Seed content: 8 Quant bundles — exponents-roots, remainders, combinatorics, mixtures, interest, sequences-functions, odds-evens-signs, and translation (8 lessons, 56 questions)

[DMDaudio]

What does this PR add or change?

Adds eight 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

• 1 lesson + 7 questions (0045–0051), easy→hard: simple interest earned, final balance under simple interest, compound interest earned over 2 years, solving for the simple annual rate, compound-minus-simple gap over 2 years, semiannual compounding, and recovering the principal behind a compounded balance.

6. Algebra → sequences-functions

• 1 lesson + 7 questions (0052–0058), easy→hard: arithmetic/geometric nth term, sum of an arithmetic sequence, function composition, a recursively-defined sequence, recovering the first term from two given terms, and the first geometric term to exceed a threshold.

7. Number Properties → odds-evens-signs

• 1 lesson + 7 questions (0059–0065), easy→hard: parity of an expression given (n) even, sign of a product of negatives, what mn odd implies, sign logic from (xy>0) and (x+y<0), why (n^2+n) is always even, divisibility of consecutive-integer sums, and an "always odd" identification.

8. Word Problems → translation (new in this update)

• 1 lesson (quant-word-problems-translation) — a phrase-to-symbol dictionary (is/sum/less than/of/per), the right-to-left reading of "less than" and "fewer than", grouping cues ("the sum of …" means parentheses: (2n+6) vs. (2(n+6))), the consecutive-integer correction ((3n+3), not (3n)), and the discipline of naming the unknown so you report the quantity actually asked for.

• 7 problem-solving questions (0066–0072) with an easy→hard progression:

  • 0066 (easy) — basic setup: "twice a number, increased by 6, is 20"
  • 0067 (easy) — sum of three consecutive integers, asking for the largest
  • 0068 (medium) — ages: "4 more than twice the brother's age," sum given
  • 0069 (medium) — nickels-and-dimes two-equation system
  • 0070 (medium) — ratio + revenue ("three times as many student tickets")
  • 0071 (hard) — before/after fractions, where adding to blue changes both numerator and denominator
  • 0072 (hard) — two-unknown "8 less than 3 times the smaller" system

• Every question's distractors are keyed to a specific common error (reporting the wrong quantity — the smaller number, the brother, the adult count; reversing subtraction with "less than"; misplacing the multiplier as (2(n+6)) vs (2n+6); dropping the consecutive-integer correction; and the "which total?" before/after mix-up).

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

• Rebuilt docs/data/content.json — now 88 questions, 16 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.