| {"id": "l5_01", "level": 5, "category": "math", "question": "What is the sum of all integers from 1 to 100 (1 + 2 + ... + 100)?", "choices": ["4950", "5000", "5050", "5500"], "answer": "C"} | |
| {"id": "l5_02", "level": 5, "category": "trick", "question": "I have two coins that together total 30 cents. One of them is not a nickel. Which two coins do I have?", "choices": ["Two dimes", "A quarter and a nickel", "Three dimes", "A half-dollar and nothing else"], "answer": "B"} | |
| {"id": "l5_03", "level": 5, "category": "sequence", "question": "Look at the sequence 1, 11, 21, 1211, 111221. What comes next? (Hint: describe what you see, digit by digit.)", "choices": ["122112", "312211", "221121", "111222"], "answer": "B"} | |
| {"id": "l5_04", "level": 5, "category": "math", "question": "A wooden cube is painted red on all six faces, then cut into 27 equal smaller cubes. How many of the small cubes have exactly two red faces?", "choices": ["6", "8", "12", "27"], "answer": "C"} | |
| {"id": "l5_05", "level": 5, "category": "logic", "question": "On an island, knights always tell the truth and knaves always lie. A islander A says: 'We are both knaves.' (A and B are two islanders.) What are A and B?", "choices": ["Both are knights", "Both are knaves", "A is a knave and B is a knight", "A is a knight and B is a knave"], "answer": "C"} | |
| {"id": "l5_06", "level": 5, "category": "math", "question": "What is the remainder when 7^100 is divided by 5?", "choices": ["0", "1", "2", "4"], "answer": "B"} | |
| {"id": "l5_07", "level": 5, "category": "math", "question": "Five people meet and each pair shakes hands exactly once. How many handshakes happen in total?", "choices": ["8", "10", "15", "20"], "answer": "B"} | |
| {"id": "l5_08", "level": 5, "category": "logic", "question": "You have an empty 3-liter jug and an empty 5-liter jug, and an unlimited water supply. What is the minimum number of pours (fills, transfers between jugs, or emptyings) needed to measure exactly 4 liters?", "choices": ["4", "6", "8", "10"], "answer": "B"} | |
| {"id": "l5_09", "level": 5, "category": "trick", "question": "A farmer had 15 sheep and all but 8 died. How many sheep are left?", "choices": ["7", "8", "15", "0"], "answer": "B"} | |
| {"id": "l5_10", "level": 5, "category": "math", "question": "If x squared equals 49, what are ALL possible values of x?", "choices": ["Only 7", "Only -7", "7 and -7", "Neither value is valid"], "answer": "C"} | |
| {"id": "l5_11", "level": 5, "category": "math", "question": "What is the remainder when 2^50 is divided by 7?", "choices": ["0", "1", "2", "4"], "answer": "D"} | |
| {"id": "l5_12", "level": 5, "category": "math", "question": "How many trailing zeros does 100! (100 factorial) have when written out in full?", "choices": ["10", "21", "24", "25"], "answer": "C"} | |
| {"id": "l5_13", "level": 5, "category": "probability", "question": "Two fair six-sided dice are rolled. What is the probability that the sum equals 8?", "choices": ["5/36", "6/36", "1/6", "1/9"], "answer": "A"} | |
| {"id": "l5_14", "level": 5, "category": "math", "question": "A train 100 m long travels at 20 m/s through a tunnel 300 m long. How long from the moment the front enters until the tail exits?", "choices": ["10 s", "15 s", "20 s", "25 s"], "answer": "C"} | |
| {"id": "l5_15", "level": 5, "category": "logic", "question": "Knights always tell the truth, knaves always lie. A says: 'Exactly one of us is a knave.' B says: 'A is a knave.' What are A and B?", "choices": ["A knight, B knight", "A knight, B knave", "A knave, B knight", "A knave, B knave"], "answer": "B"} | |
| {"id": "l5_16", "level": 5, "category": "math", "question": "How many integers from 1 to 1000 (inclusive) are divisible by neither 2 nor 5?", "choices": ["300", "350", "400", "500"], "answer": "C"} | |
| {"id": "l5_17", "level": 5, "category": "math", "question": "If log2(x) = 10, what is x?", "choices": ["100", "512", "1024", "2048"], "answer": "C"} | |
| {"id": "l5_18", "level": 5, "category": "math", "question": "On a 5x5 grid of dots... no - consider all squares formed on a 5x5 chessboard of unit cells. How many squares of ANY size (1x1 up to 5x5) does it contain?", "choices": ["25", "50", "55", "60"], "answer": "C"} | |
| {"id": "l5_19", "level": 5, "category": "probability", "question": "A fair coin is flipped 3 times. What is the probability of getting at least one head?", "choices": ["1/2", "3/4", "7/8", "1/8"], "answer": "C"} | |
| {"id": "l5_20", "level": 5, "category": "math", "question": "Which of these four numbers is the largest?", "choices": ["2^10", "3^7", "5^5", "10^3"], "answer": "C"} | |
| {"id": "l5_21", "level": 5, "category": "math", "question": "In how many ways can a committee of 2 people be chosen from a group of 5 people?", "choices": ["5", "10", "20", "25"], "answer": "B"} | |
| {"id": "l5_22", "level": 5, "category": "math", "question": "What is the sum of the interior angles of a pentagon (5-sided polygon), in degrees?", "choices": ["360", "450", "540", "720"], "answer": "C"} | |
| {"id": "l5_23", "level": 5, "category": "math", "question": "A two-digit number has tens digit t and units digit u, where t = 3u. How many such two-digit numbers exist?", "choices": ["2", "3", "4", "9"], "answer": "B"} | |
| {"id": "l5_24", "level": 5, "category": "math", "question": "What is the volume of a cylinder with radius r and height h?", "choices": ["2*pi*r*h", "pi*r^2*h", "pi*r*h^2", "(1/3)*pi*r^2*h"], "answer": "B"} | |
| {"id": "l5_25", "level": 5, "category": "math", "question": "You drive 60 km at 60 km/h, then another 60 km at 30 km/h. What is your average speed for the whole trip?", "choices": ["40 km/h", "45 km/h", "48 km/h", "50 km/h"], "answer": "A"} | |
| {"id": "l5_26", "level": 5, "category": "math", "question": "If f(x) = 2x^2 - 3x + 1, what is f(2)?", "choices": ["1", "3", "5", "7"], "answer": "B"} | |
| {"id": "l5_27", "level": 5, "category": "math", "question": "How many diagonals does a regular octagon (8-sided polygon) have?", "choices": ["8", "16", "20", "28"], "answer": "C"} | |
| {"id": "l5_28", "level": 5, "category": "math", "question": "What is the units (last) digit of 3^43?", "choices": ["1", "3", "7", "9"], "answer": "C"} | |
| {"id": "l5_29", "level": 5, "category": "math", "question": "The volume of a sphere is (4/3)*pi*r^3. If the radius doubles, by what factor does the volume multiply?", "choices": ["2", "4", "6", "8"], "answer": "D"} | |
| {"id": "l5_30", "level": 5, "category": "probability", "question": "You roll a fair die repeatedly until you roll a 6. What is the expected (average) number of rolls needed?", "choices": ["3", "4", "6", "36"], "answer": "C"} | |