— GUIDE —

QUANT INTERVIEW PRACTICE QUESTIONS (WITH ANSWERS)

14 questions of the kind asked in quant interviews and online assessments, spanning mental math, sequences, probability, and logic — each with a worked answer and the technique behind it.

UPDATED 2026-07-12 · 10 MIN READ · BY THE VARIANCE TEAM

These questions mirror the formats used in real quant screening: arithmetic at speed, next-term sequences, quick probability, and classic logic puzzles. Try each one timed before reading the answer — untimed practice tells you what you know, but timed practice tells you what you can use in an OA. For how these fit into a full study plan, see the quant OA preparation guide.

Mental math (target: under 10 seconds each)

  1. Compute 47 × 23 in your head.

    Answer: 1081. Use round anchors: 47 × 23 = 47 × 20 + 47 × 3 = 940 + 141 = 1081. Alternatively, 47 × 23 = (35² ) − 12² = 1225 − 144 = 1081 using (a+b)(a−b) with a = 35, b = 12.

  2. What is 15% of 340?

    Answer: 51. Take 10% (34), then half of that (17), and add: 34 + 17 = 51.

  3. Compute 1008 ÷ 24.

    Answer: 42. Factor the divisor: divide by 8 first (1008 ÷ 8 = 126), then by 3 (126 ÷ 3 = 42).

  4. A stock falls 20% then rises 20%. What is the net change?

    Answer: Down 4%. 0.8 × 1.2 = 0.96. Percentage moves don't cancel — a classic trap in trading arithmetic.

If these felt slow, the techniques — left-to-right arithmetic, percentage anchors, factoring the divisor — are covered in depth in our mental math guide.

Number sequences (target: under 45 seconds each)

  1. Find the next term: 2, 3, 5, 9, 17, 33, ?

    Answer: 65. Differences double each step (1, 2, 4, 8, 16, 32). Equivalently, each term is 2×previous − 1.

  2. Find the next term: 1, 2, 6, 24, 120, ?

    Answer: 720. These are factorials: n! — so the next term is 6! = 720.

  3. Find the next term: 3, 4, 7, 11, 18, 29, ?

    Answer: 47. Each term is the sum of the previous two (a Fibonacci-style recurrence with different seeds): 18 + 29 = 47.

  4. Find the next term: 1, 4, 9, 61, 52, 63, ?

    Answer: 94. The digits of the perfect squares are reversed: 1, 4, 9, 16→61, 25→52, 36→63, 49→94. When a sequence looks broken, try digit tricks.

The productive habit: check differences first, then ratios, then two-term recurrences, then digit manipulations — in that order. Most OA sequences fall to one of those four checks.

Probability (target: under 90 seconds each)

  1. You roll two fair dice. What is the probability the sum is 7?

    Answer: 1/6. There are 6 favorable outcomes (1-6, 2-5, 3-4, 4-3, 5-2, 6-1) out of 36 equally likely outcomes.

  2. You flip a fair coin 3 times. What is the probability of at least one head?

    Answer: 7/8. Complement counting: P(no heads) = (1/2)³ = 1/8, so P(at least one) = 1 − 1/8 = 7/8.

  3. A game pays $10 with probability 0.3, $0 otherwise, and costs $4 to play. What is your expected profit?

    Answer: −$1. EV of payout = 0.3 × 10 = $3; minus the $4 cost gives −$1. You should not play — and in an interview you should say so.

  4. A family has two children. Given that at least one is a boy, what is the probability both are boys?

    Answer: 1/3. The equally likely gender orderings are BB, BG, GB, GG. Conditioning on 'at least one boy' leaves {BB, BG, GB}, and only BB has two boys.

Two tools solve a remarkable share of interview probability: complement counting ("at least one" → compute the opposite) and linearity of expectation. If you find yourself enumerating a huge sample space, look for the shortcut instead.

Logic puzzles

  1. You have a 3-liter jug, a 5-liter jug, and unlimited water. Measure exactly 4 liters.

    Answer: Fill the 5L jug, pour into the 3L jug until full — 2L remain in the 5L jug. Empty the 3L jug, pour the 2L into it. Refill the 5L jug and top off the 3L jug (which takes 1L), leaving exactly 4L in the 5-liter jug.

  2. In a room of 23 people, is the probability that two share a birthday closer to 5%, 50%, or 95%?

    Answer: 50%. This is the birthday paradox: with 23 people the probability of a shared birthday is about 50.7%. The number of pairs (253) grows quadratically, which is what surprises intuition.

How to practice with these

  • Time everything. Note your time per question and your accuracy; track both weekly.
  • Re-derive, don't memorize. Interviewers change numbers. What transfers is the technique, not the answer.
  • Say your reasoning out loud for probability and logic questions — live interviews grade the path, not just the result.
  • Drill the slow categories daily. Fourteen questions is a diagnostic, not a training volume. Speed comes from hundreds of timed reps, which is exactly what the Variance app generates adaptively.