ISEE Upper Level Quantitative Reasoning Question of the Day

1. $9:24$
2. $3:8$ (correct answer)
3. $1:3$
4. $9:15$

Explanation: When you encounter ratio problems involving multiple machines or workers, focus on finding the actual production rates first, then use those to calculate any requested ratios. Given that the machines produce widgets in a $5:3$ ratio and Machine A produces 15 widgets per hour, you can find Machine B's rate. Since Machine A corresponds to the "5" part of the ratio, each ratio unit represents $15 ÷ 5 = 3$ widgets per hour. Therefore, Machine B produces $3 × 3 = 9$ widgets per hour. The total hourly production is $15 + 9 = 24$ widgets. The ratio of Machine B's production to total production is $9:24$, which simplifies to $3:8$ by dividing both terms by 3. Looking at the wrong answers: Choice A gives $9:24$, which is the unsimplified form of the correct ratio—always simplify ratios to lowest terms. Choice C shows $1:3$, which incorrectly suggests Machine B produces only one-third of the total, when it actually produces three-eighths. Choice D presents $9:15$, which compares Machine B's production to only Machine A's production rather than the total production of both machines. Strategy tip: In ratio problems, always identify what each number in the original ratio represents in real units, calculate the actual values, then build your final ratio step by step. Watch out for answer choices that give correct intermediate calculations but don't answer the specific question asked.