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ZACBENCH-600 (now 700 — file/module name kept for continuity)
Renamed from ZACBENCH-500 → ZACBENCH-600 (2026-07-11): an English-language proficiency category (100 Q) was added 2026-06-22, making it 6 categories. Expanded to 700 (2026-07-28): a 7th category, Agentic (100 Q, tool-call correctness), was added. The file and script are still named
ZACBENCH-600.md/benchmark_600.py— renaming would ripple through every launcher and doc that references them for no functional gain, so the name is historical, not descriptive of the current total. The code is the source of truth either way:finetune/benchmark_600.py+_b500_*.py(7 files, 700 questions).
Internal benchmark suite, 7 categories x 100 questions = 700 total. Every Math/Logic answer
was re-derived via real computation or brute-force constraint search before being written (not
guessed); every Coding reference solution was run against its listed test cases; every
Instruction-Following question has a programmatic verifier function (shown as a description here,
since the actual code is Python and not meaningful to print standalone); every Agentic question's
expected_tool/required_args was checked against the tool schema in _b500_agentic.py before
being committed, and the scoring function was self-tested against synthetic KNOWN-correct and
KNOWN-wrong answers before being trusted (100/100 on correct input, 20/100 — exactly the count of
distractor questions where no call is correct — on "never call a tool").
Answer extraction convention: when running this benchmark against a model, wrap the expected final
answer instruction as <answer>...</answer> in the prompt so verification doesn't depend on
parsing free-form text — except Agentic, which asks for a bare {"name":...,"arguments":{...}}
JSON object, matching the format the model is actually trained to produce
(inference/agent_loop.py's own parser), not an artificial benchmark-only format.
On why this exists as OUR benchmark, and how to check our work
We publish this alongside model scores rather than only citing recognised public benchmarks (GSM8K, HumanEval) because those cover a narrow slice of what an assistant actually does day to day, and because a large public benchmark's questions eventually leak into someone's training data across the field — deliberately or not. ZACBENCH exists to test what public sets miss, not to replace them.
The honest tradeoff: it is our benchmark, on our model, so treat any single vendor's score on their own eval with appropriate skepticism — including ours. What we can offer instead of "trust us" is everything needed to check the claim yourself: the exact questions, the exact scoring code, the exact token budget every model gets, and a written record of what was verified before a score was ever produced. Run it yourself against Zacoda or against anything else.
Automated scripts
| what | where |
|---|---|
| runner | finetune/benchmark_600.py |
| question banks | finetune/_b500_{math,coding,gk,logic,instruct,english,agentic}.py |
| local launcher | finetune/run_zacbench600_local.sh |
python3 finetune/benchmark_600.py --fused-dir <path/to/mlx/model> --model-name my-model
# or a single section while iterating:
python3 finetune/benchmark_600.py --fused-dir <path> --model-name my-model --agentic-only
Also supports --ollama-model and --claude-model backends, so a comparison across models runs
through the identical scoring code — nobody's answer gets parsed by a different, more forgiving
path (see the thinking-token section below for the token-budget half of that guarantee).
Thinking-token limitations — read before comparing scores across models
Every model gets the exact same flat token budget per section, with a prompted "think step by step" instruction — no model gets a separate reasoning/thinking-budget parameter that another model in the comparison doesn't also get. This is not a preference, it is a rule this project has been burned by breaking: on 2026-06-17 we found Claude agent calls were silently receiving +5000 tokens via the Anthropic API's extended-thinking parameter on top of the flat section budget, while every local model got the flat budget only — a real asymmetry that had already produced comparison results before it was caught.
| section | tokens | why this number |
|---|---|---|
| General Knowledge | 1700 | MCQ + XML answer tag headroom over the 380-suite's 1500 |
| Logic & Reasoning | 1700 | same |
| Math | 2500 | raised from 1000 (2026-06-20) after a live smoke test showed genuine mid-solution truncation, not a capability failure — a model correctly computed several AIME-tier answers inside its own reasoning and ran out of budget before writing the answer tag. Decided once, before testing any other model, applied to all. |
| Coding | 3200 | longest budget — full function bodies plus reasoning |
| Instruction Following | 1500 | shortest MCQ-adjacent budget — these are compliance checks, not derivations |
| English | 1700 | same as GK/Logic |
| Agentic | 1200 | lowest of all — a correct answer is either one JSON tool call or a brief direct answer, never a long derivation. Not a shortcut: it is sized to what a correct answer actually looks like, the same principle behind every other section's number. |
A structural cost every model pays identically, not a per-model penalty: native-thinking models were observed to fully solve a problem inside their reasoning trace, then RE-DERIVE the same solution a second time in the visible answer before reaching the final tag — roughly doubling the effective cost of the same reasoning for no benefit. Raising the token budget further would just chase that verbosity habit rather than fix the actual waste, so every prompt instead ends with an explicit instruction not to restate reasoning after thinking is done. This applies identically to every backend and every model, local or API.
If true equal treatment is technically impossible for a given backend (e.g. an API enforces a minimum that conflicts with the agreed budget), the rule is to stop and pick the fix deliberately rather than silently choose the least-bad option — this has been the project's standing rule since before the Claude extended-thinking incident above, and the incident is exactly why it is written down here instead of assumed.
1. Math (100 questions)
| # | Question | Gold Answer | Difficulty |
|---|---|---|---|
| 1 | What is the sum of the first 50 positive integers? | 1275 | easy |
| 2 | How many positive divisors does 360 have? | 24 | medium |
| 3 | Find the remainder when 7^2024 is divided by 13. | 3 | hard |
| 4 | Two fair six-sided dice are rolled. The probability the sum is 7 can be written as a/b in lowest terms. What is b? | 6 | medium |
| 5 | How many trailing zeros does 100! have? | 24 | hard |
| 6 | Compute |3+4i|^2 + |1-2i|^2. | 30 | medium |
| 7 | What is the smallest positive integer n such that n^2 has exactly 15 positive divisors? | 12 | hard |
| 8 | Compute the determinant of the matrix [[2,1,3],[0,4,1],[5,2,2]]. | -43 | medium |
| 9 | What is the sum of all positive divisors of 2024? | 4320 | hard |
| 10 | An arithmetic sequence has first term 5 and common difference 3. What is the sum of the first 20 terms? | 670 | easy |
| 11 | In how many ways can a 2x10 rectangular board be tiled using 1x2 dominoes? | 89 | hard |
| 12 | The polynomial x^3 - 6x^2 + 11x - 6 has three roots. What is the sum of the squares of the roots? | 14 | hard |
| 13 | Compute the binomial coefficient C(20,7). | 77520 | medium |
| 14 | What is the largest power of 2 that divides 2024! (i.e. the exponent of 2 in its prime factorization)? | 2017 | hard |
| 15 | A triangle has vertices at (0,0), (4,0), and (2,5). What is its area? | 10 | medium |
| 16 | How many ordered triples of positive integers (x,y,z) satisfy x+y+z=20? | 171 | hard |
| 17 | What is log base 2 of 1024? | 10 | easy |
| 18 | A sequence is defined by a(1)=1, a(2)=1, a(n)=a(n-1)+a(n-2) for n>2. What is a(15)? | 610 | medium |
| 19 | A fair coin is flipped 5 times. The probability of getting exactly 3 heads is a/b in lowest terms. What is a+b? | 21 | medium |
| 20 | How many positive integers from 1 to 1000 inclusive are divisible by 3 or 5, but not both? | 401 | hard |
| 21 | A bat and ball together cost $1.10. The bat costs $1.00 more than the ball. How many cents does the ball cost? | 5 | adversarial |
| 22 | A rectangle has length 8 and width 5. What is its perimeter? | 26 | easy |
| 23 | How many subsets of {1,2,...,10} (including the empty set) have a sum divisible by 3? | 344 | hard |
| 24 | Solve for x: 2^x = 32 * 4^(x-1). | -3 | medium |
| 25 | What is 2^2024 mod 9? | 4 | hard |
| 26 | A geometric series has first term 3, common ratio 2, and 10 terms. What is the sum? | 3069 | medium |
| 27 | What is the smallest positive integer n such that n! has at least 6 trailing zeros? | 25 | hard |
| 28 | What is 15% of 240? | 36 | easy |
| 29 | In how many distinct ways can the letters of the word MISSISSIPPI be arranged? | 34650 | hard |
| 30 | A right triangle has legs of length 9 and 12. What is the length of the hypotenuse? | 15 | medium |
| 31 | What is the sum of the squares of the first 20 positive integers? | 2870 | medium |
| 32 | How many prime numbers are there below 100? | 25 | easy |
| 33 | What is the greatest common divisor of 1260 and 1980? | 180 | medium |
| 34 | What is the least common multiple of 12, 18, and 20? | 180 | medium |
| 35 | What is 11^2024 mod 7? | 2 | hard |
| 36 | How many 3-digit positive integers (100-999) have all distinct digits? | 648 | hard |
| 37 | What is the sum of the first 30 positive odd numbers? | 900 | easy |
| 38 | Two cards are drawn without replacement from a standard 52-card deck. The probability both are aces is a/b in lowest terms. What is a+b? | 222 | hard |
| 39 | How many diagonals does a convex 15-sided polygon have? | 90 | medium |
| 40 | What is the sum of the decimal digits of 2^100? | 115 | hard |
| 41 | What is the smallest positive integer n such that n! is divisible by 1000? | 15 | hard |
| 42 | How many integer pairs (x,y), with x and y each allowed to be negative, zero, or positive, satisfy x^2+y^2=25? | 12 | medium |
| 43 | The sum 1/(12) + 1/(23) + 1/(34) + ... + 1/(1920) equals a/b in lowest terms. What is a+b? | 39 | hard |
| 44 | In how many ways can you make exactly 25 cents using any combination of pennies, nickels, dimes, and quarters? | 13 | hard |
| 45 | A circle has radius 7. Using pi=3.14159, what is its area rounded to the nearest integer? | 154 | easy |
| 46 | Compute the sum: 12^1 + 22^2 + 32^3 + ... + 102^10. | 18434 | hard |
| 47 | In how many distinct ways can the letters of the word BANANA be arranged? | 60 | medium |
| 48 | A triangle has sides of length 7, 8, and 9. What is its area, rounded to 2 decimal places? | 26.83 | medium |
| 49 | How many positive integers from 1 to 200 are a perfect square or a perfect cube, but NOT both? | 15 | hard |
| 50 | A sequence is defined by a(1)=2 and a(n)=3*a(n-1)-1 for n>1. What is a(6)? | 365 | medium |
| 51 | Two fair six-sided dice are rolled. In how many of the 36 outcomes is the sum greater than 8? | 10 | medium |
| 52 | What is the sum of all 3-digit positive multiples of 7? | 70336 | hard |
| 53 | How many subsets of a 6-element set have an even number of elements (including the empty set)? | 32 | medium |
| 54 | What is the smallest positive integer with exactly 10 positive divisors? | 48 | hard |
| 55 | Solve for x: 3^(2x+1) = 81. | 1.5 | medium |
| 56 | What is the sum of the interior angles, in degrees, of a convex 12-sided polygon? | 1800 | easy |
| 57 | In how many ways can you choose 3 numbers from {1,2,...,10} such that no two chosen numbers are consecutive? | 56 | hard |
| 58 | What is 7! divided by 3!? | 840 | easy |
| 59 | What is the smallest positive integer n such that 2^n > 1000? | 10 | easy |
| 60 | A regular hexagon has side length 4. What is its area, rounded to 2 decimal places? | 41.57 | medium |
| 61 | What is the sum of the first 15 Fibonacci numbers (starting 1, 1, 2, 3, 5, ...)? | 1596 | medium |
| 62 | How many trailing zeros does 50! have? | 12 | hard |
| 63 | A positive number plus its reciprocal equals 2.5. What is the larger of the two possible values for the number? | 2 | medium |
| 64 | Four distinct books A, B, C, D are arranged in a row on a shelf. In how many of the 24 arrangements are A and B NOT adjacent to each other? | 12 | medium |
| 65 | sqrt(72) simplifies to a*sqrt(b) where b is squarefree. What is a+b? | 8 | easy |
| 66 | How many integers from 1 to 500 (inclusive) are divisible by neither 2 nor 3? | 167 | medium |
| 67 | A fair coin is flipped repeatedly until the first heads appears. What is the expected number of flips? | 2 | medium |
| 68 | What is the sum of all two-digit positive integers whose digits sum to 10? | 495 | medium |
| 69 | A 3x3 magic square is filled with the numbers 1 through 9, each used once. What is the magic constant (the sum of each row, column, and diagonal)? | 15 | easy |
| 70 | In how many ways can 5 identical balls be placed into 3 distinct boxes, with boxes allowed to be empty? | 21 | hard |
| 71 | A triangle has vertices at (1,1), (4,1), and (4,5). What is its area? | 6 | easy |
| 72 | A fair six-sided die is rolled 4 times. The probability of rolling at least one 6 is a/b in lowest terms. What is a+b? | 1967 | hard |
| 73 | What is the smallest positive integer n such that C(n,2) (n choose 2) is greater than 100? | 15 | medium |
| 74 | The sum 1/1! + 1/2! + 1/3! + 1/4! + 1/5! equals a/b in lowest terms. What is a+b? | 163 | hard |
| 75 | A cube has volume 343 cubic units. What is its total surface area? | 294 | medium |
| 76 | In how many ways can the 6 vertices of a hexagon (arranged in a cycle) be colored using exactly 2 colors such that no two adjacent vertices share a color? | 2 | hard |
| 77 | Compute (2+3i)*(1-4i) and write the result as a+bi. What is a+b (the real part plus the imaginary coefficient)? | 9 | medium |
| 78 | How many zero digits appear in the binary representation of 100? | 4 | easy |
| 79 | What is the sum of all positive divisors of 28 (including 28 itself)? | 56 | easy |
| 80 | A 10-foot ladder leans against a wall with its base 6 feet from the wall. How many feet up the wall does the ladder reach? | 8 | easy |
| 81 | How many trailing zeros does 20! have? | 4 | medium |
| 82 | An infinite geometric series has first term 8 and common ratio 1/4. Its sum equals a/b in lowest terms. What is a+b? | 35 | medium |
| 83 | In how many distinct ways can a 2x3 rectangular board be tiled using 1x2 dominoes? | 3 | medium |
| 84 | What is the smallest positive integer n such that n mod 3 = 2 and n mod 5 = 3? | 8 | hard |
| 85 | How many diagonals does a regular 20-sided polygon have? | 170 | medium |
| 86 | The sum 5/8 + 3/10 equals a/b in lowest terms. What is a+b? | 77 | medium |
| 87 | A rectangle's length is 3 more than its width, and its area is 70. What is the width? | 7 | medium |
| 88 | Two fair six-sided dice are rolled. The probability their sum is 7 equals a/b in lowest terms. What is a+b? | 7 | easy |
| 89 | What is 4! + 5! - 3!? | 138 | easy |
| 90 | What is the smallest integer n greater than 1 such that n^2 - n is divisible by 100? | 25 | hard |
| 91 | In how many distinct ways can 4 people be seated around a round table, where rotations of the same arrangement are considered identical? | 6 | hard |
| 92 | What is the sum of the interior angles, in degrees, of a convex 7-sided polygon? | 900 | easy |
| 93 | A value is increased by 20%, then the result is decreased by 20%. What is the net percent change (as a signed number, negative meaning a decrease)? | -4.0 | medium |
| 94 | What is the greatest common divisor of 0 and 15? | 15 | easy |
| 95 | How many trailing zeros does 30! have? | 7 | medium |
| 96 | Simplify (3/4) divided by (9/16) to a/b in lowest terms. What is a+b? | 7 | medium |
| 97 | What is the smallest positive integer n such that 3^n > 1000? | 7 | medium |
| 98 | On an analog clock showing 3:15, what is the angle in degrees between the hour and minute hands (the smaller of the two possible angles)? | 7.5 | hard |
| 99 | In how many distinct ways can the letters of the word LEVEL be arranged? | 30 | medium |
| 100 | Compute the alternating sum: 1 - 2 + 3 - 4 + ... - 100 (ending on -100). | -50 | medium |
2. Coding (100 questions)
Each question specifies a function to implement; test cases shown as (args -> expected).
1. median_two_sorted (medium)
Write median_two_sorted(a, b) returning the median of two sorted lists merged together.
Tests: median_two_sorted([1, 3], [2]) == 2; median_two_sorted([1, 2], [3, 4]) == 2.5; median_two_sorted([], [1]) == 1
2. longest_valid_parens (hard)
Write longest_valid_parens(s) returning the length of the longest valid parentheses substring.
Tests: longest_valid_parens('(()') == 2; longest_valid_parens(')()())') == 4; longest_valid_parens('') == 0
3. min_window_substring (hard)
Write min_window_substring(s, t) returning the smallest substring of s containing all characters of t (with multiplicity). Return empty string if none exists.
Tests: min_window_substring('ADOBECODEBANC', 'ABC') == 'BANC'; min_window_substring('a', 'a') == 'a'
4. kth_largest_stream_final (medium)
Write kth_largest_stream_final(nums, k) returning the k-th largest element in the list.
Tests: kth_largest_stream_final([4, 5, 8, 2], 3) == 4; kth_largest_stream_final([1], 1) == 1
5. word_ladder_length (hard)
Write word_ladder_length(begin, end, words) returning the length of the shortest transformation sequence from begin to end, changing one letter at a time, each intermediate word must be in words. Return 0 if impossible.
Tests: word_ladder_length('hit', 'cog', ['hot', 'dot', 'dog', 'lot', 'log', 'cog']) == 5; word_ladder_length('hit', 'cog', ['hot', 'dot', 'dog', 'lot', 'log']) == 0
6. max_rectangle_in_histogram (hard)
Write max_rectangle_in_histogram(heights) returning the area of the largest rectangle in a histogram.
Tests: max_rectangle_in_histogram([2, 1, 5, 6, 2, 3]) == 10; max_rectangle_in_histogram([2, 4]) == 4; max_rectangle_in_histogram([]) == 0
7. catalan (medium)
Write catalan(n) returning the n-th Catalan number (number of distinct BST shapes with n nodes).
Tests: catalan(5) == 42; catalan(0) == 1; catalan(1) == 1
8. num_distinct_islands (hard)
Write num_distinct_islands(grid) (grid of 0/1) returning the number of islands that are distinct in SHAPE (translations of the same shape count once). 4-directional adjacency.
Tests: num_distinct_islands([[1, 1, 0, 0, 0], [1, 1, 0, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1]]) == 1
9. largest_bst_subtree_size (medium)
Write largest_bst_subtree_size(vals) returning the length of the longest strictly increasing subsequence of vals.
Tests: largest_bst_subtree_size([10, 9, 2, 5, 3, 7, 101, 18]) == 4; largest_bst_subtree_size([]) == 0
10. reconstruct_itinerary (hard)
Write reconstruct_itinerary(tickets) (list of [from,to] pairs, all from JFK) returning the lexicographically smallest valid itinerary using every ticket exactly once, as a list of airport codes.
Tests: reconstruct_itinerary([['MUC', 'LHR'], ['JFK', 'MUC'], ['SFO', 'SJC'], ['LHR', 'SFO']]) == ['JFK', 'MUC', 'LHR', 'SFO', 'SJC']
11. edit_distance (medium)
Write edit_distance(s, t) returning the minimum single-character insert/delete/substitute operations to turn s into t.
Tests: edit_distance('horse', 'ros') == 3; edit_distance('', 'abc') == 3; edit_distance('abc', 'abc') == 0
12. coin_change (medium)
Write coin_change(coins, amount) returning the minimum number of coins to make amount, or -1 if impossible.
Tests: coin_change([1, 2, 5], 11) == 3; coin_change([2], 3) == -1; coin_change([1], 0) == 0
13. num_islands (easy)
Write num_islands(grid) (grid of '1'/'0' strings) counting islands under 4-directional adjacency.
Tests: num_islands([['1', '1', '0', '0', '0'], ['1', '1', '0', '0', '0'], ['0', '0', '1', '0', '0'], ['0', '0', '0', '1', '1']]) == 3
14. sliding_window_max (medium)
Write sliding_window_max(nums, k) returning a list of the maximum value in each sliding window of size k.
Tests: sliding_window_max([1, 3, -1, -3, 5, 3, 6, 7], 3) == [3, 3, 5, 5, 6, 7]; sliding_window_max([1], 1) == [1]
15. trap_rain_water (hard)
Write trap_rain_water(heights) returning the total units of rainwater trapped between the bars.
Tests: trap_rain_water([0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]) == 6; trap_rain_water([]) == 0
16. group_anagrams (easy)
Write group_anagrams(strs) grouping anagrams together. Return a sorted list of sorted groups (sort each group's strings, then sort the list of groups).
Tests: group_anagrams(['eat', 'tea', 'tan', 'ate', 'nat', 'bat']) == [['bat'], ['nat', 'tan'], ['ate', 'eat', 'tea']]
17. topological_sort (medium)
Write topological_sort(graph) (dict of node -> list of neighbors) returning a valid topological order as a list. Raise ValueError on a cycle.
Tests: topological_sort({'A': ['B', 'C'], 'B': ['D'], 'C': ['D'], 'D': []}) -- custom check function
18. lru_cache_ops (hard)
Write lru_cache_ops(ops) simulating an LRU cache. ops is a list of tuples: ("init", capacity), ("put", key, value), ("get", key). Return a list of the results of every "get" call in order (-1 if key not present).
Tests: lru_cache_ops([('init', 2), ('put', 1, 1), ('put', 2, 2), ('get', 1), ('put', 3, 3), ('get', 2), ('put', 4, 4), ('get', 1), ('get', 3), ('get', 4)]) == [1, -1, -1, 3, 4]
19. find_all_permutations (medium)
Write find_all_permutations(nums) returning a sorted list of all unique permutations of nums (each permutation itself sorted in the order produced; the OUTER list sorted ascending).
Tests: find_all_permutations([1, 2, 3]) == [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]
20. rotate_image (medium)
Write rotate_image(matrix) that rotates an n x n matrix 90 degrees clockwise IN PLACE and returns it.
Tests: rotate_image([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) == [[7, 4, 1], [8, 5, 2], [9, 6, 3]]
21. decode_ways (hard)
Write decode_ways(s) (a string of digits) counting the number of ways to decode it into letters where 'A'=1, 'B'=2, ..., 'Z'=26. Return 0 if no valid decoding exists.
Tests: decode_ways('12') == 2; decode_ways('226') == 3; decode_ways('06') == 0
22. max_flow (hard)
Write max_flow(capacity, source, sink) using BFS-based Edmonds-Karp to compute the maximum flow from source to sink. capacity is a dict of dicts: capacity[u][v] is the edge capacity from u to v (0 if no edge).
Tests: max_flow({'S': {'A': 3, 'B': 2}, 'A': {'B': 1, 'T': 2}, 'B': {'T': 3}, 'T': {}}, 'S', 'T') == 5
23. dijkstra (medium)
Write dijkstra(graph, src) returning a dict mapping every node to its shortest distance from src. graph is a dict of dicts: graph[u][v] is the edge weight from u to v.
Tests: dijkstra({'A': {'B': 1, 'C': 4}, 'B': {'C': 2, 'D': 5}, 'C': {'D': 1}, 'D': {}}, 'A') == {'A': 0, 'B': 1, 'C': 3, 'D': 4}
24. two_sum_indices (easy)
Write two_sum_indices(nums, target) returning a sorted 2-element list of the indices of the two numbers that add up to target (assume exactly one solution exists).
Tests: two_sum_indices([2, 7, 11, 15], 9) == [0, 1]; two_sum_indices([3, 2, 4], 6) == [1, 2]
25. valid_parentheses (easy)
Write valid_parentheses(s) returning True if every bracket in s ( (), [], {} ) is properly opened and closed in the correct order, False otherwise.
Tests: valid_parentheses('()[]{}') == True; valid_parentheses('(]') == False
26. merge_intervals (medium)
Write merge_intervals(intervals) (list of [start,end] pairs) returning the merged list of overlapping intervals, sorted by start.
Tests: merge_intervals([[1, 3], [2, 6], [8, 10], [15, 18]]) == [[1, 6], [8, 10], [15, 18]]; merge_intervals([[1, 4], [4, 5]]) == [[1, 5]]
27. is_palindrome_str (easy)
Write is_palindrome_str(s) returning True if s is a palindrome ignoring case, spaces, and punctuation.
Tests: is_palindrome_str('A man, a plan, a canal: Panama') == True; is_palindrome_str('race a car') == False
28. fibonacci_n (easy)
Write fibonacci_n(n) returning the n-th Fibonacci number (0-indexed, fib(0)=0, fib(1)=1).
Tests: fibonacci_n(10) == 55; fibonacci_n(0) == 0
29. max_subarray_sum (medium)
Write max_subarray_sum(nums) returning the largest sum of any contiguous subarray (Kadane's algorithm).
Tests: max_subarray_sum([-2, 1, -3, 4, -1, 2, 1, -5, 4]) == 6
30. binary_search (easy)
Write binary_search(nums, target) on a sorted list, returning the index of target or -1 if not found.
Tests: binary_search([-1, 0, 3, 5, 9, 12], 9) == 4; binary_search([-1, 0, 3, 5, 9, 12], 2) == -1
31. reverse_linked_list_arr (easy)
Write reverse_linked_list_arr(arr) returning arr reversed (simulating reversing a singly linked list represented as a Python list).
Tests: reverse_linked_list_arr([1, 2, 3, 4, 5]) == [5, 4, 3, 2, 1]
32. count_vowels (easy)
Write count_vowels(s) returning the number of vowels (a,e,i,o,u, case-insensitive) in s.
Tests: count_vowels('Hello World') == 3
33. matrix_transpose (easy)
Write matrix_transpose(m) returning the transpose of matrix m (list of lists).
Tests: matrix_transpose([[1, 2, 3], [4, 5, 6]]) == [[1, 4], [2, 5], [3, 6]]
34. is_anagram (easy)
Write is_anagram(a, b) returning True if strings a and b are anagrams of each other.
Tests: is_anagram('listen', 'silent') == True; is_anagram('hello', 'world') == False
35. power_set (medium)
Write power_set(nums) returning all subsets of nums (including empty set and the full set), as a sorted list of sorted subsets, with no duplicate subsets.
Tests: power_set([1, 2, 3]) == [[], [1], [1, 2], [1, 2, 3], [1, 3], [2], [2, 3], [3]]
36. gcd_list (easy)
Write gcd_list(nums) returning the greatest common divisor of all numbers in the list.
Tests: gcd_list([12, 18, 24]) == 6
37. flatten_list (medium)
Write flatten_list(nested) returning a fully flattened (single-level) list from an arbitrarily nested list of lists and values.
Tests: flatten_list([1, [2, 3, [4, 5]], 6]) == [1, 2, 3, 4, 5, 6]
38. find_missing_number (easy)
Write find_missing_number(nums, n) where nums contains n-1 distinct integers from 1 to n with exactly one missing -- return the missing number.
Tests: find_missing_number([1, 2, 4, 5], 5) == 3
39. run_length_encode (medium)
Write run_length_encode(s) returning the run-length encoding of s (e.g. 'aaabbbcc' -> 'a3b3c2'). Return empty string for empty input.
Tests: run_length_encode('aaabbbcc') == 'a3b3c2'; run_length_encode('') == ''
40. reverse_words (easy)
Write reverse_words(s) returning the words of s in reverse order, joined by single spaces.
Tests: reverse_words('the sky is blue') == 'blue is sky the'
41. is_balanced_bst_heights (easy)
Write is_balanced_bst_heights(heights) returning True if the max and min of the list differ by at most 1 (treat empty list as balanced/True).
Tests: is_balanced_bst_heights([3, 4, 3]) == True; is_balanced_bst_heights([1, 5]) == False
42. chunk_list (easy)
Write chunk_list(lst, n) splitting lst into consecutive chunks of size n (the last chunk may be shorter).
Tests: chunk_list([1, 2, 3, 4, 5], 2) == [[1, 2], [3, 4], [5]]
43. first_unique_char_index (medium)
Write first_unique_char_index(s) returning the index of the first character in s that appears exactly once, or -1 if none.
Tests: first_unique_char_index('leetcode') == 0; first_unique_char_index('aabb') == -1
44. is_subsequence (easy)
Write is_subsequence(s, t) returning True if s is a subsequence of t (characters of s appear in t in order, not necessarily contiguous).
Tests: is_subsequence('abc', 'ahbgdc') == True; is_subsequence('axc', 'ahbgdc') == False
45. rotate_array (medium)
Write rotate_array(nums, k) returning nums rotated right by k positions.
Tests: rotate_array([1, 2, 3, 4, 5, 6, 7], 3) == [5, 6, 7, 1, 2, 3, 4]
46. longest_common_prefix (medium)
Write longest_common_prefix(strs) returning the longest common prefix string among a list of strings, or empty string if none.
Tests: longest_common_prefix(['flower', 'flow', 'flight']) == 'fl'; longest_common_prefix(['dog', 'racecar', 'car']) == ''
47. is_power_of_two (easy)
Write is_power_of_two(n) returning True if n is a power of two (n > 0).
Tests: is_power_of_two(16) == True; is_power_of_two(18) == False
48. merge_two_sorted_lists (easy)
Write merge_two_sorted_lists(a, b) merging two already-sorted lists into one sorted list.
Tests: merge_two_sorted_lists([1, 3, 5], [2, 4, 6]) == [1, 2, 3, 4, 5, 6]
49. count_set_bits (easy)
Write count_set_bits(n) returning the number of 1-bits in the binary representation of n.
Tests: count_set_bits(11) == 3
50. spiral_matrix (hard)
Write spiral_matrix(matrix) returning all elements of the matrix in clockwise spiral order, starting from the top-left.
Tests: spiral_matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) == [1, 2, 3, 6, 9, 8, 7, 4, 5]
51. majority_element (medium)
Write majority_element(nums) returning the element that appears more than floor(len(nums)/2) times (guaranteed to exist).
Tests: majority_element([2, 2, 1, 1, 1, 2, 2]) == 2
52. is_valid_bst_inorder (easy)
Write is_valid_bst_inorder(vals) returning True if vals is strictly increasing (i.e. would be a valid in-order traversal of a BST with no duplicate keys).
Tests: is_valid_bst_inorder([1, 2, 3, 4]) == True; is_valid_bst_inorder([1, 3, 2, 4]) == False
53. remove_duplicates_sorted (easy)
Write remove_duplicates_sorted(nums) returning nums with consecutive duplicates removed (nums is already sorted).
Tests: remove_duplicates_sorted([1, 1, 2, 2, 3]) == [1, 2, 3]
54. is_perfect_number (medium)
Write is_perfect_number(n) returning True if n equals the sum of its proper divisors (e.g. 28 = 1+2+4+7+14).
Tests: is_perfect_number(28) == True; is_perfect_number(12) == False
55. caesar_cipher (medium)
Write caesar_cipher(s, shift) shifting each letter of s forward by shift positions in the alphabet (wrapping around), preserving case and leaving non-letters unchanged.
Tests: caesar_cipher('abc', 2) == 'cde'; caesar_cipher('XYZ', 3) == 'ABC'
56. is_armstrong_number (medium)
Write is_armstrong_number(n) returning True if n equals the sum of its own digits each raised to the power of the digit count (e.g. 153 = 1^3+5^3+3^3).
Tests: is_armstrong_number(153) == True; is_armstrong_number(154) == False
57. matrix_multiply (medium)
Write matrix_multiply(a, b) returning the matrix product of a and b (lists of lists).
Tests: matrix_multiply([[1, 2], [3, 4]], [[5, 6], [7, 8]]) == [[19, 22], [43, 50]]
58. longest_word (easy)
Write longest_word(s) returning the longest word in the string s (ties broken by first occurrence).
Tests: longest_word('the quick brown fox') == 'quick'
59. is_subset_sum (medium)
Write is_subset_sum(nums, target) returning True if some subset of nums sums exactly to target.
Tests: is_subset_sum([3, 34, 4, 12, 5, 2], 9) == True; is_subset_sum([3, 34, 4, 12, 5, 2], 30) == False
60. count_words (easy)
Write count_words(s) returning the number of whitespace-separated words in s.
Tests: count_words('hello world foo') == 3
61. sum_digits_until_single (easy)
Write sum_digits_until_single(n) repeatedly summing the digits of n until a single digit remains (the digital root).
Tests: sum_digits_until_single(9875) == 2
62. find_peak_index (medium)
Write find_peak_index(nums) returning the index of any local peak (an element greater than both its neighbors; for edge elements, only the one existing neighbor needs to be smaller).
Tests: find_peak_index([1, 2, 3, 1]) == 2
63. remove_vowels (easy)
Write remove_vowels(s) returning s with all vowels (a,e,i,o,u, case-insensitive) removed.
Tests: remove_vowels('Hello World') == 'Hll Wrld'
64. is_valid_ipv4 (medium)
Write is_valid_ipv4(s) returning True if s is a valid IPv4 address (4 dot-separated parts, each 0-255, no leading zeros except the literal '0' itself).
Tests: is_valid_ipv4('192.168.1.1') == True; is_valid_ipv4('256.1.1.1') == False; is_valid_ipv4('01.1.1.1') == False
65. word_frequency (easy)
Write word_frequency(s) returning a dict mapping each lowercase word in s to its occurrence count.
Tests: word_frequency('the cat the dog') == {'the': 2, 'cat': 1, 'dog': 1}
66. is_rotation (medium)
Write is_rotation(s1, s2) returning True if s2 is a rotation of s1 (same length, and s2 appears as a substring of s1+s1).
Tests: is_rotation('waterbottle', 'erbottlewat') == True; is_rotation('abc', 'acb') == False
67. max_profit_stock (medium)
Write max_profit_stock(prices) returning the maximum profit from buying then selling once (buy before sell), or 0 if no profit is possible.
Tests: max_profit_stock([7, 1, 5, 3, 6, 4]) == 5; max_profit_stock([7, 6, 4, 3, 1]) == 0
68. is_happy_number (medium)
Write is_happy_number(n) -- repeatedly replace n with the sum of squares of its digits; return True if this reaches 1, False if it cycles without reaching 1.
Tests: is_happy_number(19) == True; is_happy_number(2) == False
69. common_elements (easy)
Write common_elements(a, b) returning a sorted list of the distinct elements present in both a and b.
Tests: common_elements([1, 2, 3, 4], [3, 4, 5, 6]) == [3, 4]
70. to_roman (medium)
Write to_roman(n) converting a positive integer (1-3999) to its Roman numeral representation.
Tests: to_roman(1994) == 'MCMXCIV'
71. diagonal_sum (medium)
Write diagonal_sum(matrix) returning the sum of both diagonals of a square matrix, counting the center cell only once if the matrix has odd size.
Tests: diagonal_sum([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) == 25
72. is_pangram (easy)
Write is_pangram(s) returning True if s contains every letter of the English alphabet at least once (case-insensitive).
Tests: is_pangram('The quick brown fox jumps over the lazy dog') == True; is_pangram('Hello world') == False
73. find_duplicates (easy)
Write find_duplicates(nums) returning a sorted list of values that appear more than once in nums (each duplicate value listed only once).
Tests: find_duplicates([1, 2, 3, 2, 1, 5, 3]) == [1, 2, 3]
74. string_compression (medium)
Write string_compression(s) returning the run-length compressed form where each run of length 1 has NO count suffix (e.g. 'aabcccccaaa' -> 'a2bc5a3').
Tests: string_compression('aabcccccaaa') == 'a2bc5a3'
75. kth_smallest (easy)
Write kth_smallest(nums, k) returning the k-th smallest element (1-indexed) in nums.
Tests: kth_smallest([3, 1, 4, 1, 5, 9, 2, 6], 3) == 2
76. num_ways_climb_stairs (medium)
Write num_ways_climb_stairs(n) returning the number of distinct ways to climb n stairs taking 1 or 2 steps at a time.
Tests: num_ways_climb_stairs(5) == 8
77. is_strobogrammatic (hard)
Write is_strobogrammatic(s) returning True if the digit string s looks the same when rotated 180 degrees (each digit maps as 0->0, 1->1, 6->9, 8->8, 9->6, reading the rotated string in reverse).
Tests: is_strobogrammatic('69') == True; is_strobogrammatic('123') == False
78. single_number (medium)
Write single_number(nums) where every element appears exactly twice except one which appears once -- return that single element (use XOR for O(n) time, O(1) space).
Tests: single_number([4, 1, 2, 1, 2]) == 4
79. is_monotonic (easy)
Write is_monotonic(nums) returning True if nums is entirely non-decreasing OR entirely non-increasing.
Tests: is_monotonic([1, 2, 2, 3]) == True; is_monotonic([1, 3, 2]) == False
80. product_except_self (hard)
Write product_except_self(nums) returning a list where each element is the product of all other elements (no division allowed, O(n) time).
Tests: product_except_self([1, 2, 3, 4]) == [24, 12, 8, 6]
81. find_all_anagram_starts (hard)
Write find_all_anagram_starts(s, p) returning a list of starting indices in s where a substring is an anagram of p.
Tests: find_all_anagram_starts('cbaebabacd', 'abc') == [0, 6]
82. count_primes_below (medium)
Write count_primes_below(n) returning the count of prime numbers strictly less than n.
Tests: count_primes_below(10) == 4
83. is_perfect_square (easy)
Write is_perfect_square(n) returning True if n is a perfect square (n >= 0).
Tests: is_perfect_square(16) == True; is_perfect_square(15) == False
84. reverse_integer (easy)
Write reverse_integer(n) returning n with its digits reversed, preserving the sign.
Tests: reverse_integer(123) == 321; reverse_integer(-456) == -654
85. move_zeros_to_end (easy)
Write move_zeros_to_end(nums) moving all zeros to the end of the list while preserving the relative order of non-zero elements.
Tests: move_zeros_to_end([0, 1, 0, 3, 12]) == [1, 3, 12, 0, 0]
86. is_unique_chars (easy)
Write is_unique_chars(s) returning True if every character in s is distinct (no repeats).
Tests: is_unique_chars('abcdef') == True; is_unique_chars('aabbcc') == False
87. fizzbuzz (easy)
Write fizzbuzz(n) returning a list of strings for 1..n: 'Fizz' if divisible by 3, 'Buzz' if divisible by 5, 'FizzBuzz' if divisible by both, else the number as a string.
Tests: fizzbuzz(3) == ['1', '2', 'Fizz']
88. max_consecutive_ones (easy)
Write max_consecutive_ones(nums) returning the length of the longest run of consecutive 1s in a list of 0s and 1s.
Tests: max_consecutive_ones([1, 1, 0, 1, 1, 1]) == 3
89. is_symmetric_list (easy)
Write is_symmetric_list(nums) returning True if the list reads the same forwards and backwards.
Tests: is_symmetric_list([1, 2, 3, 2, 1]) == True; is_symmetric_list([1, 2, 3]) == False
90. merge_dicts (easy)
Write merge_dicts(a, b) returning a new dict combining a and b, with b's values taking precedence on key collisions.
Tests: merge_dicts({'a': 1}, {'b': 2}) == {'a': 1, 'b': 2}
91. count_char_occurrences (easy)
Write count_char_occurrences(s, c) returning the number of times character c appears in string s.
Tests: count_char_occurrences('mississippi', 's') == 4
92. is_palindrome_number (easy)
Write is_palindrome_number(n) returning True if the integer n reads the same forwards and backwards.
Tests: is_palindrome_number(121) == True; is_palindrome_number(123) == False
93. sum_of_digits (easy)
Write sum_of_digits(n) returning the sum of the digits of n (n may be negative; use the absolute value).
Tests: sum_of_digits(-12345) == 15
94. title_case_words (easy)
Write title_case_words(s) capitalizing the first letter of each word and lowercasing the rest.
Tests: title_case_words('hello world') == 'Hello World'
95. is_anagram_ignoring_case_space (easy)
Write is_anagram_ignoring_case_space(a, b) returning True if a and b are anagrams of each other, ignoring case and spaces.
Tests: is_anagram_ignoring_case_space('Listen', 'Silent') == True; is_anagram_ignoring_case_space('hello', 'world') == False
96. binary_to_decimal (easy)
Write binary_to_decimal(s) converting a binary string to its decimal integer value.
Tests: binary_to_decimal('1010') == 10
97. decimal_to_binary (easy)
Write decimal_to_binary(n) converting a non-negative integer to its binary string representation (no '0b' prefix).
Tests: decimal_to_binary(10) == '1010'
98. is_leap_year (medium)
Write is_leap_year(y) returning True if year y is a leap year (divisible by 4, but not by 100 unless also by 400).
Tests: is_leap_year(2024) == True; is_leap_year(1900) == False
99. longest_palindromic_substring (hard)
Write longest_palindromic_substring(s) returning the longest substring of s that is a palindrome (any one of the longest if there's a tie).
Tests: longest_palindromic_substring('babad') -- custom check function
100. two_largest (easy)
Write two_largest(nums) returning the two largest values in nums, in descending order.
Tests: two_largest([3, 1, 4, 1, 5, 9, 2, 6]) == [9, 6]
3. General Knowledge (100 questions)
| # | Question | Gold | Category | Difficulty |
|---|---|---|---|---|
| 1 | Question: Which enzyme deficiency causes phenylketonuria (PKU)? A) Phenylalanine hydroxylase B) Tyrosine hydroxylase C) Homogentisate oxidase D) Branched-chain ketoacid dehydrogenase | A | biochemistry | hard |
| 2 | Question: The Maastricht Treaty (1992) established which of the following? A) The European Coal and Steel Community B) The European Union and a path to the euro C) The Schengen Area D) NATO's post-Cold War expansion framework | B | history | medium |
| 3 | Question: In macroeconomics, the 'liquidity trap' refers to a situation where: A) Interest rates are so low that monetary policy becomes ineffective at stimulating demand B) Banks refuse to lend due to high default rates C) Currency becomes illiquid due to capital controls D) Inflation expectations become unanchored | A | economics | hard |
| 4 | Question: Which 1803 Supreme Court case first struck down an act of Congress as unconstitutional? A) McCulloch v. Maryland B) Marbury v. Madison C) Gibbons v. Ogden D) Fletcher v. Peck | B | law | medium |
| 5 | Question: The Chandrasekhar limit (~1.4 solar masses) marks the maximum mass of a stable: A) Neutron star B) Black hole C) White dwarf D) Red giant | C | astrophysics | medium |
| 6 | Question: Which treaty formally ended the Thirty Years' War and is considered foundational to the modern concept of state sovereignty? A) Treaty of Utrecht B) Treaty of Westphalia C) Treaty of Tordesillas D) Peace of Augsburg | B | history | medium |
| 7 | Question: In immunology, regulatory T cells (Tregs) primarily function by: A) Directly killing virus-infected cells B) Producing antibodies against pathogens C) Suppressing other immune cells to maintain self-tolerance D) Presenting antigens to naive T cells | C | immunology | hard |
| 8 | Question: The Coase theorem states that, with zero transaction costs and well-defined property rights: A) Government intervention is always required to correct externalities B) Parties will bargain to an efficient outcome regardless of how rights are initially allocated C) Pigouvian taxes are the only efficient remedy for externalities D) Externalities necessarily cause permanent market failure | B | economics | hard |
| 9 | Question: Which structure in the inner ear is responsible for detecting angular (rotational) acceleration? A) Cochlea B) Semicircular canals C) Saccule D) Organ of Corti | B | physiology | medium |
| 10 | Question: The Bretton Woods system (1944-1971) pegged major currencies to: A) Gold directly B) The US dollar, which was itself pegged to gold C) A basket of commodities D) Special Drawing Rights (SDRs) | B | economics | medium |
| 11 | Question: In contract law, 'promissory estoppel' allows enforcement of a promise even without consideration when: A) The promisor is a merchant B) The promise was made in writing C) The promisee reasonably relied on the promise to their detriment D) The contract value exceeds a statutory threshold | C | law | hard |
| 12 | Question: The Krebs cycle (citric acid cycle) produces how many NADH molecules per glucose molecule, counting both turns of the cycle? A) 2 B) 4 C) 6 D) 8 | C | biochemistry | medium |
| 13 | Question: Which 1815 congress redrew the map of Europe after the Napoleonic Wars, establishing a balance-of-power system? A) Congress of Berlin B) Congress of Vienna C) Congress of Westphalia D) Treaty of Paris | B | history | easy |
| 14 | Question: In international law, 'jus cogens' refers to: A) Norms binding only between treaty signatories B) Peremptory norms from which no derogation is permitted C) Customary norms requiring reciprocity D) Norms enforceable only by the UN Security Council | B | law | hard |
| 15 | Question: The Schwarzschild radius of a black hole of mass M is given by: A) GM/c^2 B) 2GM/c^2 C) GM/c D) 4GM/c^2 | B | astrophysics | medium |
| 16 | Question: Ricardian equivalence suggests that government deficit-financed spending: A) Always boosts aggregate demand more than tax-financed spending B) Has effects on consumption similar to tax-financed spending, since rational agents anticipate future taxes C) Permanently raises the national savings rate D) Causes hyperinflation in the long run | B | economics | hard |
| 17 | Question: Which post-WWI system placed former German and Ottoman territories under the administration of other powers on behalf of the League of Nations? A) The Mandate System B) The Protectorate System C) The Trusteeship Council D) The Capitulation System | A | history | medium |
| 18 | Question: The 'hard problem of consciousness,' as framed by David Chalmers, concerns: A) Identifying the neural correlates of conscious states B) Explaining why physical processes give rise to subjective experience at all C) Determining whether animals are conscious D) Building AI systems that pass the Turing test | B | philosophy | hard |
| 19 | Question: In epidemiology, 'herd immunity threshold' for a disease with basic reproduction number R0 is approximately: A) R0 B) 1/R0 C) 1 - 1/R0 D) R0 - 1 | C | epidemiology | hard |
| 20 | Question: The Rome Statute (1998) established which institution? A) The International Court of Justice B) The International Criminal Court C) The Permanent Court of Arbitration D) The ICTY (Yugoslavia tribunal) | B | law | medium |
| 21 | Question: Which glycolytic enzyme is the primary rate-limiting (committed) step of glycolysis? A) Hexokinase B) Phosphofructokinase-1 C) Pyruvate kinase D) Aldolase | B | biochemistry | hard |
| 22 | Question: The Peace of Westphalia (1648) is most commonly cited as the origin of which modern principle? A) Universal human rights B) State sovereignty and non-interference C) Free trade between nations D) Separation of church and state within a single country | B | history | medium |
| 23 | Question: In monetary economics, the 'impossible trinity' (trilemma) states a country cannot simultaneously have: A) Low inflation, low unemployment, and high growth B) A fixed exchange rate, free capital flows, and independent monetary policy C) A trade surplus, a budget surplus, and currency appreciation D) High savings, high investment, and low interest rates | B | economics | hard |
| 24 | Question: Which Supreme Court case established the 'separate but equal' doctrine later overturned by Brown v. Board of Education? A) Dred Scott v. Sandford B) Plessy v. Ferguson C) Korematsu v. United States D) Lochner v. New York | B | law | medium |
| 25 | Question: A neutron star's maximum stable mass before collapsing further is bounded by which limit? A) Chandrasekhar limit B) Eddington limit C) Tolman-Oppenheimer-Volkoff limit D) Roche limit | C | astrophysics | hard |
| 26 | Question: The Congress of Berlin (1878) primarily revised the terms of which earlier treaty regarding the Balkans? A) Treaty of San Stefano B) Treaty of Bucharest C) Treaty of Adrianople D) Treaty of Paris (1856) | A | history | hard |
| 27 | Question: In cell biology, the process by which a cell engulfs large particles via membrane invagination is called: A) Pinocytosis B) Phagocytosis C) Exocytosis D) Facilitated diffusion | B | biology | easy |
| 28 | Question: The Modigliani-Miller theorem, in its basic form (no taxes, no bankruptcy costs), states that a firm's value is independent of: A) Its profitability B) Its capital structure (debt vs equity mix) C) Its dividend payout ratio in all cases D) Its industry sector | B | economics | hard |
| 29 | Question: Which legal doctrine allows a court to pierce the corporate veil and hold shareholders personally liable, typically in cases of fraud or undercapitalization? A) Ultra vires doctrine B) Alter ego / piercing the corporate veil doctrine C) Business judgment rule D) Doctrine of laches | B | law | hard |
| 30 | Question: Cosmic microwave background radiation is considered strong evidence for which cosmological model? A) Steady State theory B) Big Bang theory C) Eternal inflation alone D) Tired light hypothesis | B | astrophysics | easy |
| 31 | Question: The Sykes-Picot Agreement (1916) was a secret accord between which two powers concerning post-WWI division of the Middle East? A) Britain and France B) Britain and Russia C) France and Russia D) Britain and the Ottoman Empire | A | history | medium |
| 32 | Question: In genetics, a 'silent mutation' is one that: A) Changes the amino acid but not protein function B) Does not change the encoded amino acid due to codon redundancy C) Occurs only in non-coding DNA D) Always results in a premature stop codon | B | genetics | medium |
| 33 | Question: The Phillips curve traditionally depicts an inverse relationship between: A) GDP growth and interest rates B) Inflation and unemployment C) Exchange rates and trade balance D) Savings and investment | B | economics | easy |
| 34 | Question: Under the doctrine of 'stare decisis,' courts are expected to: A) Always defer to legislative intent over precedent B) Follow established precedent in deciding similar future cases C) Apply foreign law when domestic law is silent D) Rule only on questions of fact, not law | B | law | easy |
| 35 | Question: The 'Kuiper Belt' is a region of the solar system primarily composed of: A) Asteroids between Mars and Jupiter B) Icy bodies beyond Neptune's orbit C) Comets originating from interstellar space D) Dust and gas remnants of planet formation near the Sun | B | astronomy | easy |
| 36 | Question: The Treaty of Tordesillas (1494) divided newly discovered lands outside Europe between which two powers? A) Spain and Portugal B) England and France C) Spain and England D) Portugal and the Netherlands | A | history | medium |
| 37 | Question: In epidemiology, a 'case-control study' is best described as: A) Following a cohort forward in time to observe outcomes B) Comparing individuals with a disease to those without it, looking backward at exposures C) A randomized controlled trial of a treatment D) A cross-sectional survey at a single point in time | B | epidemiology | medium |
| 38 | Question: The 'tragedy of the commons' concept, as formalized by Garrett Hardin, primarily illustrates a problem of: A) Information asymmetry B) Overuse of a shared, non-excludable resource by self-interested individuals C) Monopolistic price-setting D) Moral hazard in insurance markets | B | economics | medium |
| 39 | Question: Which philosopher's 'categorical imperative' holds that one should act only according to rules one could will to be universal law? A) John Stuart Mill B) Immanuel Kant C) Jeremy Bentham D) David Hume | B | philosophy | easy |
| 40 | Question: In contract law, 'consideration' refers to: A) The subjective fairness of a deal B) Something of value exchanged by each party that makes a promise enforceable C) A court's deliberation period before ruling D) The statute of limitations on filing suit | B | law | medium |
| 41 | Question: The enzyme telomerase functions to: A) Repair double-strand DNA breaks B) Extend telomeres at chromosome ends, counteracting replicative shortening C) Unwind the DNA helix during replication D) Remove RNA primers from the lagging strand | B | biochemistry | hard |
| 42 | Question: The Berlin Conference (1884-85) is most associated with: A) Ending the Franco-Prussian War B) Formalizing the European 'Scramble for Africa' and rules for colonial claims C) Establishing the German Empire D) Negotiating the Treaty of Versailles | B | history | medium |
| 43 | Question: In economics, 'moral hazard' describes a situation where: A) Insured parties take on more risk because they are protected from its consequences B) Sellers know more about product quality than buyers C) A monopolist restricts output to raise prices D) Public goods are underprovided due to free-riding | A | economics | medium |
| 44 | Question: The legal principle 'res judicata' prevents: A) Appealing a verdict on procedural grounds B) Relitigating a claim that has already been finally decided between the same parties C) Testifying against oneself D) Introducing hearsay evidence | B | law | hard |
| 45 | Question: A pulsar is best described as: A) A black hole emitting Hawking radiation B) A rapidly rotating neutron star emitting beams of electromagnetic radiation C) An exploding white dwarf (Type Ia supernova) D) A binary star system with one giant and one dwarf component | B | astrophysics | medium |
| 46 | Question: The Defenestration of Prague (1618) is generally cited as the triggering event of: A) The Hundred Years' War B) The Thirty Years' War C) The French Revolution D) The War of the Spanish Succession | B | history | medium |
| 47 | Question: In immunology, 'antigenic drift' refers to: A) Sudden reassortment of genetic segments between two viral strains B) Gradual accumulation of point mutations in surface proteins over time C) The process by which B cells mature in the bone marrow D) Cross-reactivity between unrelated pathogens | B | immunology | hard |
| 48 | Question: The economic concept of 'comparative advantage,' developed by David Ricardo, explains why: A) Countries should be self-sufficient in all goods B) Trade can benefit both parties even if one is more efficient at producing everything C) Tariffs always increase national welfare D) Currency devaluation guarantees a trade surplus | B | economics | medium |
| 49 | Question: In US constitutional law, 'strict scrutiny' is the standard of judicial review applied to laws that: A) Regulate interstate commerce B) Burden a fundamental right or use a suspect classification like race C) Set tax rates D) Concern purely economic regulation with a rational basis | B | law | hard |
| 50 | Question: Dark matter's existence is primarily inferred from: A) Direct detection in particle accelerators B) Anomalous galactic rotation curves and gravitational lensing C) The cosmic microwave background's temperature alone D) Redshift of distant supernovae | B | astrophysics | medium |
| 51 | Question: The Munich Agreement (1938) is most notable for: A) Ending World War I B) Ceding the Sudetenland to Germany in an attempt to avoid war ('appeasement') C) Dividing Poland between Germany and the Soviet Union D) Establishing the League of Nations | B | history | easy |
| 52 | Question: In genetics, epistasis refers to: A) The effect of one gene being masked or modified by another gene B) The inheritance of acquired traits C) Mutation caused by environmental radiation D) Crossing-over during meiosis | A | genetics | medium |
| 53 | Question: The 'efficient market hypothesis' in finance asserts that: A) Markets always crash within predictable cycles B) Asset prices fully reflect all available information, making consistent outperformance via analysis difficult C) Government regulation always improves market efficiency D) Insider trading has no effect on prices | B | economics | medium |
| 54 | Question: 'Habeas corpus' is a legal mechanism that: A) Allows a person to challenge the lawfulness of their detention before a court B) Grants immunity to government officials C) Establishes the right to a jury trial D) Permits class-action lawsuits | A | law | easy |
| 55 | Question: The 'Goldilocks zone' around a star refers to the orbital region where: A) Tidal forces are minimized B) Liquid water could exist on a planet's surface given the right atmosphere C) Planets form fastest during accretion D) Magnetic fields are strongest | B | astronomy | easy |
| 56 | Question: The Marshall Plan (1948) was primarily aimed at: A) Rebuilding Japan's economy after WWII B) Providing US economic aid to rebuild Western European economies after WWII C) Establishing NATO D) Funding the Manhattan Project | B | history | easy |
| 57 | Question: In epidemiology, 'sensitivity' of a diagnostic test refers to: A) The proportion of true negatives correctly identified B) The proportion of true positives correctly identified C) The overall accuracy of the test D) The cost-effectiveness of the test | B | epidemiology | medium |
| 58 | Question: A 'public good' in economics is defined by being: A) Excludable and rivalrous B) Non-excludable and non-rivalrous C) Produced only by governments D) Always underpriced relative to its cost | B | economics | medium |
| 59 | Question: The mitochondrion's inner membrane is the site of which process? A) Glycolysis B) The electron transport chain and oxidative phosphorylation C) DNA replication for the whole cell D) Protein synthesis on free ribosomes | B | biochemistry | medium |
| 60 | Question: The Yalta Conference (1945) primarily addressed: A) Terms of Japan's surrender B) Post-WWII reorganization of Europe and the war against Japan, among the Big Three Allied leaders C) Founding the European Union D) The partition of the Ottoman Empire | B | history | medium |
| 61 | Question: In macroeconomics, 'crowding out' refers to: A) Private investment declining due to increased government borrowing raising interest rates B) Small firms being driven out by large monopolies C) Immigration reducing domestic wages D) Consumers substituting imports for domestic goods | A | economics | hard |
| 62 | Question: The exclusionary rule in US criminal law primarily concerns: A) Excluding jurors with bias B) Barring evidence obtained through an unconstitutional search or seizure from trial C) Preventing double jeopardy D) Excluding hearsay testimony | B | law | medium |
| 63 | Question: A solar eclipse occurs when: A) Earth passes between the Sun and Moon B) The Moon passes between the Sun and Earth, blocking sunlight C) The Moon enters Earth's shadow D) The Sun's corona becomes visible during solar maximum | B | astronomy | easy |
| 64 | Question: The Potsdam Conference (1945) was held primarily to: A) Plan the D-Day invasion B) Decide the post-war administration of defeated Germany and issue surrender terms to Japan C) Establish the United Nations charter D) Negotiate the Treaty of Versailles | B | history | medium |
| 65 | Question: In cell biology, apoptosis refers to: A) Uncontrolled cell division (cancerous growth) B) Programmed cell death C) Cell division during mitosis D) The process of cells engulfing pathogens | B | biology | easy |
| 66 | Question: Keynesian economics generally argues that, during a recession, governments should: A) Cut spending to balance the budget regardless of demand B) Increase deficit spending to boost aggregate demand C) Rely solely on monetary policy and avoid fiscal action D) Raise interest rates to encourage saving | B | economics | medium |
| 67 | Question: 'Mens rea' in criminal law refers to: A) The physical act of committing a crime B) The mental intent or knowledge of wrongdoing required for criminal liability C) The sentence imposed after conviction D) A legal defense based on insanity | B | law | medium |
| 68 | Question: Nuclear fusion in the Sun's core primarily converts: A) Helium into carbon B) Hydrogen into helium C) Carbon into iron D) Helium directly into energy with no byproduct | B | astrophysics | easy |
| 69 | Question: The Truman Doctrine (1947) committed the US to: A) Direct military intervention in Korea B) Providing economic and military aid to countries resisting communist expansion, starting with Greece and Turkey C) Establishing NATO D) Recognizing the People's Republic of China | B | history | medium |
| 70 | Question: In statistics, a Type I error refers to: A) Failing to reject a false null hypothesis B) Incorrectly rejecting a true null hypothesis (a false positive) C) Using the wrong sample size D) Confusing correlation with causation | B | statistics | medium |
| 71 | Question: The doctrine of 'separation of powers' is most directly associated with which philosopher's formulation? A) John Locke B) Montesquieu C) Thomas Hobbes D) Jean-Jacques Rousseau | B | philosophy | medium |
| 72 | Question: A 'black swan event' in risk theory, per Nassim Taleb, refers to: A) A common, predictable market fluctuation B) A rare, high-impact event that is difficult to predict in advance but seems obvious in hindsight C) A government bailout of a failing bank D) Seasonal stock market volatility | B | economics | medium |
| 73 | Question: DNA polymerase synthesizes new DNA strands in which direction relative to the template? A) 3' to 5' B) 5' to 3' C) Bidirectionally from the origin only D) Direction is random per nucleotide | B | biochemistry | hard |
| 74 | Question: The Opium Wars (19th century) were fought primarily between China and which power(s)? A) Japan B) Britain (and later France) C) Russia D) The Netherlands | B | history | medium |
| 75 | Question: In economics, 'sticky wages' help explain why: A) Labor markets clear instantly after a demand shock B) Unemployment can persist after a negative demand shock, since wages don't fall quickly to restore equilibrium C) Minimum wage laws are unnecessary D) Inflation always reduces real wages permanently | B | economics | hard |
| 76 | Question: The 'fruit of the poisonous tree' doctrine in US law holds that: A) Evidence derived from an illegal search is also inadmissible, not just the initial evidence B) Only the directly seized evidence is excluded C) Civil suits cannot use criminal evidence D) Plea bargains void all prior evidence | A | law | hard |
| 77 | Question: A 'main sequence' star, like the Sun, generates energy primarily through: A) Gravitational contraction alone B) Hydrogen fusion in its core C) Radioactive decay of heavy elements D) Accretion of surrounding gas | B | astrophysics | easy |
| 78 | Question: The Cuban Missile Crisis (1962) was triggered by: A) A US invasion of Cuba B) The Soviet Union placing nuclear missiles in Cuba, discovered by US intelligence C) Cuba's nationalization of US oil companies D) A failed coup against Castro | B | history | easy |
| 79 | Question: In statistics, 'regression toward the mean' describes the tendency for: A) Extreme observations to be followed by less extreme ones on repeated measurement B) Sample means to always equal population means C) Variance to increase over repeated trials D) Correlation to imply causation | A | statistics | medium |
| 80 | Question: The utilitarian philosophy of Jeremy Bentham and John Stuart Mill holds that the morally right action is the one that: A) Follows a strict set of universal duties regardless of outcome B) Maximizes overall happiness or utility C) Reflects the actor's virtuous character D) Conforms to divine command | B | philosophy | easy |
| 81 | Question: A 'leveraged buyout' (LBO) in finance refers to: A) Acquiring a company using a significant amount of borrowed money, often secured against the target's own assets B) A government bailout of a failing firm C) Issuing new equity to raise capital without debt D) A hostile takeover using only cash reserves | A | economics | medium |
| 82 | Question: The 'chain of custody' in evidence law refers to: A) The order in which witnesses testify B) Documentation tracking who handled physical evidence from collection to trial, to establish its integrity C) The hierarchy of appellate courts D) The sequence of charges in an indictment | B | law | medium |
| 83 | Question: An 'event horizon' of a black hole is best described as: A) The point of maximum density at the singularity B) The boundary beyond which nothing, including light, can escape the black hole's gravity C) The accretion disk's outer edge D) The region where Hawking radiation is emitted most intensely | B | astrophysics | easy |
| 84 | Question: CRISPR-Cas9 gene editing works by: A) Directly synthesizing new proteins from RNA templates B) Using a guide RNA to direct the Cas9 enzyme to cut DNA at a specific sequence C) Inserting whole chromosomes into a cell D) Silencing genes via methylation alone | B | biochemistry | hard |
| 85 | Question: The Treaty of Versailles (1919) is most associated with: A) Ending World War II B) Formally ending World War I and imposing reparations/territorial losses on Germany C) Establishing the United Nations D) The partition of British India | B | history | easy |
| 86 | Question: 'Quantitative easing' as a central bank policy tool involves: A) Raising interest rates to combat inflation B) Large-scale asset purchases to inject liquidity into the economy when conventional rate cuts are exhausted C) Imposing capital controls on foreign exchange D) Reducing the money supply directly | B | economics | hard |
| 87 | Question: The 'rule of lenity' in criminal law dictates that: A) Ambiguous criminal statutes should be interpreted in favor of the defendant B) Repeat offenders receive automatically harsher sentences C) Judges must defer entirely to jury sentencing recommendations D) Civil penalties always take precedence over criminal ones | A | law | hard |
| 88 | Question: Gravitational waves, first directly detected by LIGO in 2015, are produced by: A) Stars undergoing nuclear fusion B) Accelerating massive objects, such as merging black holes or neutron stars C) Light bending around massive objects D) Cosmic ray collisions in the upper atmosphere | B | astrophysics | medium |
| 89 | Question: The Berlin Wall fell in which year, marking a major symbolic end to the Cold War's division of Europe? A) 1985 B) 1989 C) 1991 D) 1994 | B | history | easy |
| 90 | Question: In economics, 'externality' refers to: A) A cost or benefit affecting a third party not involved in a transaction B) Profit earned from foreign trade C) A firm's expenses outside its core operations D) Government spending unrelated to GDP | A | economics | easy |
| 91 | Question: The legal concept of 'negligence' generally requires proving: A) Intent to cause harm B) Duty of care, breach of that duty, causation, and damages C) A signed contract between the parties D) Criminal intent (mens rea) | B | law | medium |
| 92 | Question: A 'supernova' occurs when: A) A star slowly cools into a white dwarf B) A massive star exhausts its nuclear fuel and undergoes a catastrophic core collapse and explosion C) Two galaxies merge D) A planet's atmosphere escapes into space | B | astrophysics | easy |
| 93 | Question: The Marshall Court (under Chief Justice John Marshall) significantly strengthened which branch of the US federal government? A) The legislative branch B) The executive branch C) The judicial branch, via judicial review and broad federal power rulings D) State governments collectively | C | law | medium |
| 94 | Question: In statistics, the 'central limit theorem' states that: A) All distributions are normal B) The sampling distribution of the mean approaches a normal distribution as sample size grows, regardless of the population's distribution C) Larger samples always have smaller variance than the population D) Correlation implies causation in large samples | B | statistics | medium |
| 95 | Question: Mitochondria are often called the 'powerhouse of the cell' because they primarily produce: A) DNA B) ATP via oxidative phosphorylation C) Ribosomes D) Lipids for the cell membrane | B | biology | easy |
| 96 | Question: The Iranian Revolution (1979) resulted in: A) The restoration of the Shah's monarchy B) The overthrow of the Shah and establishment of an Islamic Republic C) A democratic parliamentary system aligned with the West D) Annexation by neighboring Iraq | B | history | medium |
| 97 | Question: 'Adverse selection' in insurance markets refers to: A) Insurers selecting only low-risk customers B) High-risk individuals being more likely to seek insurance than low-risk individuals, given asymmetric information C) Government mandates increasing premiums D) Insurers going bankrupt due to natural disasters | B | economics | hard |
| 98 | Question: The 'exclusionary rule' aside, 'Miranda rights' (from Miranda v. Arizona) require police to inform a suspect of: A) Their right to a speedy trial only B) Their right to remain silent and to an attorney before custodial interrogation C) Their right to bail D) Their right to a jury of their peers | B | law | easy |
| 99 | Question: A 'white dwarf' is the remnant of a star that has: A) Exhausted its nuclear fuel and shed its outer layers, leaving a dense, cooling core supported by electron degeneracy pressure B) Collapsed entirely into a black hole C) Exploded completely with no remnant D) Merged with a companion star to form a neutron star | A | astrophysics | medium |
| 100 | Question: The 'domino theory,' invoked during the Cold War (notably regarding Vietnam), held that: A) Communist economies would naturally collapse one after another B) If one country fell to communism, neighboring countries would follow in a chain reaction C) Nuclear weapons would spread uncontrollably between allied nations D) Trade agreements would cascade across a region | B | history | medium |
4. Logic & Reasoning (100 questions)
| # | Question | Gold | Category | Difficulty |
|---|---|---|---|---|
| 1 | Question: All Bloops are Razzies. All Razzies are Lazzies. Some Lazzies are Wuzzies. Which must be true? A) All Bloops are Wuzzies B) All Bloops are Lazzies C) Some Wuzzies are Bloops D) No Bloops are Wuzzies | B | syllogism | medium |
| 2 | Question: The argument 'If it rains, the ground is wet. The ground is wet. Therefore it rained.' commits which fallacy? A) Denying the antecedent B) Affirming the consequent C) Modus tollens (correctly applied) D) Circular reasoning | B | propositional | easy |
| 3 | Question: By De Morgan's law, NOT(P AND Q) is logically equivalent to: A) NOT P AND NOT Q B) P OR Q C) NOT P OR NOT Q D) P AND Q | C | propositional | easy |
| 4 | Question: In modal logic, the axiom T (□P -> P) corresponds to the accessibility relation being: A) Symmetric B) Transitive C) Reflexive D) Euclidean | C | modal | hard |
| 5 | Question: Five people (A,B,C,D,E) sit in a row of 5 seats. A is immediately left of B. C is leftmost (seat 1). D is immediately right of C. E is not adjacent to D. Where must E sit? A) Seat 2 B) Seat 3 C) Seat 4 D) Seat 5 | D | spatial | hard |
| 6 | Question: From the resolution rule, (P OR Q) and (NOT P OR R) together imply: A) P B) Q OR R C) P AND R D) NOT Q OR NOT R | B | propositional | medium |
| 7 | Question: 'All cats are mammals. Some mammals are not pets. Therefore some cats are not pets.' This argument is: A) Valid B) Invalid -- the conclusion doesn't follow from the premises C) Valid only if all pets are mammals D) A tautology | B | syllogism | hard |
| 8 | Question: A bag has only red and blue balls. If you draw 2 balls and at least one is red is a CERTAIN event, what is the minimum number of blue balls possible, given there are also at least 2 red balls and the bag has more than 2 balls total? A) 0 B) 1 C) 2 D) Cannot be determined | A | deduction | medium |
| 9 | Question: The statement 'This statement is false' is an example of: A) A tautology B) The liar's paradox -- it cannot be consistently assigned true or false C) A valid syllogism D) An example of modus ponens | B | paradox | easy |
| 10 | Question: In a room, everyone who wears glasses also wears a watch. Tom wears a watch but no glasses. What can you conclude about Tom? A) Tom must wear glasses B) Tom cannot wear glasses C) Nothing can be concluded about Tom's glasses from this alone D) Tom is lying | C | deduction | medium |
| 11 | Question: Which of these is a tautology (true under every truth assignment)? A) P AND NOT P B) P OR Q C) (P -> Q) <-> (NOT Q -> NOT P) D) P -> (P AND Q) | C | propositional | medium |
| 12 | Question: Four boxes are stacked. Box 1 is directly on top of Box 2. Box 3 is below Box 2. Box 4 is on top of Box 1. From top to bottom, what is the order? A) 4,1,2,3 B) 1,4,2,3 C) 4,1,3,2 D) 1,2,3,4 | A | spatial | medium |
| 13 | Question: A set of propositional formulas is CONSISTENT if and only if: A) No formula in the set is a tautology B) Some truth assignment satisfies every formula in the set simultaneously C) The set has exactly one model D) No two formulas in the set share a variable | B | propositional | hard |
| 14 | Question: 'Every even number greater than 2 can be written as a sum of two primes' is the statement of: A) Fermat's Last Theorem B) Goldbach's Conjecture C) The Twin Prime Conjecture D) The Collatz Conjecture | B | general_logic | easy |
| 15 | Question: Knights always tell the truth, knaves always lie. A says 'B and I are both knights.' B says 'A is a knave.' What are A and B? A) A is a knight, B is a knave B) A is a knave, B is a knight C) Both are knights D) Both are knaves | B | deduction | hard |
| 16 | Question: The predicate formula 'for all x, there exists y such that x < y' means: A) There is an x greater than all y B) For every x, there is some y greater than it (no maximum element) C) There exist some x and y with x<y D) For all x and y, x<y | B | predicate | medium |
| 17 | Question: A implies B. B implies C. C is false. What can be concluded? A) A is false B) A is true C) B is true D) Nothing can be concluded about A | A | propositional | easy |
| 18 | Question: In a knights-and-knaves puzzle, knights always tell the truth and knaves always lie. A says 'I am a knave.' What is A? A) A knight B) A knave C) Neither -- the statement is a contradiction, no consistent assignment exists D) Could be either | C | paradox | medium |
| 19 | Question: 'No reptiles are warm-blooded. All snakes are reptiles. Therefore no snakes are warm-blooded.' This syllogism is: A) Valid B) Invalid due to undistributed middle term C) Invalid due to illicit major D) Valid only for some snakes | A | syllogism | medium |
| 20 | Question: Material implication P -> Q is FALSE only when: A) P is true B) Q is true C) P is true and Q is false D) P is false | C | propositional | easy |
| 21 | Question: Four people (W,X,Y,Z) sit in a row of 4 seats. W is somewhere to the left of X. Y is immediately to the right of Z. X is not at either end. What seat is Y in? A) Seat 1 B) Seat 2 C) Seat 3 D) Seat 4 | D | spatial | hard |
| 22 | Question: Five people (A,B,C,D,E) sit in a row of 5 seats. B sits exactly two seats to the right of A. E sits immediately to the right of D. A is NOT in the leftmost seat. What seat is C in? A) Seat 1 B) Seat 2 C) Seat 3 D) Seat 4 | D | spatial | hard |
| 23 | Question: Knights always tell the truth, knaves always lie. A says 'B is a knave.' B says 'C is a knight.' C says 'A and B are both knaves.' What are A, B, and C? A) A knight, B knave, C knave B) A knave, B knight, C knight C) All three are knights D) All three are knaves | A | deduction | hard |
| 24 | Question: P implies Q. Q implies R. R is false. By modus tollens chaining, what can be concluded? A) P is true B) P is false C) Q is true D) Nothing can be concluded about P | B | propositional | medium |
| 25 | Question: Four boxes are stacked vertically. Box S is directly above Box P. Box P is directly above Box Q. Box Q is directly above Box R. From top to bottom, what is the order? A) S,P,Q,R B) R,Q,P,S C) P,S,Q,R D) S,Q,P,R | A | spatial | easy |
| 26 | Question: The NAND operation (NOT(P AND P)) applied to a single variable P twice is logically equivalent to: A) P B) NOT P C) Always true D) Always false | B | propositional | medium |
| 27 | Question: 'All squares are rectangles. Some rectangles are not rhombi. Therefore some squares are not rhombi.' This argument is: A) Valid B) Invalid -- the conclusion does not follow; in fact all squares ARE rhombi C) Valid only for non-square rectangles D) A tautology | B | syllogism | hard |
| 28 | Question: In a 2x2 grid of 4 cells, you must place 2 black tokens such that no two black tokens are in the same row or column. How many distinct placements are possible? A) 1 B) 2 C) 4 D) 6 | B | spatial | medium |
| 29 | Question: By contraposition, the statement 'If P then Q' is logically equivalent to: A) If Q then P B) If NOT Q then NOT P C) If NOT P then NOT Q D) P and NOT Q | B | propositional | easy |
| 30 | Question: Three switches outside a room each control one of three bulbs inside, but you can only enter the room once to observe. You may flip switches any number of times before entering. What is the minimum number of times you must enter the room to determine which switch controls which bulb? A) 3 B) 2 C) 1 D) 0 (impossible without entering twice) | C | deduction | hard |
| 31 | Question: 'Some Glorps are Trundles. All Trundles are Wexels. Therefore some Glorps are Wexels.' This syllogism is: A) Valid B) Invalid due to undistributed middle C) Invalid due to illicit minor D) Valid only if no Glorps are Wexels | A | syllogism | medium |
| 32 | Question: A statement and its converse are logically equivalent: A) Always B) Never C) Only for biconditional (if-and-only-if) statements D) Only when both P and Q are true | C | propositional | easy |
| 33 | Question: 'If the alarm is armed, then entering triggers a siren. The siren did not sound when someone entered. Therefore the alarm was not armed.' This is an application of: A) Modus ponens B) Modus tollens C) Affirming the consequent (a fallacy) D) Denying the antecedent (a fallacy) | B | propositional | easy |
| 34 | Question: In an exclusive-or (XOR) gate, the output is true exactly when: A) Both inputs are true B) Both inputs are false C) Exactly one input is true D) At least one input is true | C | propositional | easy |
| 35 | Question: A is taller than B. C is shorter than B. D is taller than A. Who is the shortest? A) A B) B C) C D) D | C | deduction | easy |
| 36 | Question: 'No fish are mammals. All whales are mammals. Therefore no whales are fish.' This syllogism's logical form is: A) Valid B) Invalid due to undistributed middle C) Invalid due to four terms D) An enthymeme missing a premise | A | syllogism | medium |
| 37 | Question: For a biconditional P <-> Q to be FALSE, which must be true? A) P and Q have the same truth value B) P and Q have different truth values C) Both P and Q must be false D) Both P and Q must be true | B | propositional | easy |
| 38 | Question: Three suspects each make one statement; truth-tellers' statements are true and liars' statements are false. X says 'Y is lying.' Y says 'Z is lying.' Z says 'X and Y are both lying.' Exactly one of the three is telling the truth -- who is it? A) X B) Y C) Z D) No consistent assignment exists | B | deduction | hard |
| 39 | Question: A valid argument with true premises must have: A) A true conclusion B) A false conclusion C) An ambiguous conclusion D) No necessary relationship to its conclusion's truth | A | general_logic | easy |
| 40 | Question: In set theory, if A is a subset of B and B is a subset of A, then: A) A and B are disjoint B) A equals B C) A is the empty set D) B is the universal set | B | predicate | easy |
| 41 | Question: Four people occupy the four rooms of a 2x2 grid (NW, NE, SW, SE). A is directly north of C. B is directly east of A. Which room is D in? A) NW B) NE C) SW D) SE | D | spatial | medium |
| 42 | Question: Five runners (Alice, Bob, Carol, Dave, Eve) finish a race with no ties. Alice finishes before Bob. Carol finishes immediately after Alice. Dave finishes last. Eve finishes before Carol. Who finishes first? A) Alice B) Bob C) Carol D) Eve | D | spatial | hard |
| 43 | Question: Four people each make a statement, in a cycle: A says 'B lies.' B says 'C lies.' C says 'D lies.' D says 'A lies.' Truth-tellers' statements are true, liars' statements are false. How many of the four are telling the truth? A) 0 B) 1 C) 2 D) 4 | C | deduction | hard |
| 44 | Question: (P OR Q) AND (NOT P OR NOT Q) is logically equivalent to: A) P AND Q B) P XOR Q (exactly one of P, Q is true) C) NOT P AND NOT Q D) Always false | B | propositional | medium |
| 45 | Question: Set A has 5 elements, set B has 4 elements, and A intersect B has 2 elements. How many elements are in A union B? A) 5 B) 6 C) 7 D) 9 | C | predicate | easy |
| 46 | Question: Six people (A-F) sit evenly spaced around a round table. D sits directly opposite A. B sits immediately clockwise of A. C sits immediately counter-clockwise of D. How many people sit between B and C going clockwise (not counting B or C themselves)? A) 0 B) 1 C) 2 D) 3 | A | spatial | hard |
| 47 | Question: 'If it is sunny, we go to the beach. If we go to the beach, we get a tan. We did not get a tan.' By chained modus tollens, what follows? A) It was not sunny B) It was sunny C) We went to the beach D) Nothing can be concluded | A | propositional | medium |
| 48 | Question: A statement of the form 'P AND NOT P' is called: A) A tautology B) A contradiction (always false) C) A contingency D) A biconditional | B | propositional | easy |
| 49 | Question: Five people (A,B,C,D,E) sit in a row of 5 seats. C sits in the exact middle seat (seat 3). A sits at one of the two ends. B sits immediately to the right of A. D sits immediately to the right of E. Which seat is A in? A) Seat 1 B) Seat 2 C) Seat 4 D) Seat 5 | A | spatial | hard |
| 50 | Question: Three people A, B, C each make a statement. Exactly 2 of the 3 are knights (truth-tellers); the rest are knaves (liars). A says 'I am a knight.' B says 'A is a knight.' C says 'B is a knave.' Who is the knave? A) A B) B C) C D) No consistent assignment exists | C | deduction | hard |
| 51 | Question: NOT(P OR Q) is logically equivalent to: A) NOT P OR NOT Q B) NOT P AND NOT Q C) P AND Q D) P OR Q | B | propositional | easy |
| 52 | Question: Four students rank 1st through 4th on a test with no ties. Tom scores higher than Jerry. Sue scores lower than Jerry. Ann scores highest of all. What rank does Sue have? A) 1st B) 2nd C) 3rd D) 4th (last) | D | spatial | medium |
| 53 | Question: If 'All A are B' and 'All B are C' are both true, then by transitivity: A) All C are A B) All A are C C) Some A are not C D) No conclusion about A and C follows | B | syllogism | easy |
| 54 | Question: A->B is true. B is false. What follows about A by modus tollens? A) A is true B) A is false C) A could be either D) B must actually be true | B | propositional | easy |
| 55 | Question: In predicate logic, the statement 'there exists x such that for all y, x loves y' means: A) Everyone loves everyone B) There is at least one person who loves everyone C) Everyone loves at least one person D) No one loves anyone | B | predicate | medium |
| 56 | Question: Six people (A-F) sit in a row of 6 seats. F is at one of the two ends. A sits immediately to the right of F. D sits immediately to the right of C. B is not adjacent to A. E sits somewhere between C and B. Which seat is F in? A) Seat 1 B) Seat 3 C) Seat 4 D) Seat 6 | A | spatial | hard |
| 57 | Question: In how many ways can the 4 nodes of a path graph (1-2-3-4, each node adjacent only to its immediate neighbor(s)) be properly colored using exactly 2 colors such that no two adjacent nodes share a color? A) 1 B) 2 C) 4 D) 8 | B | general_logic | medium |
| 58 | Question: In how many ways can a triangle (3 mutually adjacent nodes) be properly colored using exactly 3 available colors, with no two adjacent nodes sharing a color? A) 3 B) 6 C) 9 D) 27 | B | general_logic | medium |
| 59 | Question: P <-> Q (biconditional) is logically equivalent to: A) (P AND Q) OR (NOT P AND NOT Q) B) (P OR Q) AND (NOT P OR NOT Q) C) P AND Q only D) NOT P AND NOT Q only | A | propositional | medium |
| 60 | Question: By disjunctive syllogism, from '(P OR Q) is true' and 'P is false', what follows? A) Q is true B) Q is false C) P is true D) Nothing follows | A | propositional | easy |
| 61 | Question: Four houses in a row are painted red, blue, green, and yellow (each used once). The red house is not at either end. The green house is immediately right of the blue house. The yellow house is at one end. The blue house is also not at either end. Which color is the second house from the left? A) Red B) Blue C) Green D) Yellow | A | spatial | hard |
| 62 | Question: 'All A are B. All B are C. Some C are not D.' Does it necessarily follow that 'some A are not D'? A) Yes, it is a valid conclusion B) No -- a concrete counterexample shows A can be entirely within D even when the premises hold C) Only if A and D are disjoint D) Only if B equals C | B | syllogism | hard |
| 63 | Question: Five students (Sam, Pat, Kim, Lee, Jo) are assigned lockers numbered 1-5, each a different number. Sam's locker number is prime. Pat's locker number is immediately after Sam's. Kim has locker 1. Lee's locker number is even and greater than Pat's. What locker number does Jo get? A) 2 B) 3 C) 4 D) 5 | D | spatial | hard |
| 64 | Question: P implies Q. Q implies R. P is true. By chained modus ponens, what follows? A) R is true B) R is false C) Q is false D) Nothing can be concluded about R | A | propositional | easy |
| 65 | Question: A statement that is true under every possible truth assignment of its variables is called: A) A contradiction B) A contingency C) A tautology D) An antecedent | C | propositional | easy |
| 66 | Question: A deck has 4 cards face down: 2 red, 2 black. You flip 2 of the 4 cards at random (without replacement). The probability both flipped cards are the same color is a/b in lowest terms. What is a+b? A) 3 B) 4 C) 5 D) 7 | B | deduction | medium |
| 67 | Question: In classical logic, the statement 'P only if Q' is logically translated as: A) Q -> P B) P -> Q C) P <-> Q D) NOT P -> NOT Q | B | propositional | medium |
| 68 | Question: 4 cups are in a row at positions 1,2,3,4. A ball starts under the cup at position 1. Three swaps occur in order: swap positions 1&2, then swap positions 2&3, then swap positions 1&3. Which position is the ball under now? A) Position 1 B) Position 2 C) Position 3 D) Position 4 | A | spatial | medium |
| 69 | Question: Five books A,B,C,D,E are ranked by height. Book A is shorter than Book B. Book A is taller than Book C. Book D is shorter than Book C. Book E is the shortest of all five. Ranking from tallest to shortest, which book is in the middle (3rd)? A) A B) B C) C D) D | C | spatial | hard |
| 70 | Question: By De Morgan's law extended to three variables, NOT(P AND Q AND R) is equivalent to: A) NOT P AND NOT Q AND NOT R B) NOT P OR NOT Q OR NOT R C) P OR Q OR R D) (P AND Q) OR R | B | propositional | medium |
| 71 | Question: By hypothetical syllogism, from 'P implies Q' and 'Q implies R', what follows? A) P implies R B) R implies P C) Q implies P D) Nothing follows about P and R directly | A | propositional | easy |
| 72 | Question: By constructive dilemma, from '(P implies Q) AND (R implies S)' and '(P OR R)', what follows? A) Q OR S B) Q AND S C) P AND R D) Nothing follows | A | propositional | medium |
| 73 | Question: Alice is currently twice as old as Bob. In 5 years, Alice will be 1.5 times Bob's age. How old is Alice right now? A) 5 B) 8 C) 10 D) 12 | C | deduction | hard |
| 74 | Question: Amy, Ben, and Cara each own a different pet: a cat, a dog, or a fish. Amy does not own the cat. Ben does not own the fish. Amy does not own the dog. What pet does Amy own? A) Cat B) Dog C) Fish D) Cannot be determined | C | deduction | medium |
| 75 | Question: Five runners finish a race with no ties. Diana finishes before Eve. Eve finishes before Frank. Carol finishes before Diana. Bella finishes last. Who finishes first? A) Carol B) Diana C) Eve D) Frank | A | spatial | medium |
| 76 | Question: 'No A are B. No B are C.' Does it necessarily follow that 'no A are C'? A) Yes, always B) No -- a concrete counterexample shows A and C can fully overlap even when both premises hold C) Only if A and B are the same size D) Only if C is empty | B | syllogism | hard |
| 77 | Question: 'Some students passed the exam. All who passed received a certificate.' Does it follow that 'some students received a certificate'? A) Yes, this is a valid conclusion B) No, it's a fallacy C) Only if all students passed D) Only if no students passed | A | syllogism | easy |
| 78 | Question: Three friends Joe, Kim, and Lee each have a different number of marbles: 5, 8, and 12 (each number used once). Joe has more marbles than Kim. Lee has fewer marbles than Joe. How many marbles does Joe have? A) 5 B) 8 C) 12 D) Cannot be determined | C | deduction | medium |
| 79 | Question: Are the statements 'For every box, there exists a key that opens it' and 'There exists a key that opens every box' logically equivalent? A) Yes, always equivalent B) No -- the first allows different keys for different boxes, the second requires one universal key C) Only when there is exactly one box D) Only when there is exactly one key | B | predicate | hard |
| 80 | Question: 'If it is not raining, the picnic happens. The picnic did not happen.' What follows? A) It is raining B) It is not raining C) The picnic happened D) Nothing can be concluded | A | propositional | medium |
| 81 | Question: Four cars (red, blue, green, yellow) are parked in spots 1-4 in some order. The red car is in spot 1. The blue car is immediately to the right of the red car. The green car is in spot 4. Which spot is the yellow car in? A) Spot 1 B) Spot 2 C) Spot 3 D) Spot 4 | C | spatial | medium |
| 82 | Question: B is taller than A. A is taller than C. By transitivity, what can be concluded about B and C? A) B is taller than C B) C is taller than B C) B and C are the same height D) Nothing can be concluded | A | deduction | easy |
| 83 | Question: You have 8 coins, one of which is fake and lighter than the rest (identical otherwise). Using a balance scale, what is the minimum number of weighings needed to guarantee finding the fake coin? A) 1 B) 2 C) 3 D) 4 | B | deduction | hard |
| 84 | Question: The NAND operation P NAND Q is defined as: A) P AND Q B) NOT(P AND Q) C) P OR Q D) NOT(P OR Q) | B | propositional | easy |
| 85 | Question: Four people A, B, C, D stand evenly spaced in a circle. A is directly opposite C. B is immediately clockwise of A. D is immediately counter-clockwise of A. Who is directly opposite B? A) A B) C C) D D) Cannot be determined | C | spatial | medium |
| 86 | Question: 'P or Q (at least one is true). Q is false.' By disjunctive syllogism, what follows? A) P is true B) P is false C) Q is true D) Nothing follows | A | propositional | easy |
| 87 | Question: Tom is older than Sam. Sam is older than Ria. Ria is older than Bo. Who is the youngest? A) Tom B) Sam C) Ria D) Bo | D | deduction | easy |
| 88 | Question: 'You get a bonus if and only if you exceed quota.' You did NOT get a bonus. What follows? A) You exceeded quota B) You did not exceed quota C) You might or might not have exceeded quota D) The statement is contradictory | B | propositional | medium |
| 89 | Question: The statement 'Neither P nor Q' is logically equivalent to: A) P AND Q B) P OR Q C) NOT P AND NOT Q D) NOT P OR NOT Q | C | propositional | easy |
| 90 | Question: Four racers A, B, C, D finish a race; one of gold/silver/bronze/no medal is awarded by finishing order. A beat B. C got no medal. B beat D. Who got the gold medal? A) A B) B C) C D) D | A | spatial | hard |
| 91 | Question: Five boxes labeled 1-5 are stacked. Box 3 is at the very bottom. Box 1 is directly on top of box 4. Box 5 is directly on top of box 1. Box 2 is at the very top. From bottom to top, what is the order? A) 3,4,1,5,2 B) 3,1,4,5,2 C) 3,4,5,1,2 D) 2,5,1,4,3 | A | spatial | hard |
| 92 | Question: 'All efficient markets are unpredictable. This market is unpredictable. Therefore this market is efficient.' This argument is: A) Valid B) Invalid -- affirming the consequent; a market can be unpredictable without being efficient C) Valid only for stock markets D) A tautology | B | syllogism | medium |
| 93 | Question: The contrapositive of 'All A are B' is: A) All B are A B) All non-B are non-A C) All non-A are non-B D) Some A are not B | B | syllogism | medium |
| 94 | Question: By the exportation law, '(P AND Q) implies R' is logically equivalent to: A) P implies (Q implies R) B) Q implies (P implies R) C) Both A and B are correct equivalent forms D) (P implies R) AND (Q implies R) | C | propositional | hard |
| 95 | Question: By the absorption law, 'P OR (P AND Q)' simplifies to: A) Q B) P C) P AND Q D) True (always) | B | propositional | medium |
| 96 | Question: By the idempotent law, 'P AND P' and 'P OR P' both simplify to: A) True B) False C) P D) NOT P | C | propositional | easy |
| 97 | Question: Four people stand in a cycle, each saying 'the next person (clockwise) is a knight.' Knights always tell the truth, knaves always lie. How many self-consistent assignments of knight/knave are possible for the whole group? A) 0 B) 1 C) 2 D) 4 | C | deduction | hard |
| 98 | Question: By the distributive law, 'P AND (Q OR R)' is logically equivalent to: A) (P AND Q) OR (P AND R) B) (P OR Q) AND (P OR R) C) P AND Q AND R D) P OR Q OR R | A | propositional | medium |
| 99 | Question: If equality is transitive and A=B and B=C, what can be concluded? A) A=C B) A is not C C) B is undefined D) Nothing can be concluded | A | deduction | easy |
| 100 | Question: A 'sound' argument, in formal logic, is one that is: A) Merely persuasive B) Valid AND has all true premises (guaranteeing a true conclusion) C) Valid but with at least one false premise D) Any argument with a true conclusion | B | general_logic | medium |
5. Instruction Following (100 questions)
Verified programmatically (Python verifier function per question, not shown -- the constraint is fully specified in the question text itself).
| # | Question | Difficulty |
|---|---|---|
| 1 | Write a short sentence about a cat sitting on a mat, WITHOUT using the letter 'e' anywhere in your response. | medium |
| 2 | List exactly 3 fruits, each on its own line starting with a dash (-). No other text. | easy |
| 3 | Respond with ONLY a valid JSON object with exactly two keys: "name" (a string) and "age" (an integer). No other text, no markdown code fences. | medium |
| 4 | Write a sentence that contains the word 'banana' exactly twice. | medium |
| 5 | Respond with EXACTLY one sentence (exactly one terminal punctuation mark: period, exclamation point, or question mark, and nothing after it). | easy |
| 6 | Respond in ALL UPPERCASE letters only. | easy |
| 7 | Describe the number five in words, WITHOUT using any digit characters (0-9) anywhere in your response. | medium |
| 8 | Respond with EXACTLY 5 words, no more, no less. Separate words by single spaces, no punctuation. | medium |
| 9 | Respond with a single English palindrome word (a word spelled the same forwards and backwards) that is at least 4 letters long. Respond with only the word. | hard |
| 10 | Respond with ONLY a valid JSON array of exactly 3 integers, sorted in ascending order. No other text. | medium |
| 11 | Respond with the date January 1, 2025 written ONLY in ISO 8601 format (YYYY-MM-DD). No other text. | easy |
| 12 | Write a sentence of at least 5 words in which NO word is repeated (case-insensitive, ignoring punctuation). | medium |
| 13 | Respond with a single integer between 1 and 100 (inclusive) that is BOTH a perfect square AND even. Number only. | hard |
| 14 | Respond with a single word or token containing NO whitespace characters at all. | easy |
| 15 | Respond with ONLY a valid JSON object of the exact shape {"items": [a, b, c]} where a, b, c are three NEGATIVE integers. No other text. | hard |
| 16 | Respond with EXACTLY 10 words, no more, no less. | medium |
| 17 | Write a short phrase (at least 3 words) that contains NO vowels (a, e, i, o, u) anywhere, uppercase or lowercase. | hard |
| 18 | Respond with ONLY a valid JSON array of exactly 4 strings. No other text. | medium |
| 19 | Write a short phrase where the first word and the last word are identical (ignoring punctuation and case). | medium |
| 20 | Write the number 4,200 entirely in English words, with NO digit characters anywhere in your response. | medium |
| 21 | Respond with exactly 2 question marks and no periods or exclamation points anywhere in your response. | medium |
| 22 | Respond with exactly 5 distinct single letters (A-Z), separated by commas, e.g. 'A, B, C, D, E'. No other text. | medium |
| 23 | Respond with ONLY a valid JSON object of the exact shape {"valid": true} or {"valid": false} -- a single boolean field named "valid". No other text. | medium |
| 24 | Write a sentence that contains the substring '42' exactly once. | easy |
| 25 | Respond with a single English word that is an anagram of the word LISTEN. Respond with only the word. | hard |
| 26 | Respond with a single word that contains a double letter (the same letter appearing twice in a row), with no spaces. | easy |
| 27 | Respond with exactly 3 lines, each line a different color name, no duplicates. | easy |
| 28 | Respond with a single word wrapped in markdown bold (e.g. word) and nothing else. | easy |
| 29 | Respond with ONLY a valid JSON object of the exact shape {"min": X, "max": Y} where X and Y are integers and X is strictly less than Y. No other text. | medium |
| 30 | Respond with a single English word, at least 3 letters, ending in the letters 'at'. | easy |
| 31 | Write a short sentence containing EXACTLY one capital letter in the entire response (including the first letter). | medium |
| 32 | Write a sentence of at least 4 words where each word is strictly longer than the previous word. | hard |
| 33 | Respond with a single integer that is equal to its own square root rounded to the nearest integer. | medium |
| 34 | Write a single English word (at least 5 letters) in which no letter repeats. | medium |
| 35 | Write a sentence containing exactly 3 commas. | easy |
| 36 | Respond with the 26 letters of the English alphabet in REVERSE order (Z first, A last), comma-separated, no spaces, no other text. | easy |
| 37 | Respond with a single lowercase word of at least 6 letters, no spaces, no punctuation, no digits. | easy |
| 38 | Write a sentence that ends with a colon followed by exactly 3 comma-separated items. | medium |
| 39 | Respond with ONLY a valid JSON array of exactly 3 numbers, each between 0 and 1 inclusive. No other text. | medium |
| 40 | Respond with a single English word that is EXACTLY 5 letters long and reads the same forwards and backwards. | medium |
| 41 | Respond with a single English word that is EXACTLY 7 letters long. | easy |
| 42 | Respond with ONLY a valid 6-digit hex color code in the format #rrggbb (e.g. #1a2b3c). No other text. | easy |
| 43 | Write a sentence of at least 4 words containing NO letter 't' or 'T' anywhere. | medium |
| 44 | Respond with ONLY a valid JSON array of exactly 2 objects, each of the shape {"x": int, "y": int}. No other text. | medium |
| 45 | Write a sentence of at least 3 words in which every word is exactly 4 letters long. | medium |
| 46 | Write a sentence that uses each of the words 'red', 'blue', and 'green' exactly once. | medium |
| 47 | Respond with a markdown numbered list of EXACTLY 3 items, numbered 1. 2. 3. | easy |
| 48 | Respond with a single English word (at least 4 letters) that starts and ends with the same letter. | easy |
| 49 | Respond with ONLY a valid JSON object of the exact shape {"count": N} where N is a positive even integer. No other text. | medium |
| 50 | Write a sentence of at least 4 words where every word starts with the same letter (alliteration). | medium |
| 51 | Respond with a single English word (at least 4 letters) in which no letter appears more than twice. | medium |
| 52 | Write a sentence containing exactly one semicolon. | easy |
| 53 | Respond with ONLY a valid JSON object of the exact shape {"items": [a, b, c]} where a, b, c are 3 distinct lowercase strings. No other text. | medium |
| 54 | Respond with text that is EXACTLY 20 characters long, including spaces. | medium |
| 55 | Write a question (ending in a question mark) that contains the word 'why'. | easy |
| 56 | Respond with exactly the lowercase word 'yes' or the lowercase word 'no', nothing else. | easy |
| 57 | Respond with ONLY a valid JSON array of exactly 5 consecutive ascending integers (e.g. [3,4,5,6,7]). No other text. | medium |
| 58 | Respond with a single English word, at least 5 letters, ending in 'ing'. | easy |
| 59 | Respond with exactly two words, both of which are the same length (ignoring trailing punctuation). | medium |
| 60 | Write a phrase of at least 7 letters (ignoring spaces and punctuation, case-insensitive) that is a palindrome. | hard |
| 61 | Write a sentence that contains both an exclamation point and a question mark. | easy |
| 62 | Respond with ONLY a valid JSON object of the exact shape {"name": str, "tags": [str, str, ...]} where tags has at least 2 strings. No other text. | medium |
| 63 | Respond with a single English word that is identical in its singular and plural form (e.g. one such animal name). | medium |
| 64 | Write a sentence in lowercase except for exactly one word written in ALL CAPS for emphasis. | medium |
| 65 | Write a sentence that contains a Roman numeral (e.g. IX, IV, XII). | medium |
| 66 | Write a sentence of at least 4 words where the 2nd word and the 2nd-to-last word are identical (case-insensitive, ignoring punctuation). | medium |
| 67 | Respond with exactly the text 'null' (lowercase, nothing else) -- the valid JSON null literal. | easy |
| 68 | Write a sentence containing a contraction (a word with an apostrophe, e.g. can't, it's, don't). | easy |
| 69 | Respond with exactly 3 words, in strict alphabetical order. | medium |
| 70 | Write a sentence where the total number of words equals the number of letters in the first word. | hard |
| 71 | Write a sentence of at least 3 words where no word is longer than 4 letters. | medium |
| 72 | Respond with ONLY a valid JSON array of at least 2 numbers whose sum is exactly 100. No other text. | medium |
| 73 | Respond with a single English word (at least 4 letters) using only letters from the first half of the alphabet (a through m). | medium |
| 74 | Write a sentence that ends with an ellipsis (...). | easy |
| 75 | Write a phrase (at least 4 letters total) with an EQUAL number of vowels and consonants. | medium |
| 76 | Write a sentence that spells out a number in words (e.g. 'three') and uses NO digit characters anywhere. | medium |
| 77 | Respond with ONLY a valid JSON array of exactly 4 booleans, with exactly 2 of them true. No other text. | medium |
| 78 | Respond with a single English word that contains all 5 vowels (a, e, i, o, u) at least once. | hard |
| 79 | Write a sentence of at least 4 words where each word is strictly SHORTER than the previous word. | hard |
| 80 | Write a phrase of at least 3 words that reads the same sequence of words forwards and backwards (a word-level palindrome, e.g. 'dog cat dog'). | hard |
| 81 | Respond with ONLY a valid JSON object with at least 2 keys, where every value is an integer (no strings, no booleans, no floats). No other text. | medium |
| 82 | Write at least 2 sentences (separated by periods) where each sentence starts with a different word. | medium |
| 83 | Write a sentence with exactly one capital letter total, and it must NOT be the first letter of the sentence. | medium |
| 84 | Respond with ONLY a valid JSON array of exactly 2 different strings that are anagrams of each other. No other text. | hard |
| 85 | Write a word chain of at least 3 words where the last letter of each word matches the first letter of the next word. | hard |
| 86 | Write a sentence of at least 4 words containing NO letter 's' or 'S' anywhere. | medium |
| 87 | Respond with ONLY a valid JSON object with at least 3 keys, where the keys appear in alphabetical order. No other text. | medium |
| 88 | Write a sentence containing both a word and its plural form (e.g. 'cat' and 'cats'). | medium |
| 89 | Write a sentence containing EXACTLY one numeral digit total (0-9), anywhere in the text. | easy |
| 90 | Respond with ONLY a valid JSON array of exactly 3 strings, each a different length, sorted by length ascending. No other text. | medium |
| 91 | Respond with ONLY a valid JSON object of the exact shape {"status": "active"} or {"status": "inactive"} -- a single field named "status" with one of those two exact values. No other text. | easy |
| 92 | Respond with a single lowercase word containing no spaces. | easy |
| 93 | Write a sentence of exactly 6 words where the 2nd word is 'and'. | medium |
| 94 | Respond with ONLY a valid JSON array of exactly 4 consecutive ascending integers. No other text. | medium |
| 95 | Write a sentence entirely in lowercase that ends with an exclamation point. | easy |
| 96 | Respond with text wrapped in a single pair of parentheses, e.g. (like this), and nothing outside the parentheses. | easy |
| 97 | Write a phrase of at least 3 words where the first and last word are identical, and every word in between is distinct. | hard |
| 98 | Respond with ONLY a valid JSON object with exactly 2 keys, both string values, and the two values must be DIFFERENT from each other. No other text. | medium |
| 99 | Write text containing at least one pair of parentheses, where every opening parenthesis has a matching closing parenthesis (parentheses may be nested). | medium |
| 100 | Respond with EXACTLY 3 digit characters and nothing else (a 3-digit number as a string). | easy |
6. English (100 questions)
Added 2026-06-22 (the ZACBENCH-500 → 600 change). Language proficiency, distinct from Instruction-Following. Subcats: usage/confused-words, grammar, idiom, vocab/etymology, syntactic ambiguity, rhetorical devices, register, reading comprehension, reference resolution, subject-verb agreement. MCQ, single correct letter. Rendered from
_b500_english.py.
| # | Question | Gold | Category | Difficulty |
|---|---|---|---|---|
| 1 | Question: Choose the correct word: The committee's decision will _____ on whether the budget is approved. A) hinge B) hedge C) hatch D) hinder | A | usage | hard |
| 2 | Question: Which is correct? 'The evidence was so _____ that the jury reached a verdict in twenty minutes.' A) incredulous B) incredible C) credulous D) credible | B | usage | hard |
| 3 | Question: 'The two proposals are _____ in every meaningful respect.' (= cannot be distinguished) A) discrete B) disparate C) indiscreet D) indistinguishable | D | usage | hard |
| 4 | Question: Choose correctly: 'Her argument, though _____, ultimately failed to persuade the board.' A) cogent B) cogitative C) contingent D) congenital | A | usage | hard |
| 5 | Question: 'He was _____ by the implication that he had lied.' (= made indignant) A) nonplussed B) piqued C) appeased D) placated | B | usage | hard |
| 6 | Question: Which word correctly completes: 'The new evidence _____ the prosecution's entire case.' A) eviscerated B) emaciated C) extricated D) eradicated | A | usage | hard |
| 7 | Question: 'The senator's remarks were widely seen as _____ rather than a genuine policy proposal.' (= for show) A) perfunctory B) performative C) pertinent D) permeable | B | usage | hard |
| 8 | Question: Choose correctly: 'She remained _____ despite the overwhelming pressure to concede.' (= firm, unyielding) A) intransigent B) intransitive C) introspective D) intemperate | A | usage | hard |
| 9 | Question: 'His explanation only served to _____ the confusion.' (= make worse) A) ameliorate B) exacerbate C) extenuate D) exonerate | B | usage | hard |
| 10 | Question: 'The author's prose style is notably _____, favoring short declarative sentences.' (= sparse, economical) A) ornate B) verbose C) laconic D) loquacious | C | usage | hard |
| 11 | Question: Which sentence is grammatically correct? A) Neither the manager nor the employees was aware of the policy change. B) Neither the manager nor the employees were aware of the policy change. C) Neither the manager or the employees were aware of the policy change. D) Neither the manager nor employees was aware about the policy change. | B | grammar | hard |
| 12 | Question: Which sentence is grammatically correct? A) Each of the candidates have submitted their portfolio. B) Each of the candidates has submitted their portfolio. C) Each of the candidates have submitted his or her portfolio. D) Each of the candidates having submitted their portfolio. | B | grammar | hard |
| 13 | Question: Which sentence correctly uses 'whom'? A) Whom do you think will win the election? B) She is the candidate whom I believe will win. C) Whom did you give the report to? D) Whom is responsible for this decision? | C | grammar | hard |
| 14 | Question: Which sentence is grammatically correct? A) If I was you, I would reconsider the offer. B) If I were you, I would reconsider the offer. C) If I would be you, I would reconsider the offer. D) If I am you, I would reconsider the offer. | B | grammar | hard |
| 15 | Question: Which sentence is grammatically correct? A) The data suggests that the hypothesis is correct. B) The data suggest that the hypothesis is correct. C) The data suggesting that the hypothesis is correct. D) The datum suggest that the hypothesis is correct. | B | grammar | hard |
| 16 | Question: Which sentence correctly uses 'lay' and 'lie'? A) I'm going to lay down for an hour. B) The book was laying on the table all day. C) She lay awake for hours thinking about the exam. D) He has lain the documents on your desk. | C | grammar | hard |
| 17 | Question: Which sentence is grammatically correct? A) The committee, who meets monthly, has approved the budget. B) The committee, which meets monthly, has approved the budget. C) The committee, whom meets monthly, has approved the budget. D) The committee, that meets monthly, has approved the budget. | B | grammar | hard |
| 18 | Question: Which sentence avoids a dangling modifier? A) Having finished the report, the printer was turned off. B) Having finished the report, she turned off the printer. C) The printer, having finished the report, was turned off. D) Having been finished, she turned off the printer's report. | B | grammar | hard |
| 19 | Question: Which sentence is grammatically correct? A) Between you and I, the plan will fail. B) Between you and me, the plan will fail. C) Between you and myself, the plan will fail. D) Between yourself and I, the plan will fail. | B | grammar | hard |
| 20 | Question: Which sentence correctly uses the subjunctive? A) I wish I was taller. B) I wish I were taller. C) I wish I am taller. D) I wish I will be taller. | B | grammar | hard |
| 21 | Question: Complete the idiom correctly: 'He couldn't care _____ about the outcome.' A) less B) more C) much D) any | A | idiom | hard |
| 22 | Question: Which is the correct idiom? A) for all intents and purposes B) for all intensive purposes C) for all intense purposes D) for all intent of purposes | A | idiom | hard |
| 23 | Question: Which is the correct idiom? A) a moot point B) a mute point C) a mood point D) a moot point of view | A | idiom | hard |
| 24 | Question: Which is the correct idiom? A) champing at the bit B) chomping at the bit C) chumping at the bit D) chopping at the bit | A | idiom | hard |
| 25 | Question: Which is the correct idiom? A) one and the same B) one in the same C) one of the same D) one with the same | A | idiom | hard |
| 26 | Question: What does 'to beg the question' correctly mean in formal/logical usage? A) to raise an obvious follow-up question B) to assume the conclusion one is trying to prove C) to ask an inappropriate question D) to avoid answering a question | B | idiom | hard |
| 27 | Question: Which is the correct idiom? A) tow the line B) toe the line C) toll the line D) tone the line | B | idiom | hard |
| 28 | Question: Which is the correct idiom? A) a wolf in cheap clothing B) a wolf in sheep's clothing C) a wolf in sheep clothing D) a wolf and sheep's clothing | B | idiom | hard |
| 29 | Question: Which is the correct idiom? A) nip it in the butt B) nip it in the bud C) nip it at the bud D) nip it to the bud | B | idiom | hard |
| 30 | Question: Which is the correct idiom? A) take it with a grain of salt B) take it with a grain assault C) take it with a grand of salt D) take it with a pinch of pepper | A | idiom | hard |
| 31 | Question: 'Sesquipedalian' most precisely describes: A) a person who is extremely tall B) writing or speech characterized by long words C) a fear of long sentences D) a type of ancient measurement | B | vocabulary | hard |
| 32 | Question: The word 'salary' derives from the Latin word for which substance, which Roman soldiers were partly paid in? A) gold B) wine C) salt D) grain | C | vocabulary | hard |
| 33 | Question: 'Perspicacious' most precisely means: A) having keen insight or discernment B) speaking very clearly C) overly cautious D) easily perceived by others | A | vocabulary | hard |
| 34 | Question: 'Ubiquitous' most precisely means: A) extremely rare B) present everywhere C) ancient in origin D) difficult to find | B | vocabulary | hard |
| 35 | Question: The word 'salient' most precisely means: A) most noticeable or important B) extremely salty C) moving in a wave-like pattern D) calm and composed | A | vocabulary | hard |
| 36 | Question: 'Pernicious' most precisely means: A) having a harmful effect, especially gradually or subtly B) extremely stubborn C) overly meticulous D) quick to anger | A | vocabulary | hard |
| 37 | Question: The word 'disinterested' (in its strict, traditional sense) means: A) bored or uninterested B) impartial, having no personal stake C) actively opposed D) confused about the topic | B | vocabulary | hard |
| 38 | Question: 'Obsequious' most precisely describes someone who is: A) excessively eager to please or obey B) hostile and confrontational C) extremely knowledgeable D) indifferent to others' opinions | A | vocabulary | hard |
| 39 | Question: The word 'inchoate' most precisely means: A) just begun and not fully formed B) thoroughly completed C) intentionally vague D) chaotic and destructive | A | vocabulary | hard |
| 40 | Question: 'Pellucid' most precisely describes writing that is: A) deliberately ambiguous B) extremely clear and easy to understand C) full of complex vocabulary D) emotionally charged | B | vocabulary | hard |
| 41 | Question: 'The chicken is ready to eat.' Which paraphrase captures the MORE natural, default reading of this sentence in context (e.g., spoken at a dinner table)? A) The chicken is hungry and about to eat something B) The chicken has been cooked and is ready to be eaten C) The chicken is capable of eating D) The chicken refuses to eat | B | syntax | hard |
| 42 | Question: 'I saw the man with the telescope.' Under the reading where the PREPOSITIONAL PHRASE modifies the verb (not the noun), who has the telescope? A) The man B) The speaker (the one who saw) C) Neither — the sentence is not ambiguous D) It's unclear from the sentence | B | syntax | hard |
| 43 | Question: 'Visiting relatives can be tiresome.' Under the reading where 'visiting' is a gerund acting as the subject (not an adjective), what does the sentence mean? A) Relatives who are visiting can be tiresome B) The act of visiting relatives can be tiresome C) Relatives dislike visiting D) Tiresome relatives often visit | B | syntax | hard |
| 44 | Question: 'They are cooking apples.' Under the reading where 'cooking' functions as an adjective (not a present-participle verb), what does the sentence mean? A) Some people are in the process of cooking apples B) The apples in question are a variety used for cooking C) They have finished cooking D) Apples are cooking themselves | B | syntax | hard |
| 45 | Question: 'The professor said on Monday she would give the exam.' Under the reading where 'on Monday' modifies 'said' (not 'would give'), when did the professor make the statement? A) On Monday B) On the day of the exam C) The timing is unspecified D) Before the exam was scheduled | A | syntax | hard |
| 46 | Question: 'Flying planes can be dangerous.' Under the reading where 'flying' is a gerund (the activity itself), what is dangerous? A) Planes that are currently airborne B) The act of piloting planes C) Planes in general, whether flying or not D) Birds near airports | B | syntax | hard |
| 47 | Question: 'I won't tell you because you are my friend.' Under the standard reading (negation scoping over the main clause, reason given for not telling), why won't the speaker tell? A) Because they ARE the listener's friend B) Because they are NOT the listener's friend C) The sentence doesn't specify D) Both readings are equally natural with no default | A | syntax | hard |
| 48 | Question: 'Police shot the man with a knife.' Under the reading where the prepositional phrase modifies 'the man' (not 'shot'), who had the knife? A) The police B) The man C) Neither, a bystander D) It cannot be determined which reading is intended without more context, but under THIS specified reading specifically, who has it? | B | syntax | hard |
| 49 | Question: 'Old men and women were evacuated first.' Under the reading where 'old' modifies only 'men' (not 'women' as well), who was evacuated? A) Old men and old women B) Old men and women of any age C) Only old men D) Old women and men of any age | B | syntax | hard |
| 50 | Question: 'The man who hunted the deer with a rifle was arrested.' Under the reading where 'with a rifle' modifies 'hunted' (the method), what does the rifle belong to/describe? A) The deer B) The method of hunting C) The arrest D) A second, unnamed hunter | B | syntax | hard |
| 51 | Question: 'The pen is mightier than the sword.' This sentence primarily relies on which literary device? A) Simile B) Metonymy C) Onomatopoeia D) Alliteration | B | rhetoric | hard |
| 52 | Question: 'I have a thousand things to do today' (said by someone who has perhaps twelve tasks) is an example of: A) Litotes B) Hyperbole C) Understatement D) Irony | B | rhetoric | hard |
| 53 | Question: 'She was not unhappy with the result' is an example of: A) Hyperbole B) Litotes C) Synecdoche D) Personification | B | rhetoric | hard |
| 54 | Question: 'All hands on deck' uses which device to refer to the whole sailors via a part of them? A) Metaphor B) Synecdoche C) Apostrophe D) Oxymoron | B | rhetoric | hard |
| 55 | Question: 'Bittersweet' and 'jumbo shrimp' are examples of: A) Paradox B) Oxymoron C) Antithesis D) Chiasmus | B | rhetoric | hard |
| 56 | Question: 'Ask not what your country can do for you — ask what you can do for your country.' This famous line primarily employs which device? A) Anaphora B) Chiasmus C) Hyperbole D) Synecdoche | B | rhetoric | hard |
| 57 | Question: A speaker addressing an absent or non-human entity directly ('O Death, where is thy sting?') is using: A) Apostrophe B) Soliloquy C) Personification D) Anaphora | A | rhetoric | hard |
| 58 | Question: 'It was the best of times, it was the worst of times' relies primarily on repeated sentence structure with contrasting ideas, known as: A) Antithesis B) Anaphora alone C) Zeugma D) Litotes | A | rhetoric | hard |
| 59 | Question: 'He stole my money and my heart' uses one verb ('stole') governing two very different kinds of objects — this device is called: A) Synecdoche B) Zeugma C) Metonymy D) Catachresis | B | rhetoric | hard |
| 60 | Question: A statement that seems self-contradictory but reveals a deeper truth upon reflection (e.g., 'less is more') is best classified as: A) Oxymoron B) Paradox C) Irony D) Antithesis | B | rhetoric | hard |
| 61 | Question: Which sentence is most appropriate for a formal academic paper? A) The results were pretty much what we expected. B) The results were largely consistent with our expectations. C) The results were basically what we thought would happen. D) The results kind of matched our predictions. | B | register | hard |
| 62 | Question: In formal written English, which is preferred? A) The report, that was submitted late, was rejected. B) The report, which was submitted late, was rejected. C) The report who was submitted late was rejected. D) The report submitted late, was rejected. | B | register | hard |
| 63 | Question: Which sentence avoids an inappropriate colloquialism in formal writing? A) The data kind of suggests a trend. B) The data suggest a trend. C) The data sort of point to a trend. D) The data, like, show a trend. | B | register | hard |
| 64 | Question: Which is the more formally correct way to begin a sentence? A) Plus, the budget was over the limit. B) Additionally, the budget exceeded the limit. C) And also, the budget went over. D) On top of that, the budget was too much. | B | register | hard |
| 65 | Question: Which is correct in formal register: ending a sentence with a preposition is traditionally avoided; which sentence avoids it most naturally? A) This is the topic I am most interested in. B) This is the topic in which I am most interested. C) This is the topic that I am interested about. D) This is the topic I am interested in about. | B | register | hard |
| 66 | Question: Which word choice is more appropriate in a formal cover letter? A) I'm super excited about this opportunity. B) I am very enthusiastic about this opportunity. C) I'm totally psyched for this role. D) This job sounds awesome to me. | B | register | hard |
| 67 | Question: Which sentence correctly avoids a split infinitive while preserving meaning, in a context where formal style discourages it? A) She decided to quickly finish the report. B) She decided to finish the report quickly. C) She decided quickly to finish the report (ambiguous meaning). D) She decided to finish quickly the report. | B | register | hard |
| 68 | Question: Which is more appropriate in formal writing: contractions are generally avoided. Which sentence correctly avoids them? A) The committee doesn't agree with the proposal. B) The committee does not agree with the proposal. C) The committee don't agree with the proposal. D) The committee won't be agreeing with the proposal. | B | register | hard |
| 69 | Question: Which transition is most appropriate in a formal academic argument (avoiding casual conjunctions to start a sentence)? A) But the results contradicted this. B) However, the results contradicted this. C) Yet, the results contradicted this, but. D) So the results went against it. | B | register | hard |
| 70 | Question: In formal writing, which sentence correctly avoids the vague, overused intensifier 'very' in favor of a more precise word? A) The findings were very surprising. B) The findings were startling. C) The findings were very very surprising. D) The findings were quite very surprising. | B | register | hard |
| 71 | Question: "Although the new policy was framed as a cost-saving measure, internal memos suggest the primary motivation was to consolidate decision-making power within a smaller executive group." What can be most reasonably inferred? A) The policy genuinely saved costs and nothing else B) The stated justification may not be the full or true reason for the policy C) The internal memos were written before the policy was framed publicly D) The executive group opposed the policy | B | comprehension | hard |
| 72 | Question: "She thanked him for his 'thorough' feedback, though she later admitted to colleagues that most of it had missed the point entirely." The word 'thorough' as used here is best understood as: A) Sincere praise B) Politely insincere or diplomatically misleading C) A factual, neutral description D) An accusation of laziness | B | comprehension | hard |
| 73 | Question: "The committee approved the measure unanimously, which surprised no one familiar with how thoroughly its outcome had been negotiated beforehand." What does this sentence imply about the unanimous vote? A) It reflects genuine spontaneous agreement among all members B) It was likely a formality, the real decision having been settled in advance C) The committee members had never met before the vote D) The measure was controversial and narrowly passed | B | comprehension | hard |
| 74 | Question: "He claimed to have read the entire report, but his questions revealed he had skipped straight to the conclusion." What is the most reasonable inference? A) He read the report carefully from start to finish B) His claim of having read the whole report was likely untrue or exaggerated C) The conclusion was the only useful part of the report D) He wrote the report himself | B | comprehension | hard |
| 75 | Question: "The restaurant's reviews praised its 'creative' interpretation of the classic dish, though several regulars noted it bore little resemblance to the original." The word 'creative' here most likely functions as: A) Straightforward praise with no underlying critique B) A polite way of signaling a significant, possibly unwelcome departure from tradition C) A factual culinary classification D) An insult with no positive connotation at all | B | comprehension | hard |
| 76 | Question: "The spokesperson said the company 'takes the allegations seriously,' a phrase that, in corporate communications, often precedes either a substantive response or none at all." What does this sentence suggest about the phrase itself? A) It always guarantees a substantive response B) Its actual meaning/follow-through is often ambiguous or non-committal in practice C) It is a legally binding admission of guilt D) It is rarely used in real corporate statements | B | comprehension | hard |
| 77 | Question: "Despite describing the merger as 'mutually beneficial,' the smaller company's shareholders received a far smaller share of the combined entity than their original stake would have suggested." What is implied about the term 'mutually beneficial'? A) Both companies benefited exactly equally B) The framing may understate an imbalance favoring the larger company C) The smaller company's shareholders gained more than expected D) The merger was illegal | B | comprehension | hard |
| 78 | Question: "The professor's syllabus described the course as 'rigorous but accessible' — a description that, after the first exam, half the class would have only agreed with the first half of." What does this imply about the first exam? A) Most students found the exam easy and accessible B) The exam turned out to be rigorous but not very accessible for at least half the class C) The professor changed the syllabus after the exam D) The course description was entirely accurate for everyone | B | comprehension | hard |
| 79 | Question: "He prefaced his criticism with 'with all due respect,' a phrase whose presence often inversely correlates with the respect actually being shown." What is the passage suggesting about that phrase? A) It always indicates genuine respect B) It is sometimes used ironically, preceding remarks that are not very respectful C) It is a legal disclaimer D) It is only used by lawyers | B | comprehension | hard |
| 80 | Question: "The annual report described growth as 'steady,' though the underlying figures showed three consecutive quarters of decline followed by one quarter of modest recovery." What does this suggest about the word 'steady' as used in the report? A) It accurately and neutrally describes the data B) It may be a euphemistic or misleading characterization of an actually volatile/declining trend C) The figures were fabricated D) Growth was consistently strong throughout the year | B | comprehension | hard |
| 81 | Question: "When Sarah told Maria that she had won the award, she was thrilled." In the most natural default reading (same-subject continuation), who was thrilled? A) Sarah B) Maria C) Both equally, with no preferred reading D) Neither — the sentence is meaningless | B | reference | hard |
| 82 | Question: "The trophy didn't fit into the brown suitcase because it was too big." What does 'it' refer to? A) The suitcase B) The trophy C) Either, equally ambiguous with no resolution possible D) Neither, it refers to an unstated third object | B | reference | hard |
| 83 | Question: "The city council refused the protesters a permit because they feared violence." What does 'they' most naturally refer to? A) The protesters B) The city council C) Both groups equally D) A third, unmentioned party | B | reference | hard |
| 84 | Question: "After John argued with his brother, he apologized." In the most natural reading, who apologized? A) John B) John's brother C) Both simultaneously D) The sentence cannot be resolved without more context, and there is no preferred default reading | A | reference | hard |
| 85 | Question: "The lawyer cross-examined the witness, but he remained calm throughout." Who most naturally remained calm? A) The lawyer B) The witness C) Both equally D) Neither, an unnamed bystander | B | reference | hard |
| 86 | Question: "Emma gave her sister a gift before she left for college." In the most natural reading, who was leaving for college? A) Emma B) Emma's sister C) Both of them D) Cannot be determined at all, even with a default preference | A | reference | hard |
| 87 | Question: "The ball broke the window because it was thrown too hard." What does 'it' refer to? A) The window B) The ball C) An unnamed thrower D) Either equally, with no resolvable default | B | reference | hard |
| 88 | Question: "The teacher praised the student because she had worked so hard." In the most natural reading, who had worked hard? A) The teacher B) The student C) Both equally D) Cannot be resolved by default | B | reference | hard |
| 89 | Question: "The company sued the contractor because it breached the agreement." What does 'it' most naturally refer to? A) The company B) The contractor C) Neither, an unnamed subcontractor D) Both equally, unresolvable | B | reference | hard |
| 90 | Question: "The novelist thanked her editor because she had improved the manuscript significantly." In the most natural reading, who improved the manuscript? A) The novelist B) The editor C) Both equally D) An unnamed third party | B | reference | hard |
| 91 | Question: Which is correct? 'The number of applicants _____ increased significantly this year.' A) have B) has C) having D) were | B | agreement | hard |
| 92 | Question: Which is correct? 'A number of applicants _____ already submitted their forms.' A) has B) have C) is D) was | B | agreement | hard |
| 93 | Question: Which is correct? 'The committee members, along with their chairperson, _____ scheduled to arrive at noon.' A) is B) are C) was D) being | B | agreement | hard |
| 94 | Question: Which is correct? 'Neither the players nor the coach _____ satisfied with the result.' A) was B) were C) being D) is being | B | agreement | hard |
| 95 | Question: Which is correct? 'Mathematics _____ my favorite subject in school.' A) are B) is C) were D) have been | B | agreement | hard |
| 96 | Question: Which is correct? 'The jury _____ still deliberating after six hours.' (referring to the jury acting as a single unit) A) is B) are C) were being D) have been | A | agreement | hard |
| 97 | Question: Which is correct? 'Politics _____ a topic many people avoid at dinner.' A) are B) is C) were D) have been | B | agreement | hard |
| 98 | Question: Which is correct? 'Either the manager or the employees _____ responsible for submitting the report.' (verb agrees with the nearer subject) A) is B) are C) was D) being | B | agreement | hard |
| 99 | Question: Which is correct? 'The list of items needed for the trip _____ on the refrigerator.' A) are B) is C) were D) have been | B | agreement | hard |
| 100 | Question: Which is correct? 'Each of the proposed amendments _____ its own set of consequences.' A) have B) has C) having D) were having | B | agreement | hard |
7. Agentic (100 questions)
Added 2026-07-28 to make the total 700. Tool-call correctness across 4 execution-checked
categories — see finetune/_b500_agentic.py's module docstring for the exact scoring contract
(the full 100 questions and the 15-tool schema live there, not duplicated into this table, since
every field's meaning is scoring-relevant and best read next to the code that checks it):
| category | count | tests |
|---|---|---|
single_call |
55 | one clearly correct tool + arguments for a plain request |
distractor |
20 | the request needs NO tool call — a model that calls a tool for everything scores 0 here even if it looks capable elsewhere |
ambiguous_arg |
15 | a call is correct, but one argument is under-specified — inventing a precise value that was never given is scored WRONG, the same standard as fabricating a fact |
multi_step |
10 | a two-tool chain; scored on the first call only, since real chaining needs a live tool executor this static bank does not run — documented so nobody reads it as testing something it doesn't |
Every expected_tool/required_args pair was checked against the 15-tool schema before being
committed (same "verified, not vibes" bar as the Coding section's run-before-commit reference
solutions), and the scoring function itself was self-tested against synthetic answers before
being trusted: 100/100 on known-correct input, exactly 20/100 (matching the distractor count, not
approximately) on an "always refuse to call anything" baseline.
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