DAT Quantitative Reasoning Question of the Day

1. 135
2. 180
3. 225 (correct answer)
4. 240

Explanation: Ratio problems test your ability to work with proportional relationships. When you see a ratio like 3:5, think of it as representing parts of a whole rather than actual quantities. The ratio 3:5 means that for every 3 small brackets, there are 5 large brackets. This gives us a total of 3 + 5 = 8 parts in the ratio. Since 360 brackets were ordered total, each part represents $\frac{360}{8} = 45$ brackets. Large brackets make up 5 parts of the ratio, so the number of large brackets is $5 \times 45 = 225$. You can verify this: small brackets would be $3 \times 45 = 135$, and $135 + 225 = 360$ ✓ Looking at the wrong answers: A) 135 is the number of small brackets, not large ones—this represents the classic trap of solving for the wrong part of the ratio. B) 180 would result if you incorrectly calculated each part as $\frac{360}{10} = 36$ (perhaps by adding an extra step), then multiplied by 5. D) 240 comes from miscalculating the total parts as 6 instead of 8, giving $\frac{360}{6} = 60$ per part, then $60 \times 4 = 240$—but this uses the wrong ratio interpretation entirely. The key strategy for ratio problems: always find the total number of parts first, then determine what each part represents. Double-check by ensuring your parts add up to the given total. This systematic approach prevents the common mistake of solving for the wrong component.