Interpreting a Proportional Statement — Percent Greater If dividing a first number by 12 gives one-fourth of a second number (i.e., first/12 = second/4), by what percent is the first number greater than the second number?

Introduction / Context:This question requires careful interpretation of a verbal proportional statement and conversion to an equation. Once the relationship between the two numbers is clarified, computing the percentage difference is straightforward and relies on a basic percent-change formula.

Given Data / Assumptions:

• Interpretation (Recovery-First): “When a number is divided by 12 then [the result] becomes 1/4 of the other number,” i.e., first/12 = second/4.
• Let the first number be A and the second be B.
• We seek percent by which A is greater than B.

Concept / Approach:From A/12 = B/4, multiply both sides by 12 to get A = 3B. Percent greater is computed as ((A − B)/B) * 100%. Substitute A = 3B to obtain a numerical percentage independent of specific values of A and B.

Step-by-Step Solution:Start: A/12 = B/4.Multiply by 12: A = 3B.Compute percent greater: ((A − B)/B) * 100% = ((3B − B)/B) * 100% = (2) * 100%.Therefore, A is 200% greater than B.

Verification / Alternative check:Example: Let B = 10 → A = 30. Then A/12 = 2.5 and B/4 = 2.5, satisfying the condition. A is 200% greater than B since (30 − 10)/10 * 100% = 200%.

Why Other Options Are Wrong:150% and 300% misrepresent the 3:1 ratio; “Data inadequate” is incorrect because the proportional statement fully determines A/B; 100% would only hold for A = 2B.

Common Pitfalls:Misreading the phrase and setting A/12 = 1/4 (numberless), or mixing dividend/divisor terminology; computing “percent of” instead of “percent greater than.”

Final Answer:200