Seed content: Quant exponents & roots, remainders, combinatorics, mixtures, and interest (5 lessons, 35 questions)

[DMDaudio]

What does this PR add or change?

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

1. Arithmetic → exponents-roots

• 1 lesson + 7 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 + 7 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

• 1 lesson + 7 questions (0031–0037), easy→hard: committee selection, arranging distinct objects, choose-and-multiply across groups, arrangements with repeated letters, circular seating, "at least one" via the complement, and an adjacency restriction via the block method.

4. Word Problems → mixtures

• 1 lesson + 7 questions (0038–0044), easy→hard: amount = concentration × total, ingredient-as-percent, weighted-average concentration, dilution to a target percent, price mixture / alligation, successive replacement (drain-and-refill), and solving for the volume to hit a target concentration.

5. Word Problems → interest (new in this update)

• 1 lesson (quant-word-problems-interest) — simple interest ((I = Prt)), compound interest ((A = P(1+r)^t)), interest earned vs. final balance, sub-annual compounding ((R/n), (ny)), and the 2-year compound-minus-simple gap (P r^2).

• 7 problem-solving questions (0045–0051) with an easy→hard progression:

  • 0045 (easy) — simple interest earned, (I = Prt)
  • 0046 (easy) — final balance under simple interest (add the principal back)
  • 0047 (medium) — compound interest earned over 2 years
  • 0048 (medium) — solve for the simple annual rate given the interest
  • 0049 (medium) — how much more compound earns than simple over 2 years
  • 0050 (hard) — semiannual compounding (halve the rate, double the periods)
  • 0051 (hard) — recover the principal behind a compounded balance

• Every question's distractors are keyed to a specific common error (e.g. answering with the balance when asked for interest, forgetting to multiply by time, using simple where compound is meant, applying the full annual rate each sub-period, and subtracting a percentage instead of dividing to reverse compound growth).

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

• Rebuilt docs/data/content.json — now 67 questions, 13 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.