"Cindy Drove Her Car 290 Miles, Rounded to the Nearest 10..." — GMAT® Worked Solution

Source: Official Guide for GMAT® Review, 11th Edition

On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy's car got on this trip must have been between

(A) $\dfrac{290}{12.5}$ and $\dfrac{290}{11.5}$

(B) $\dfrac{295}{12}$ and $\dfrac{285}{11.5}$

(C) $\dfrac{285}{12}$ and $\dfrac{295}{12}$

(D) $\dfrac{285}{12.5}$ and $\dfrac{295}{11.5}$

(E) $\dfrac{295}{12.5}$ and $\dfrac{285}{11.5}$

Try it before reading on.

Step 1: Find the Range of Each Rounded Value

Cindy drove 290 miles, rounded to the nearest 10 miles. What actual distances would round to 290?

A value rounded to the nearest 10 could be anywhere from 285 (which rounds up to 290) to 295 (which rounds down to 290). But the problem says "between," which on the GMAT® excludes the endpoints. So the actual distance is somewhere strictly greater than 285 and strictly less than 295.

She used 12 gallons, rounded to the nearest gallon. What actual amounts would round to 12?

A value rounded to the nearest gallon could be anywhere from 11.5 (which rounds up to 12) to 12.5 (which rounds down to 12). Again, "between" excludes the endpoints, so the actual gallons are strictly greater than 11.5 and strictly less than 12.5.

Step 2: Set Up the Fraction

Miles per gallon is a fraction: $\frac{\text{miles}}{\text{gallons}}$. We need to find the range of this fraction given that the numerator is between 285 and 295, and the denominator is between 11.5 and 12.5.

The key principle for optimizing a fraction:

• Minimum fraction = minimum numerator $\div$ maximum denominator
• Maximum fraction = maximum numerator $\div$ minimum denominator

A fraction gets smaller when the numerator decreases or the denominator increases. So the smallest possible fraction combines both effects: the smallest numerator with the largest denominator. The largest fraction does the opposite.

Step 3: Compute Both Endpoints

Minimum miles per gallon:

$\frac{285}{12.5}$

Maximum miles per gallon:

$\frac{295}{11.5}$

The actual miles per gallon must be between $\frac{285}{12.5}$ and $\frac{295}{11.5}$.

The answer is (D).

Why This Problem Matters

This problem has a 30% miss rate, the highest of the three problems in this episode. The math is simpler than either of the other two problems. No exponents, no repeating decimals, no multi-step arithmetic. The difficulty is entirely conceptual.

The dominant trap answer is (E), chosen by about 15% of test takers. Answer (E) shows correct rounding logic: 295 is the upper limit for the miles, 12.5 is the upper limit for the gallons. But dividing maximum miles by maximum gallons gives a middle value, not an endpoint. It's neither the minimum nor the maximum miles per gallon.

To see why, consider: $\frac{295}{12.5}$ gives you the "best gas mileage if she used the most gas." That's a contradiction. If she used the most gas, her mileage should be worse, not better. The maximum miles per gallon comes from driving the most miles on the least gas: $\frac{295}{11.5}$.

The fix is a simple habit: write both endpoints before scanning answer choices. The minimum is min numerator over max denominator. The maximum is max numerator over min denominator. Writing them down prevents the mental shortcut that leads to (E).

One more detail worth noting: "between" on the GMAT® excludes the endpoints. If a problem says a value is "between X and Y," neither X nor Y is included. The endpoints represent the limits of the range, not the actual values. The exception is when the problem explicitly says "inclusive," which includes both endpoints. This distinction matters on any problem that asks about ranges derived from rounded values.

Want the full strategy behind this problem? Read: GMAT® Quant: Three Systems for Percents, Exponents, and Rounding

From Episode 31 of Real GMAT® Problems (The GMAT® Strategy Podcast).