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Q048 ·Product ·Estimation

Car X vs. Car Y Fuel Efficiency — Which Technology Saves More Gas?

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1Problem

A country produces two types of cars in equal numbers:

Car X: currently 50 MPG
Car Y: currently 10 MPG

Two technologies are proposed:

Technology A: improves Car X from 50 → 75 MPG
Technology B: improves Car Y from 10 → 11 MPG

Which should the country implement to save the most gasoline?

2HintsThink first, then tap to reveal

Hint 1 MPG is a rate — what actually matters is gallons per mile. Tap →

Hint 2 The reciprocal matters, not the raw numbers. Tap →

Hint 3 Fixing the worst performer often beats improving the best. Tap →

3Solution

▶The Intuition Trap

The naive read is that Technology A is obviously better — it adds 25 MPG vs. only 1 MPG. That's how most candidates answer at first glance.

But the naive read is wrong. Technology B saves more gas.

The trap: MPG is a rate, and intuitions built on rates deceive you. What matters for gas consumption is gallons used per mile driven, which is 1/MPG. We want to minimize gallons, not maximize MPG — and improvements at the low-MPG end save way more gallons than improvements at the high-MPG end.

▶The Math

Let D = miles driven per car (same for X and Y, since the population drives equally).

Gas used per car:

Car X current: D / 50
Car X with A: D / 75
Car Y current: D / 10
Car Y with B: D / 11

Gas saved per car:

Technology	Calculation	Savings
A (X: 50→75)	D/50 − D/75 = D(75−50) / (50·75) = D · 25/3750 = D/150	D/150
B (Y: 10→11)	D/10 − D/11 = D(11−10) / (10·11) = D/110	D/110

Since D/110 > D/150 (smaller denominator = larger fraction), Technology B saves more gas.

To be concrete: if D = 1000 miles,

A saves 1000/150 ≈ 6.67 gallons
B saves 1000/110 ≈ 9.09 gallons

B saves ~36% more gas than A.

▶Why This Works Intuitively

MPG scales inversely with gas consumption. At the low end (10 MPG), each incremental MPG cuts a big chunk of gas. At the high end (50 MPG), each incremental MPG saves only a tiny sliver of gas, because the car is already very efficient.

Example: at 10 MPG, a car uses 100 gallons per 1000 miles. Going to 11 MPG brings that down to ~91 gallons — 9 gallons saved. At 50 MPG, the car uses 20 gallons per 1000 miles. Going to 75 MPG brings that to ~13 gallons — only 7 gallons saved. A 1-MPG improvement on a gas-guzzler saves more than a 25-MPG improvement on a Prius.

The principle: for rates where you care about the reciprocal (MPG / throughput / bandwidth / any "X per Y"), gains matter most at the bad end of the distribution. The law of diminishing returns applies in reverse: fixing the worst performers is always higher leverage than making the best performers better.

▶Why This Is the Right Answer for Real Policy

This is the reason the U.S. EPA switched from MPG-based fuel-economy reporting to gallons-per-100-miles (GPM) as a parallel measure. MPG is misleading because the relationship between MPG and gas consumption is nonlinear. Gallons-per-mile is linear and gives the right intuition. It's also why CAFE standards focus on fleet-average gallons, not fleet-average MPG — you'd get very different policy conclusions.

▶Extensions the Interviewer May Ask

"What if the two cars drive different amounts?"

If Car X drives $D_X$ miles and Car Y drives $D_Y$ miles:

A saves $D_X \cdot (1/50 - 1/75) = D_X \cdot 25/3750 = D_X / 150$
B saves $D_Y \cdot (1/10 - 1/11) = D_Y \cdot 1/110 = D_Y / 110$

B still wins unless $D_Y / D_X < 110/150 \approx 0.73$ — i.e., Y drivers would have to drive less than 73% as much as X drivers for A to win. In reality, gas-guzzlers (trucks, SUVs) often drive more than efficient cars, so B wins even more strongly.

"What if the cars represent different fractions of the population?"

Multiply the per-car savings by the number of cars of each type. If Car Y represents 30% instead of 50%, A might win. Walk through the math:

A saves: 0.5 × D/150 = D/300
B saves: 0.3 × D/110 = D/367

Now A saves more. Answer depends on the population mix.

"Which technology should we fund to develop first?"

Adds a cost / feasibility dimension. If Technology A is 10× cheaper to develop and deploy than Technology B, the gas savings ratio could be reversed by cost-effectiveness. Real-world answer: depends on cost, but policy-wise, we should at least recognize that B has bigger gas-savings impact per car.

▶When Candidates Fail This Question

They answer "A, obviously" without doing any math, trusting the 25 > 1 heuristic. This is the majority of candidates.
They do the math wrong. Often forget to do 1/MPG and instead compute (75−50) × fraction − (11−10) × fraction.
They do the math right but present weakly. Get the answer but don't articulate the intuition behind why low-MPG improvements win.

▶The Insight to Communicate

"MPG is a rate, and the relationship between MPG and gas consumption is reciprocal, not linear. A 1-MPG improvement at 10 MPG saves an order of magnitude more gas than a 25-MPG improvement at 50 MPG. The intuition that bigger MPG gains are better breaks down at the efficient end of the spectrum. The right framing is always gallons per mile, not miles per gallon."

4Interview

Interviewer

A country has equal numbers of Car X and Car Y. Car X gets 50 MPG, Car Y gets 10 MPG. Two technologies: Technology A brings Car X from 50 to 75 MPG. Technology B brings Car Y from 10 to 11 MPG. Which one saves more gas?

Instinct would say A — going from 50 to 75 is a 25-point jump, going from 10 to 11 is only 1. But MPG is a rate, and intuitions on rates are tricky. Let me actually do the math before answering.

The relevant quantity is gas used per car, which is miles / MPG. If each car drives D miles:

Car X at 50: uses D/50 gallons
Car X at 75 (with A): uses D/75 gallons
A saves D/50 − D/75 = D × (75−50) / (50×75) = D/150
Car Y at 10: uses D/10 gallons
Car Y at 11 (with B): uses D/11 gallons
B saves D/10 − D/11 = D × (11−10) / (10×11) = D/110

D/110 > D/150, so B saves more gas. About 36% more actually — 1/110 ≈ 0.0091 vs. 1/150 ≈ 0.0067.

Self-rate:

Interviewer · Follow-up

Why is that, intuitively?

At 10 MPG, a car uses 100 gallons per 1000 miles. Moving it to 11 MPG brings that down to roughly 91 gallons — saves 9 gallons. At 50 MPG, a car uses 20 gallons per 1000 miles. Moving it to 75 MPG brings that down to 13.3 gallons — saves only about 6.7 gallons.

The key insight is that MPG and gas consumption are inversely related. At the low end, each incremental MPG saves a lot of gas because you're cutting from a big base. At the high end, each incremental MPG saves very little because the car was already efficient. A 1-MPG improvement on a gas-guzzler is always worth more in absolute gas than a 25-MPG improvement on a Prius.

This is actually why the EPA reports gallons-per-100-miles alongside MPG now. MPG is a deceptive metric for comparing improvements. Gallons-per-mile is linear and gives the right intuition.

Self-rate:

Interviewer · Follow-up

Does this change if the two cars drive different amounts?

Yes, but not easily. Car X drives $D_X$ and Car Y drives $D_Y$ . A saves $D_X / 150$ ; B saves $D_Y / 110$ . B still wins as long as $D_Y / D_X > 110/150 \approx 0.73$ — i.e., Y drivers drive at least 73% as much as X drivers.

In practice, gas-guzzlers are often trucks and SUVs that drive more miles than efficient cars — delivery fleets, ride-sharing, long commutes. So the realistic case strengthens B's advantage, not weakens it.

Self-rate:

Interviewer · Follow-up

What if the cars aren't in equal proportions?

Then you scale by the count. If 70% of cars are X and 30% are Y:

Population-level A saves: 0.7 × D/150 ≈ D/214
Population-level B saves: 0.3 × D/110 ≈ D/367

Now A wins. So the answer depends on the mix. But for the 50/50 split in the problem, B wins decisively.

Self-rate:

Interviewer · Follow-up

Last thing — in policy, would you recommend B?

The gas math says B. But real policy needs cost too — what does it cost to develop and deploy each technology? If Technology A is 10× cheaper per car to retrofit, the cost-per-gallon-saved might favor A.

The interesting policy insight here is more general: environmental policy should target the inefficient end of the distribution, not the efficient end. Incremental improvements on gas-guzzlers have way more leverage than incremental improvements on already-efficient cars. This is exactly why CAFE standards and the EPA started measuring gallons-per-mile instead of just MPG.

Self-rate:

Interviewer

Candidate

Instinct would say A — going from 50 to 75 is a 25-point jump, going from 10 to 11 is only 1. But MPG is a rate, and intuitions on rates are tricky. Let me actually do the math before answering.

The relevant quantity is gas used per car, which is miles / MPG. If each car drives D miles:

Car X at 50: uses D/50 gallons
Car X at 75 (with A): uses D/75 gallons
A saves D/50 − D/75 = D × (75−50) / (50×75) = D/150
Car Y at 10: uses D/10 gallons
Car Y at 11 (with B): uses D/11 gallons
B saves D/10 − D/11 = D × (11−10) / (10×11) = D/110

D/110 > D/150, so B saves more gas. About 36% more actually — 1/110 ≈ 0.0091 vs. 1/150 ≈ 0.0067.

Interviewer

Why is that, intuitively?

Candidate

This is actually why the EPA reports gallons-per-100-miles alongside MPG now. MPG is a deceptive metric for comparing improvements. Gallons-per-mile is linear and gives the right intuition.

Interviewer

Does this change if the two cars drive different amounts?

Candidate

Interviewer

What if the cars aren't in equal proportions?

Candidate

Then you scale by the count. If 70% of cars are X and 30% are Y:

Population-level A saves: 0.7 × D/150 ≈ D/214
Population-level B saves: 0.3 × D/110 ≈ D/367

Now A wins. So the answer depends on the mix. But for the 50/50 split in the problem, B wins decisively.

Interviewer

Last thing — in policy, would you recommend B?

Candidate

Interviewer

Good.

5Notes

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6Mock interview debrief

This question has a debrief tool attached. Practice it aloud with a voice-mode AI interviewer, paste the transcript, and get a graded debrief against the reference answer.

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How to do a mock interview

1
Open DS Mock Interviewer in ChatGPT
2

Copy this question and paste it as your first message:

A country produces two types of cars in equal numbers: - **Car X**: currently 50 MPG - **Car Y**: currently 10 MPG Two technologies are proposed: - **Technology A**: improves Car X from 50 → 75 MPG - **Technology B**: improves Car Y from 10 → 11 MPG **Which should the country implement to save the most gasoline?**
3

Switch to voice mode (mic icon in the chat input). Speak through each follow-up — aim for 4–6 turns.
4

When the interviewer says "thank you, that's all I had", type or speak this:

Print the full transcript of our conversation as alternating "Interviewer:" and "Candidate:" lines. Include every exchange verbatim. Do not paraphrase, summarize, or skip turns. Do not add commentary.
5

Copy ChatGPT's response, paste it below, and run the debrief.

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