This problem uses proportional price relations. By translating the verbal statements into algebraic equalities, we can compare the unit prices of pencils, erasers, and rulers to see if the claim follows necessarily. Given Data / Assumptions: Let P = price of one pencil; E = price of one eraser; R = price of one ruler. 3 pencils = 2 erasers → 3P = 2E. 4 erasers = 1 ruler → 4E = R. All prices are positive real numbers. Concept / Approach: Solve the equalities for unit prices and then compare P versus R. Use substitution to express all items in terms of E. Step-by-Step Solution: From 3P = 2E, get P = (2/3) * E.From 4E = R, get R = 4 * E.Compare P and R: P = 0.666… * E, whereas R = 4 * E → clearly, P < R.Thus the claim “pencils are more expensive than rulers” is false. Verification / Alternative check: Normalize E = 3 (arbitrary). Then P = 2 and R = 12. The rankings agree: ruler is much costlier than a pencil, refuting the claim. Why Other Options Are Wrong: true: Directly contradicts the derived inequality P < R.uncertain: The premises are sufficient to determine the exact comparative result.both true and false: Not applicable; with fixed premises, the inference is determinate. Common Pitfalls: Mistaking bundle equivalence for unit equivalence without doing the division; or comparing 3P with R instead of P with R. Final Answer: false

Quantitative logic — Compare item costs from linked equivalences Premise 1: Three pencils cost the same as two erasers. Premise 2: Four erasers cost the same as one ruler. Claim (to evaluate): Pencils are more expensive than rulers.

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