SSAT Middle Level Quantitative Question of the Day

1. $15$ cups
2. $20$ cups (correct answer)
3. $18$ cups
4. $7.2$ cups
5. $9.6$ cups

Explanation: When you encounter ratio problems, you're working with proportional relationships between quantities. The key is recognizing that ratios tell you how parts relate to each other, and this relationship stays constant even when the actual amounts change. The recipe calls for flour and sugar in a $3:5$ ratio, meaning for every 3 parts flour, you need 5 parts sugar. Since Maria uses 12 cups of flour, you need to find how much this amount has been scaled up from the original ratio. Divide 12 by 3 to get the scaling factor: $12 \div 3 = 4$. This means the recipe has been multiplied by 4. Therefore, the sugar amount must also be multiplied by 4: $5 \times 4 = 20$ cups. You can verify this using a proportion: $\frac{3}{5} = \frac{12}{x}$. Cross-multiplying gives $3x = 60$, so $x = 20$. Choice A (15 cups) represents adding 12 + 3 instead of using the scaling factor—a common arithmetic error. Choice C (18 cups) might come from incorrectly thinking the ratio is $2:3$ instead of $3:5$, then scaling up. Choice D (7.2 cups) results from flipping the ratio and calculating $\frac{3}{5} \times 12$, which gives you less sugar than flour—impossible when the ratio calls for more sugar. The correct answer is B (20 cups). Strategy tip: In ratio problems, always identify the scaling factor by dividing the given quantity by its corresponding ratio number, then apply that same factor to find the unknown quantity.