Coding and algorithms (SWE / QR)
2-4 problems · 60-90 minutes
What it tests. Data structures (hash maps, heaps, graphs), optimization (two-pointer, sliding window, DP) and algorithmic efficiency.
Worked example. Given daily stock prices and an integer K, compute the maximum profit with at most K non-overlapping buy/sell transactions (a DP solution; the equivalent of unlimited transactions when K >= n/2).
Common traps. Over-engineering with class hierarchies; failing hidden edge cases (empty arrays, negatives, duplicates, integer overflow).
How to handle it. Read the constraints first: if N is up to 100,000 your solution must be O(N) or O(N log N), since O(N^2) times out for partial credit.
Mental math and arithmetic speed (QT)
A classic "80 questions in 8 minutes" (some variants 60 in 8) · ~8 minutes
What it tests. Raw numerical fluency under intense time pressure: arithmetic, fractions, percentages.
Worked example. 37 x 43 = (40 - 3)(40 + 3) = 1600 - 9 = 1591; 15% of 840 = 84 + 42 = 126.
Common traps. The perfectionist freeze (20 seconds on one hard item costs five easy ones); sign and decimal errors.
How to handle it. Use structural shortcuts (difference of squares, 10%+5% decomposition) and keep a steady rhythm; calculators and aids are prohibited.
Number sequences and pattern recognition
20-30 sequences · 10-15 minutes
What it tests. Rapid inductive reasoning across arithmetic, geometric, Fibonacci and interleaved patterns.
Worked example. 3, 7, 15, 31, 63, ... follows a_n = 2 a_(n-1) + 1, so the next term is 127. Differences of 2, 3, 6, 11, 18 are +1, +3, +5, +7, so the next term is 27.
Common traps. Tunnel vision on simple addition; missing alternating odd/even-index rules.
How to handle it. Check first-order differences first, then second-order differences, geometric ratios and square/cube offsets.
Probability, statistics and combinatorics
10-15 problems · 30-45 minutes
What it tests. Conditional probability, Bayes, expected value, variance, dice/card/urn counting and game-theoretic optimization.
Worked example. Two fair dice with sum at least 10: of the 6 outcomes, 5 contain at least one 6, so P(at least one 6 | sum >= 10) = 5/6. A committee of 4 from 8 juniors and 4 seniors: P(exactly 2 and 2) = (C(8,2) x C(4,2)) / C(12,4) = 168/495 = 56/165.
Common traps. Base-rate fallacy (forgetting to adjust the denominator); double-counting dice or card combinations.
How to handle it. Use linearity of expectation, symmetry and complementary counting to bypass long summations.
Trading / market-making game simulation (QT)
What it tests. Capturing expected value while managing inventory and adverse selection.
Worked example. True value uniform on $10-$30 (E[V] = $20). Quote 18 bid / 22 ask; as samples or clues arrive, update fair value and skew quotes to flatten inventory.
Common traps. Holding a fixed fair value despite the order flow; quoting absurdly wide (1 / 100) and getting zero trades and a zero score.
How to handle it. If you go heavily long, lower both bid and ask to attract sellers away and incentivize buyers; take calibrated risk to generate P&L.