🎯 Interview & Career · Chapter 7

Aptitude and estimation under pressure

Aptitude tests aren't testing whether you can do maths. They're testing whether you can do enough maths, fast, while a timer runs — and whether you know when to skip.

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The basics

Aptitude and estimation show up in two places in data engineering hiring:

• Online assessments — timed multiple-choice sections: percentages, ratios, averages, speed and time, data interpretation, logical reasoning. Often around a minute per question.
• Live estimation — “how much storage for a year of ride events?” or “how many cabs does Shillong need at peak?” asked out loud in technical or design rounds.

Why they're hard: not the maths — the pressure. A question you'd solve in two minutes at home takes five when the clock is visible, and one stubborn question can eat the time for four easy ones.

The mental model:

• In timed tests: triage — answer the quick ones, mark and skip the slow ones, return if time remains. Use options to eliminate.
• In estimation: assumptions out loud → round numbers → multiply → sanity check. Being within a factor of 2–3 is a good answer; showing the chain is what's scored.

Words to know: triage, elimination, Fermi estimate, order of magnitude, successive percentage, harmonic mean.

Explained

Online assessment, aptitude section: 20 questions, 20 minutes.

Question 4 is a ‘pipes filling a tank’ problem. Ravi knows he can solve it. Six minutes later he does — correctly.

He runs out of time at question 15. Questions 16–20 were three percentages and two table readings, about 40 seconds each.

One correct answer cost him five easy ones. The skill being tested wasn't the tank. It was knowing when to walk away from it.

The vegetable market

At Iewduh market, a seasoned shopper doesn't calculate exact totals. Tomatoes ₹38/kg, she wants 2.5 kg — “about ₹95”. Onions ₹42, 2 kg — “₹84, call it 85”. Total “around ₹180, I have ₹200, fine.”

She's rounding, adding, and sanity-checking in seconds. She'd catch a ₹450 bill instantly without knowing the exact right number.

That's estimation: fast, roughly right, and good enough to catch something badly wrong. In an interview, saying “about 6 terabytes a year — so not big data” is worth more than 5.84 TB delivered after three minutes of silence.

The patterns that come up again and again

Successive percentages multiply: +20% then −20% → 1.2 × 0.8 = 0.96, a 4% fall. Never add them.

Percentage swap: x% of y = y% of x. 18% of 50 = 50% of 18 = 9.

Percentage change vs points: share from 40% to 50% is +10 percentage points but +25%.

Average speed over equal distances is the harmonic mean: 40 and 60 km/h → 2×40×60/(40+60) = 48 km/h, not 50.

Weighted average: don't average averages from groups of different sizes.

Work rate: add rates, not times. A does it in 6 h (1/6 per h), B in 3 h (1/3 per h) → together 1/2 per h → 2 h.

Data interpretation: check units and whether the question asks for absolute or percentage change — the trap is usually there.

Estimation, out loud: a year of ride events

Q: “How much storage for a year of Meghalaya Cabs ride events?”

Assume  1M rides/day                       (say it — they can correct it)
        ~8 events per ride                 (request, accept, arrive, start,
                                            end, pay, rate, receipt)
      → 8M events/day

Assume  ~1 KB per JSON event
      → 8M × 1 KB = 8 GB/day raw

Year  → 8 GB × 365 ≈ 3 TB raw
        compressed Parquet ~5–10× smaller → ~300–600 GB
        with 3× replication on the raw copy → ~9 TB

Sanity  8M/day ÷ 86,400 ≈ 93 events/sec — small for one database.
Answer  “About 3 TB raw a year, well under 1 TB compressed.
         Not big data — but keep raw for replays.”

The interviewer is grading the chain: assumptions stated, round numbers, units carried, a sanity check, and a conclusion that means something.

Timed test: the triage loop

Check the instructions for negative marking before the test. Without it, never leave a blank; with it, guess only when you can eliminate at least two options.

A live Fermi question

Interviewer: “How many cabs does Meghalaya Cabs need in Shillong at evening peak?”

Strong answer: “Let me assume greater Shillong has around 5 lakh people. Say 2% take one of our rides on a weekday — 10,000 rides a day. Evening peak, 6 to 7 PM, might be 12% of the day — about 1,200 rides in that hour. A trip plus pickup is about 30 minutes, so each cab can do 2 rides an hour. That's 600 cabs on the road at peak, maybe 700 to cover uneven demand by area. Sanity check: 600 cabs for 5 lakh people is roughly one per 800 people at peak, which feels plausible for a hill city. I'd check the 2% assumption first — it's the most uncertain.”

Note the last sentence: naming which assumption matters most is the senior touch.

Gotchas

• Sunk-cost on one question. Three minutes in and stuck → mark it and move on.
• Adding percentages. +10% and +10% is +21%, not +20%.
• Averaging speeds. Equal distances at 40 and 60 km/h average 48, not 50.
• Ignoring units. GB vs GiB rarely matters; KB vs MB always does.
• Exact arithmetic in estimation. 86,400 → 10⁵. 365 → 400 if needed. Say you're rounding.
• Silent estimation. The number alone scores little; the stated chain scores a lot.
• No sanity check. An answer of ‘40 petabytes of ride data a year’ should feel wrong before you say it.
• Not reading negative-marking rules. Guessing strategy depends on it.

Timed: triage, eliminate, move on. Live: assume out loud, round hard, sanity-check, give a range.

Successive percentages multiply. Average speed is harmonic. 1M a day ≈ 12 a second.

Words to know

In two minutes

• Timed aptitude tests reward triage: quick ones first, mark and skip anything over ~90 seconds, return later.
• Use the options: eliminate impossible answers and approximate before calculating exactly.
• Know the classic traps: successive percentages don't add, average speed is not the average of speeds.
• Live estimation is scored on the chain of assumptions, not the final digit — say each step out loud.
• Round aggressively: 86,400 seconds a day ≈ 10⁵; a year ≈ 3 × 10⁷ seconds.
• Always sanity-check against something you know, and state the answer with its unit and a range.
• Practise under a timer; speed comes from familiarity with patterns, not from doing harder problems.

Test yourself

There are 8 questions, 3 puzzles and 5 recall cards for this lesson in the app — the recall cards come back on later days, just before you would forget.