Quant interview preparation

Find the gaps in your quant interview preparation.

Eight questions. Full explanations. No email required. These original exercises help you decide what to practice next; they are not taken from a live employer assessment.

Try all eight questions without looking at the explanations. Allow about 15 minutes if you want a timed practice session. Your answers stay on this page and are not submitted.

1. Arithmetic

What is 48 × 52?

Worked solution and follow-up

Answer: 2,496. (50 − 2)(50 + 2) = 50² − 2² = 2,496. Check with 48 × 50 + 48 × 2 = 2,400 + 96.

Use the same idea to calculate 97 × 103: 10,000 − 9 = 9,991.

2. Probability

A bag has 3 red and 5 blue balls. Draw two without replacement. What is the probability both are red?

Worked solution and follow-up

Answer: 3/28. Multiply 3/8 by 2/7. The second probability changes after the first red ball is removed. The answer is 6/56 = 3/28.

With replacement the answer would be 9/64. Explain which assumption changes.

3. Conditional probability

Choose equally between a fair coin and a double-headed coin. Toss it once and observe heads. What is the probability it is double-headed?

Worked solution and follow-up

Answer: 2/3. The double-headed-and-heads branch has probability 1/2; the fair-and-heads branch has probability 1/4. Condition on heads: (1/2)/(1/2 + 1/4) = 2/3.

After two heads from the same coin, the probability becomes 4/5.

4. Expected value

A fair die game costs $5 and pays $25 only on a six. What is the expected net profit per play?

Worked solution and follow-up

Answer: −$5/6. Expected payout is $25/6. The entry fee is paid on every outcome, so net expectation is $25/6 − $5 = −$5/6.

The fair entry price for a risk-neutral player is $25/6. A fair price does not remove outcome risk.

5. Expected value

Roll a fair die. You may keep the result or reroll once and must accept the second result. Which first-roll values should you reroll to maximize expected score?

Worked solution and follow-up

Answer: 1, 2, and 3. A forced reroll has expected value 3.5. Reroll any observed value below 3.5; keep 4, 5, and 6. The resulting expected score is (3 × 3.5 + 4 + 5 + 6)/6 = 4.25.

If you must pay one point to reroll, the reroll value is 2.5, so reroll only 1 and 2.

6. Statistics

X and Y are independent with variance 1 each. What is Var(2X − Y)?

Worked solution and follow-up

Answer: 5. Variance scales with the square of the coefficient. Independence removes the covariance term: 4 Var(X) + Var(Y) = 5.

Without independence, subtract 4 Cov(X,Y). The covariance term cannot be ignored just because the means are zero.

7. Research judgment

You predict tomorrow’s return. Which validation choice is most likely to leak information?

Worked solution and follow-up

Answer: Choose features using all dates before splitting the data. Feature selection on all dates uses the evaluation period to influence the model. Put every learned step inside the training window; then evaluate on data that did not affect those choices.

Time ordering alone does not fix leakage if normalization, feature selection, or repeated model tuning sees the holdout.

8. Coding reasoning

For n sorted distinct values, what is the worst-case number of comparisons for binary search, in big-O notation?

Worked solution and follow-up

Answer: O(log n). Each comparison approximately halves the remaining interval. After k steps there are about n/2ᵏ candidates; reducing that to one takes O(log n) steps.

Explain why this does not make insertion into an array O(log n): shifting elements can still cost O(n).

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