Seed content: Quant exponents & roots, remainders, and combinatorics (3 lessons, 21 questions)

[DMDaudio]

What does this PR add or change?

Adds three previously-uncovered but high-frequency Quant subtopic bundles.

1. Arithmetic → exponents-roots

• 1 lesson (quant-arithmetic-exponents-roots) — power rules, negative/zero/fractional exponents, radical simplification, factoring common powers.
• 7 problem-solving questions (0017–0023), easy→hard: power rules, negative/zero exponents, same-base equations, fractional exponents, radicals, factoring a sum of equal powers, ratio of powers.

2. Number Properties → remainders

• 1 lesson (quant-number-properties-remainders) — the division identity (n = dq + r), combining remainders across sums and products (reduce again at the end), power cyclicity / units digits, and simultaneous-condition (lcm) problems.
• 7 problem-solving questions (0024–0030), easy→hard: remainder of a sum, translating quotient/remainder, remainder of a product, remainder of a power via units-digit cyclicity, simultaneous remainder conditions, reasoning from the remainder of (n^2) back to (n), and combining mod-4 / mod-6 to get a remainder mod 12.

3. Counting & Probability → combinatorics (new in this update)

• 1 lesson (quant-counting-probability-combinatorics) — the central "does order matter?" decision, factorials, permutations vs combinations ((C = P/k!)), the multiplication/addition principles, identical-item arrangements, circular seating ((n-1)!), and the at-least-one complement.

• 7 problem-solving questions (0031–0037) with an easy→hard progression:

  • 0031 (easy) — basic committee selection (combination vs permutation)
  • 0032 (easy) — arranging distinct objects in a row ((n!))
  • 0033 (medium) — choose-and-multiply across two groups (multiplication principle)
  • 0034 (medium) — arrangements of a word with repeated letters
  • 0035 (medium) — circular seating, ((n-1)!)
  • 0036 (hard) — "at least one" via the complement
  • 0037 (hard) — adjacency restriction via the block method

• Every question's distractors are keyed to a specific common error (e.g. using (P) where (C) belongs, adding instead of multiplying independent stages, forgetting to divide out repeated letters, treating a round table like a row, double-counting "at least one," and solving for the "not-adjacent" complement by mistake).

• Choice-level and body math is wrapped in \( \) / \[ \] for KaTeX rendering; currency uses a literal $.

• Rebuilt docs/data/content.json — now 53 questions, 11 lessons; node scripts/build.mjs reports zero warnings.

Type of change

• New question(s)
• New lesson(s)
• Fix to existing content (answer / explanation / tag)
• Tooling / docs / schema

Author checklist

• This is my own original work — not copied or paraphrased from any real GMAT question or prep material.
• Front-matter follows CONTENT_SCHEMA.md (id matches the filename; topic/subtopic exist in curriculum.md).
• I solved every question myself and confirmed exactly one answer choice is correct.
• Each explanation would help someone who got the question wrong, and names the trap where relevant.
• status is in-review. I did not set my own content to verified.

For reviewers

• I solved the question(s) without reading the keyed answer first and got the same answer.
• Exactly one choice is correct; distractors are plausible.
• Explanation and tags (section / topic / difficulty) are accurate.
• If approving: bumped status to verified and added my handle to reviewers.