A car's fuel efficiency is 32 miles per gallon. Using the conversions mile kilometers and gallon liters, which choice is closest to the car's fuel consumption in liters per 100 kilometers?

Solution available with step-by-step explanation

Super-Hard SAT Math Question 36 | Free SAT Prep | Aniko

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Question 36·200 Super-Hard SAT Math Questions·Problem Solving and Data Analysis

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A car's fuel efficiency is 32 miles per gallon. Using the conversions $1$ mile $= 1.61$ kilometers and $1$ gallon $= 3.79$ liters, which choice is closest to the car's fuel consumption in liters per 100 kilometers?

For unit-rate conversion problems, write the given rate as a fraction and multiply by conversion factors so units cancel until you reach the target units. Here, liters per 100 kilometers is an inverse of miles per gallon, so either (1) convert to km/L and then take the reciprocal and multiply by 100, or (2) build one expression that directly converts $\frac{1}{32}$ gallon per mile into liters per kilometer and then scales by 100.

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Track the units

Write the given rate as a fraction and decide what unit you want in the end: liters per 100 kilometers.

Convert before you invert

It can help to convert miles per gallon into kilometers per liter first.

Remember L per 100 km is the reciprocal idea

Liters per 100 kilometers measures fuel used, so it comes from inverting a distance-per-fuel rate and then multiplying by 100.

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Compute liters per 100 kilometers directly

In an expression line, enter:

100*(1/32)*(3.79/1.61)

This matches

100\cdot \frac{\text{gallon}}{32\ \text{miles}}\cdot \frac{3.79\ \text{L}}{1\ \text{gallon}}\cdot \frac{1\ \text{mile}}{1.61\ \text{km}}

Choose the closest option

Look at the decimal result and select the answer choice that is closest to it.

Step-by-step Explanation

Convert to kilometers per liter

Start with $32$ miles per gallon.

Convert miles to kilometers and gallons to liters:

32\ \frac{\text{miles}}{\text{gallon}}\cdot \frac{1.61\ \text{km}}{1\ \text{mile}}\cdot \frac{1\ \text{gallon}}{3.79\ \text{L}}

This gives kilometers per liter (km/L).

Compute km/L and convert to L per 100 km

Compute the km/L value:

32\cdot \frac{1.61}{3.79}\approx \frac{51.52}{3.79}\approx 13.6\ \frac{\text{km}}{\text{L}}

Now invert to get liters per kilometer:

\frac{1}{13.6}\approx 0.0735\ \frac{\text{L}}{\text{km}}

Multiply by $100$ km to get liters per 100 km:

100\cdot 0.0735\approx 7.35

Match to the closest choice

The value $7.35$ liters per 100 kilometers is closest to $\boxed{7.4}$ .

Strategy

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Step-by-step Explanation

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Strategy

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Step-by-step Explanation