— GUIDE —

QUANT INTERVIEW PRACTICE QUESTIONS (WITH ANSWERS)

Fourteen timed practice questions covering mental math, sequences, probability, and logic. Each answer shows the shortest useful route.

UPDATED 2026-08-12 · 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 work shows what you know. A timer shows whether you can retrieve it 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 do not cancel because the second move starts from a smaller base.

If these felt slow, review left-to-right arithmetic, percentage anchors, and divisor factoring 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, 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.

Check differences first, then ratios, two-term recurrences, and digit manipulations. A fixed order keeps you from chasing elaborate rules too early.

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.

  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 do a lot of work here: use the complement for "at least one" questions, and use linearity of expectation when you need an average count. Before listing a large sample space, check whether one of those gives you a shorter route.

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 and pour into the 3L jug until full. The 5L jug now holds 2L. Empty the 3L jug, pour those 2L into it, then refill the 5L jug and top off the 3L jug. That takes 1L and leaves exactly 4L in the 5L 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. In a live interview, the interviewer needs to follow your path, not just hear the result.
  • Drill the slow categories daily. Fourteen questions is a diagnostic, not a full training program. Variance can supply the timed volume after you know which categories are slow.