SSAT Upper Level Quantitative Question of the Day

1. $12$ gallons
2. $16$ gallons
3. $15$ gallons
4. $14$ gallons (correct answer)

Explanation: This is a rate problem that tests your ability to set up and solve proportions. When you see a question giving you one rate and asking for another quantity at the same rate, think proportion or unit rate. First, find the car's fuel efficiency (miles per gallon): $180 \text{ miles} ÷ 6 \text{ gallons} = 30 \text{ miles per gallon}$. Now you can find how many gallons are needed for 420 miles: $420 \text{ miles} ÷ 30 \text{ miles per gallon} = 14 \text{ gallons}$. Alternatively, you can set up a proportion: $\frac{180 \text{ miles}}{6 \text{ gallons}} = \frac{420 \text{ miles}}{x \text{ gallons}}$. Cross-multiply: $180x = 420 × 6 = 2520$, so $x = 2520 ÷ 180 = 14$ gallons. Choice A (12 gallons) might result from incorrectly calculating the unit rate as 15 miles per gallon instead of 30, then dividing 420 by 35. Choice B (16 gallons) could come from setting up the proportion incorrectly or making arithmetic errors in cross-multiplication. Choice C (15 gallons) might result from dividing 420 by 28 instead of 30, suggesting a calculation error in finding the unit rate. For rate problems, always identify what stays constant (the rate itself) and what changes (the quantities). Calculate the unit rate first—it makes the math cleaner and helps you catch errors. Double-check by multiplying your answer by the unit rate to see if you get back to 420 miles.