| {"question": "Harry and Terry are each told to calculate $8-(2+5)$ . Harry gets the correct answer. Terry ignores the parentheses and calculates $8-2+5$ . If Harry's answer is $H$ and Terry's answer is $T$ , what is $H-T$ ?", "options": ["6", "-10", "-6", "10"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "The first AMC $8$ was given in $1985$ and it has been given annually since that time. Samantha turned $12$ years old the year that she took the seventh AMC $8$ . In what year was Samantha born?", "options": ["1979", "1981", "1980", "1982"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "A magazine printed photos of three celebrities along with three photos of the celebrities as babies. The baby pictures did not identify the celebrities. Readers were asked to match each celebrity with the correct baby pictures. What is the probability that a reader guessing at random will match all three correctly?", "options": ["\\frac{1}{2}", "\\frac{1}{9}", "\\frac{1}{6}", "\\frac{1}{3}"], "answer": "C", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "If $n$ and $m$ are integers and $n^2+m^2$ is even, which of the following is impossible?", "options": [" n and m are even ", " n and m are odd ", " n+m is even ", " n+m is odd "], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "The \"Middle School Eight\" basketball conference has $8$ teams. Every season, each team plays every other conference team twice (home and away), and each team also plays $4$ games against non-conference opponents. What is the total number of games in a season involving the \"Middle School Eight\" teams?", "options": ["88", "60", "160", "96"], "answer": "A", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} | |
| {"question": "George walks $1$ mile to school. He leaves home at the same time each day, walks at a steady speed of $3$ miles per hour, and arrives just as school begins. Today he was distracted by the pleasant weather and walked the first $\\frac{1}{2}$ mile at a speed of only $2$ miles per hour. At how many miles per hour must George run the last $\\frac{1}{2}$ mile in order to arrive just as school begins today?", "options": ["4", "8", "10", "6"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} | |
| {"question": "Four children were born at City Hospital yesterday. Assume each child is equally likely to be a boy or a girl. Which of the following outcomes is most likely?", "options": [" 3 are of one gender and 1 is of the other gender", " 2 are girls and 2 are boys", " all of these outcomes are equally likely", " all 4 are boys"], "answer": "A", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "A cube with $3$ -inch edges is to be constructed from $27$ smaller cubes with $1$ -inch edges. Twenty-one of the cubes are colored red and $6$ are colored white. If the $3$ -inch cube is constructed to have the smallest possible white surface area showing, what fraction of the surface area is white?", "options": ["\\frac{5}{27}", "\\frac{1}{9}", "\\frac{5}{54}", "\\frac{2}{9}"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "Paul owes Paula $35$ cents and has a pocket full of $5$ -cent coins, $10$ -cent coins, and $25$ -cent coins that he can use to pay her. What is the difference between the largest and the smallest number of coins he can use to pay her?", "options": ["1", "4", "3", "5"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "The $7$ -digit numbers $\\underline{7} \\underline{4} \\underline{A} \\underline{5} \\underline{2} \\underline{B} \\underline{1}$ and $\\underline{3} \\underline{2} \\underline{6} \\underline{A} \\underline{B} \\underline{4} \\underline{C}$ are each multiples of $3$ . Which of the following could be the value of $C$ ?", "options": ["5", "2", "1", "3"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "A $2$ -digit number is such that the product of the digits plus the sum of the digits is equal to the number. What is the units digit of the number?", "options": ["5", "9", "3", "7"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "Three members of the Euclid Middle School girls' softball team had the following conversation.\n\nAshley: I just realized that our uniform numbers are all $2$ -digit primes.\n\nBrittany : And the sum of your two uniform numbers is the date of my birthday earlier this month.\n\nCaitlin: That's funny. The sum of your two uniform numbers is the date of my birthday later this month.\n\nAshley: And the sum of your two uniform numbers is today's date.\n\nWhat number does Caitlin wear?", "options": ["23", "13", "17", "11"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "One day the Beverage Barn sold $252$ cans of soda to $100$ customers, and every customer bought at least one can of soda. What is the maximum possible median number of cans of soda bought per customer on that day?", "options": ["3.5", "3.0", "4.5", "4.0"], "answer": "A", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "Isabella had a week to read a book for a school assignment. She read an average of $36$ pages per day for the first three days and an average of $44$ pages per day for the next three days. She then finished the book by reading $10$ pages on the last day. How many pages were in the book?", "options": ["270", "240", "250", "260"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "The sum of two prime numbers is $85$ . What is the product of these two prime numbers?", "options": ["85", "115", "133", "166"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Margie's car can go $32$ miles on a gallon of gas, and gas currently costs \\$ $4$ per gallon. How many miles can Margie drive on $\\$ 20$ worth of gas?", "options": ["160", "64", "640", "128"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} | |
| {"question": "Six rectangles each with a common base width of $2$ have lengths of $1, 4, 9, 16, 25$ , and $36$ . What is the sum of the areas of the six rectangles?", "options": ["182", "162", "93", "202"], "answer": "A", "topic": "Middle--Basic Geometry--Quadrilaterals"} | |
| {"question": "There are four more girls than boys in Ms. Raub's class of $28$ students. What is the ratio of number of girls to the number of boys in her class?", "options": ["3 : 4", "3 : 2", "2 : 1", "4 : 3"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "Eleven members of the Middle School Math Club each paid the same amount for a guest speaker to talk about problem solving at their math club meeting. They paid their guest speaker $\\$\\underline{1} \\underline{A} \\underline{2}$ . What is the missing digit $A$ of this $3$ -digit number?", "options": ["4", "1", "3", "2"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Onkon wants to cover his room's floor with his favourite red carpet. How many square yards of red carpet are required to cover a rectangular floor that is $12$ feet long and $9$ feet wide? (There are 3 feet in a yard.)", "options": ["12", "972", "108", "36"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "How many integers between $1000$ and $9999$ have four distinct digits?", "options": ["6561", "5040", "4536", "6480"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "In the small country of Mathland, all automobile license plates have four symbols. The first must be a vowel (A, E, I, O, or U), the second and third must be two different letters among the 21 non-vowels, and the fourth must be a digit (0 through 9). If the symbols are chosen at random subject to these conditions, what is the probability that the plate will read \"AMC8\"?", "options": [" \\frac{1}{10,500}", " \\frac{1}{2,100} ", " \\frac{1}{21,000}", " \\frac{1}{1,050}"], "answer": "C", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "How many subsets of two elements can be removed from the set $\\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\\}$ so that the mean (average) of the remaining numbers is 6?", "options": ["\\text{ 6}", "\\text{ 5}", "\\text{ 1}", "\\text{ 2}"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Which of the following integers cannot be written as the sum of four consecutive odd integers?", "options": ["\\text{ 40}", "\\text{ 100}", "\\text{ 16}", "\\text{ 200}"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If $\\frac{1}{3}$ of all the ninth graders are paired with $\\frac{2}{5}$ of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?", "options": [" \\frac{11}{15}", " \\frac{2}{15} ", " \\frac{4}{11} ", " \\frac{3}{8} "], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far in miles is it to school?", "options": [" 8 ", " 9 ", " 6 ", " 12"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "Ralph went to the store and bought 12 pairs of socks for a total of \\$24. Some of the socks he bought cost \\$1 a pair, some of the socks he bought cost \\$3 a pair, and some of the socks he bought cost \\$4 a pair. If he bought at least one pair of each type, how many pairs of \\$1 socks did Ralph buy?", "options": [" 6 ", " 4 ", " 5 ", " 7 "], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} | |
| {"question": "On June 1, a group of students is standing in rows, with 15 students in each row. On June 2, the same group is standing with all of the students in one long row. On June 3, the same group is standing with just one student in each row. On June 4, the same group is standing with 6 students in each row. This process continues through June 12 with a different number of students per row each day. However, on June 13, they cannot find a new way of organizing the students. What is the smallest possible number of students in the group?", "options": [" 30 ", " 60 ", " 90 ", " 21 "], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Tom has twelve slips of paper which he wants to put into five cups labeled $A$ , $B$ , $C$ , $D$ , $E$ . He wants the sum of the numbers on the slips in each cup to be an integer. Furthermore, he wants the five integers to be consecutive and increasing from $A$ to $E$ . The numbers on the papers are $2, 2, 2, 2.5, 2.5, 3, 3, 3, 3, 3.5, 4,$ and $4.5$ . If a slip with $2$ goes into cup $E$ and a slip with $3$ goes into cup $B$ , then the slip with $3.5$ must go into what cup?", "options": [" E", " D ", " C ", " A "], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "A baseball league consists of two four-team divisions. Each team plays every other team in its division $N$ games. Each team plays every team in the other division $M$ games with $N>2M$ and $M>4$ . Each team plays a $76$ game schedule. How many games does a team play within its own division?", "options": [" 72", " 54 ", " 60 ", " 48 "], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "Jack and Jill are going swimming at a pool that is one mile from their house. They leave home simultaneously. Jill rides her bicycle to the pool at a constant speed of $10$ miles per hour. Jack walks to the pool at a constant speed of $4$ miles per hour. How many minutes before Jack does Jill arrive?", "options": ["5", "8", "10", "9"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "The Blue Bird High School chess team consists of two boys and three girls. A photographer wants to take a picture of the team to appear in the local newspaper. She decides to have them sit in a row with a boy at each end and the three girls in the middle. How many such arrangements are possible?", "options": ["12", "6", "4", "2"], "answer": "A", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} | |
| {"question": "Billy's basketball team scored the following points over the course of the first $11$ games of the season. If his team scores $40$ in the $12^{th}$ game, which of the following statistics will show an increase?\n\n $42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73$", "options": [" \\text{median} ", " \\text{mean} ", " \\text{mode} ", " \\text{range} "], "answer": "D", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "In $\\bigtriangleup ABC$ , $AB=BC=29$ , and $AC=42$ . What is the area of $\\bigtriangleup ABC$ ?", "options": ["701", "420", "500", "609"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} | |
| {"question": "Each of two boxes contains three chips numbered $1$ , $2$ , $3$ . A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even?", "options": ["\\frac{5}{9}", "\\frac{2}{9}", "\\frac{4}{9}", "\\frac{1}{9}"], "answer": "A", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "What is the smallest whole number larger than the perimeter of any triangle with a side of length $5$ and a side of length $19$ ?", "options": ["24", "48", "29", "43"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} | |
| {"question": "On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working $20$ days?", "options": ["400", "210", "40", "401"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} | |
| {"question": "The longest professional tennis match ever played lasted a total of $11$ hours and $5$ minutes. How many minutes was this?", "options": ["605", "1005", "665", "655"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Suppose that $a * b$ means $3a-b.$ What is the value of $x$ if\n $2 * (5 * x)=1$", "options": ["2", "10", "\\frac{10}{3} ", "14"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is $132.$", "options": ["9", "7", "12", "5"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "Jefferson Middle School has the same number of boys and girls. $\\frac{3}{4}$ of the girls and $\\frac{2}{3}$ \nof the boys went on a field trip. What fraction of the students on the field trip were girls?", "options": ["\\frac{1}{2}", "\\frac{2}{3}", "\\frac{7}{13}", "\\frac{9}{17}"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "Two different numbers are randomly selected from the set $\\{ - 2, -1, 0, 3, 4, 5\\}$ and multiplied together. What is the probability that the product is $0$ ?", "options": ["\\dfrac{1}{5}", "\\dfrac{1}{4}", "\\dfrac{1}{6}", "\\dfrac{1}{3}"], "answer": "D", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "Karl's car uses a gallon of gas every $35$ miles, and his gas tank holds $14$ gallons when it is full. One day, Karl started with a full tank of gas, drove $350$ miles, bought $8$ gallons of gas, and continued driving to his destination. When he arrived, his gas tank was half full. How many miles did Karl drive that day?", "options": ["595", "525", "560", "665"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "What is the largest power of $2$ that is a divisor of $13^4 - 11^4$ ?", "options": ["16", "8", "64", "32"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "Annie and Bonnie are running laps around a $400$ -meter oval track. They started together, but Annie has pulled ahead, because she runs $25\\%$ faster than Bonnie. How many laps will Annie have run when she first passes Bonnie?", "options": ["1\\dfrac{1}{4}", "4", "5", "3\\dfrac{1}{3}"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "An ATM password at Fred's Bank is composed of four digits from $0$ to $9$ , with repeated digits allowable. If no password may begin with the sequence $9,1,1,$ then how many passwords are possible?", "options": ["30", "9990", "9000", "9999"], "answer": "B", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} | |
| {"question": "In an All-Area track meet, $216$ sprinters enter a $100-$ meter dash competition. The track has $6$ lanes, so only $6$ sprinters can compete at a time. At the end of each race, the five non-winners are eliminated, and the winner will compete again in a later race. How many races are needed to determine the champion sprinter?", "options": ["36", "72", "42", "43"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "The sum of $25$ consecutive even integers is $10,000$ . What is the largest of these $25$ consecutive integers?", "options": ["360", "416", "424", "388"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "The least common multiple of $a$ and $b$ is $12$ , and the least common multiple of $b$ and $c$ is $15$ . What is the least possible value of the least common multiple of $a$ and $c$ ?", "options": ["120", "20", "60", "30"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "A top hat contains 3 red chips and 2 green chips. Chips are drawn randomly, one at a time without replacement, until all 3 of the reds are drawn or until both green chips are drawn. What is the probability that the 3 reds are drawn?", "options": ["\\dfrac{1}{2}", "\\dfrac{3}{5}", "\\dfrac{3}{10}", "\\dfrac{2}{5}"], "answer": "D", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "Two congruent circles centered at points $A$ and $B$ each pass through the other circle's center. The line containing both $A$ and $B$ is extended to intersect the circles at points $C$ and $D$ . The circles intersect at two points, one of which is $E$ . What is the degree measure of $\\angle CED$ ?", "options": ["150", "120", "105", "135"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} | |
| {"question": "The digits $1$ , $2$ , $3$ , $4$ , and $5$ are each used once to write a five-digit number $PQRST$ . The three-digit number $PQR$ is divisible by $4$ , the three-digit number $QRS$ is divisible by $5$ , and the three-digit number $RST$ is divisible by $3$ . What is $P$ ?", "options": ["3", "2", "1", "5"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Four students take an exam. Three of their scores are $70, 80,$ and $90$ . If the average of their four scores is $70$ , then what is the remaining score?", "options": ["70", "50", "60", "40"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "When Cheenu was a boy, he could run $15$ miles in $3$ hours and $30$ minutes. As an old man, he can now walk $10$ miles in $4$ hours. How many minutes longer does it take for him to walk a mile now compared to when he was a boy?", "options": ["6", "30", "10", "18"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "The number $N$ is a two-digit number.\n\n• When $N$ is divided by $9$ , the remainder is $1$ .\n\n• When $N$ is divided by $10$ , the remainder is $3$ .\n\nWhat is the remainder when $N$ is divided by $11$ ?", "options": ["0", "2", "7", "5"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Which of the following numbers is not a perfect square?", "options": ["2^{2017}", "3^{2018}", "4^{2019}", "1^{2016}"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Find the value of the expression\n $100-98+96-94+92-90+\\cdots+8-6+4-2.$", "options": ["100", "80", "40", "50"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "What is the sum of the distinct prime integer divisors of $2016$ ?", "options": ["16", "63", "9", "12"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Which of the following values is largest?", "options": ["2 \\times 0 +1+7", "2+0 \\times 1 + 7", "2+0+1+7", "2 \\times 0 \\times 1 \\times 7"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected randomly without replacement from the box. What is the probability that 4 is the largest value selected?", "options": ["\\frac{3}{10}", "\\frac{1}{5}", "\\frac{1}{10}", "\\frac{2}{5}"], "answer": "A", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor?", "options": ["1369", "324", "361", "148"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "The smallest positive integer greater than 1 that leaves a remainder of 1 when divided by 4, 5, and 6 lies between which of the following pairs of numbers?", "options": ["20\\text{ and }39", "80\\text{ and }124", "40\\text{ and }59", "60\\text{ and }79"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Peter, Emma, and Kyler played chess with each other. Peter won 4 games and lost 2 games. Emma won 3 games and lost 3 games. If Kyler lost 3 games, how many games did he win?", "options": ["3", "0", "1", "2"], "answer": "C", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} | |
| {"question": "Chloe and Zoe are both students in Ms. Demeanor's math class. Last night, they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to only $80\\%$ of the problems she solved alone, but overall $88\\%$ of her answers were correct. Zoe had correct answers to $90\\%$ of the problems she solved alone. What was Zoe's overall percentage of correct answers?", "options": ["93", "92", "96", "98"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Starting with some gold coins and some empty treasure chests, I tried to put 9 gold coins in each treasure chest, but that left 2 treasure chests empty. So instead I put 6 gold coins in each treasure chest, but then I had 3 gold coins left over. How many gold coins did I have?", "options": ["27", "63", "81", "45"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "For any positive integer $M$ , the notation $M!$ denotes the product of the integers $1$ through $M$ . What is the largest integer $n$ for which $5^n$ is a factor of the sum $98!+99!+100!$ ?", "options": ["26", "23", "24", "27"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "An integer between $1000$ and $9999$ , inclusive, is chosen at random. What is the probability that it is an odd integer whose digits are all distinct?", "options": ["\\frac{7}{25}", "\\frac{9}{25}", "\\frac{14}{75}", "\\frac{56}{225}"], "answer": "D", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "Suppose $a$ , $b$ , and $c$ are nonzero real numbers, and $a+b+c=0$ . What are the possible value(s) for $\\frac{a}{|a|}+\\frac{b}{|b|}+\\frac{c}{|c|}+\\frac{abc}{|abc|}$ ?", "options": ["0,2,\\text{ and }-2", "0", "0,1,\\text{ and }-1", "2\\text{ and }-2"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. Each day after the first, her speed decreased so that the number of minutes to travel one mile increased by $5$ minutes over the preceding day. Each of the four days, her distance traveled was also an integer number of miles. What was the total number of miles for the four trips?", "options": ["10", "82", "25", "50"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} | |
| {"question": "What is the value of the expression $\\sqrt{16\\sqrt{8\\sqrt{4}}}$ ?", "options": ["8", "8\\sqrt{2}", "4\\sqrt{2}", "4"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "When $0.000315$ is multiplied by $7,928,564$ the product is closest to which of the following?", "options": ["24000", "2400", "2100", "240"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "What is the value of the expression $\\frac{1 \\cdot 2 \\cdot 3 \\cdot 4 \\cdot 5 \\cdot 6 \\cdot 7 \\cdot 8}{1+2+3+4+5+6+7+8}$ ?", "options": ["3360", "1120", "1020", "2240"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "If the degree measures of the angles of a triangle are in the ratio $3:3:4$ , what is the degree measure of the largest angle of the triangle?", "options": ["72", "60", "90", "18"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} | |
| {"question": "Let $Z$ be a 6-digit positive integer, such as 247247, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of $Z$ ?", "options": ["19", "1111", "111", "11"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn't know her house number. She tells him, \"My house number has two digits, and exactly three of the following four statements about it are true.\"\n\n(1) It is prime.\n\n(2) It is even.\n\n(3) It is divisible by 7.\n\n(4) One of its digits is 9.\n\nThis information allows Malcolm to determine Isabella's house number. What is its units digit?", "options": ["4", "7", "6", "8"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "All of Marcy's marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and six of them are green. What is the smallest number of yellow marbles that Macy could have?", "options": ["3", "1", "5", "4"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "An amusement park has a collection of scale models, with a ratio of $1: 20$ , of buildings and other sights from around the country. The height of the United States Capitol is $289$ feet. What is the height in feet of its duplicate to the nearest whole number?", "options": ["14", "16", "15", "18"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "The harmonic mean of a set of non-zero numbers is the reciprocal of the average of the reciprocals of the numbers. What is the harmonic mean of 1, 2, and 4?", "options": ["\\frac{7}{3}", "\\frac{3}{7}", "\\frac{7}{12}", "\\frac{12}{7}"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "The clock in Sri's car, which is not accurate, gains time at a constant rate. One day as he begins shopping, he notes that his car clock and his watch (which is accurate) both say 12:00 noon. When he is done shopping, his watch says 12:30 and his car clock says 12:35. Later that day, Sri loses his watch. He looks at his car clock and it says 7:00. What is the actual time?\n\n $\\textbf{ (A) }5:50", "options": ["5:50", "8:10", "6:00", "6:55"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "Laila took five math tests, each worth a maximum of 100 points. Laila's score on each test was an integer between 0 and 100, inclusive. Laila received the same score on the first four tests, and she received a higher score on the last test. Her average score on the five tests was 82. How many values are possible for Laila's score on the last test?", "options": ["10", "4", "18", "5"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "Let $N$ be the greatest five-digit number whose digits have a product of $120$ . What is the sum of the digits of $N$ ?", "options": ["16", "20", "15", "18"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Professor Chang has nine different language books lined up on a bookshelf: two Arabic, three German, and four Spanish. How many ways are there to arrange the nine books on the shelf keeping the Arabic books together and keeping the Spanish books together?", "options": ["182,440", "362,880", "2880", "5760"], "answer": "D", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} | |
| {"question": "Bella begins to walk from her house toward her friend Ella's house. At the same time, Ella begins to ride her bicycle toward Bella's house. They each maintain a constant speed, and Ella rides $5$ times as fast as Bella walks. The distance between their houses is $2$ miles, which is $10,560$ feet, and Bella covers $2 \\tfrac{1}{2}$ feet with each step. How many steps will Bella take by the time she meets Ella?", "options": ["1056", "3520", "704", "1760"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "How many positive factors does $23,232$ have?", "options": ["36", "12", "9", "42"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "What is the value of the product\n\n $\\left(1+\\frac{1}{1}\\right)\\cdot\\left(1+\\frac{1}{2}\\right)\\cdot\\left(1+\\frac{1}{3}\\right)\\cdot\\left(1+\\frac{1}{4}\\right)\\cdot\\left(1+\\frac{1}{5}\\right)\\cdot\\left(1+\\frac{1}{6}\\right)?$", "options": ["\\frac{7}{6}", "\\frac{7}{2}", "7", "\\frac{4}{3}"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "How many positive three-digit integers have a remainder of 2 when divided by 6, a remainder of 5 when divided by 9, and a remainder of 7 when divided by 11?", "options": ["1", "4", "2", "5"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "How many perfect cubes lie between $2^8+1$ and $2^{18}+1$ , inclusive?", "options": ["4", "57", "9", "58"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in a circle. They start counting: Arn first, then Bob, and so forth. When the number contains a 7 as a digit (such as 47) or is a multiple of 7 that person leaves the circle and the counting continues. Who is the last one present in the circle?", "options": ["\\text{Dan}", "\\text{Eve}", "\\text{Cyd}", " \\text{Arn}"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "What is the value of $1+3+5+\\cdots+2017+2019-2-4-6-\\cdots-2016-2018$ ?", "options": ["1008", "-1010", "1010", "-1009"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "On a trip to the beach, Anh traveled 50 miles on the highway and 10 miles on a coastal access road. He drove three times as fast on the highway as on the coastal road. If Anh spent 30 minutes driving on the coastal road, how many minutes did his entire trip take?", "options": ["90", "80", "70", "50"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "The $5$ -digit number $\\underline{2}$ $\\underline{0}$ $\\underline{1}$ $\\underline{8}$ $\\underline{U}$ is divisible by $9$ . What is the remainder when this number is divided by $8$ ?", "options": ["5", "3", "6", "1"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Tyler is tiling the floor of his 12-foot by 16-foot living room. He plans to place one-foot by one-foot square tiles to form a border along the edges of the room and to fill in the rest of the floor with two-foot by two-foot square tiles. How many tiles will he use?", "options": ["120", "87", "48", "89"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "Ike and Mike go into a sandwich shop with a total of $\\$30.00$ to spend. Sandwiches cost $\\$4.50$ each and soft drinks cost $\\$1.00$ each. Ike and Mike plan to buy as many sandwiches as they can,\nand use any remaining money to buy soft drinks. Counting both sandwiches and soft drinks, how\nmany items will they buy?", "options": ["7", "10", "9", "6"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "The faces of a cube are painted in six different colors: red $(R)$ , white $(W)$ , green $(G)$ , brown $(B)$ , aqua $(A)$ , and purple $(P)$ . Three views of the cube are shown below. What is the color of the face opposite the aqua face?\n\n $", "options": ["\\text{red}", "\\text{green}", "\\text{purple}", "\\text{white}"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "A palindrome is a number that has the same value when read from left to right or from right to left. (For example, 12321 is a palindrome.) Let $N$ be the least three-digit integer which is not a palindrome but which is the sum of three distinct two-digit palindromes. What is the sum of the digits of $N$ ?", "options": ["6", "2", "3", "4"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Isabella has $6$ coupons that can be redeemed for free ice cream cones at Pete's Sweet Treats. In order to make the coupons last, she decides that she will redeem one every $10$ days until she has used them all. She knows that Pete's is closed on Sundays, but as she circles the $6$ dates on her calendar, she realizes that no circled date falls on a Sunday. On what day of the week does Isabella redeem her first coupon?", "options": ["\\text{Monday}", "\\text{Thursday}", "\\text{Wednesday}", "\\text{Friday}"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "On a beach $50$ people are wearing sunglasses and $35$ people are wearing caps. Some people are wearing both sunglasses and caps. If one of the people wearing a cap is selected at random, the probability that this person is also wearing sunglasses is $\\frac{2}{5}$ . If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap?", "options": ["\\frac{4}{7}", "\\frac{7}{25}", "\\frac{7}{10}", "\\frac{2}{5}"], "answer": "B", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "Qiang drives $15$ miles at an average speed of $30$ miles per hour. How many additional miles will he have to drive at $55$ miles per hour to average $50$ miles per hour for the entire trip?", "options": ["45", "90", "110", "135"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "What is the value of the product \n\n $\\left(\\frac{1\\cdot3}{2\\cdot2}\\right)\\left(\\frac{2\\cdot4}{3\\cdot3}\\right)\\left(\\frac{3\\cdot5}{4\\cdot4}\\right)\\cdots\\left(\\frac{97\\cdot99}{98\\cdot98}\\right)\\left(\\frac{98\\cdot100}{99\\cdot99}\\right)?$", "options": ["\\frac{100}{99}", "\\frac{1}{2}", "\\frac{9800}{9801}", "\\frac{50}{99}"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "The faces of each of two fair dice are numbered $1$ , $2$ , $3$ , $5$ , $7$ , and $8$ . When the two dice are tossed, what is the probability that their sum will be an even number?", "options": ["\\frac{2}{3}", "\\frac{3}{5}", "\\frac{5}{9}", "\\frac{1}{2}"], "answer": "C", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "In a tournament there are six teams that play each other twice. A team earns $3$ points for a win, $1$ point for a draw, and $0$ points for a loss. After all the games have been played it turns out that the top three teams earned the same number of total points. What is the greatest possible number of total points for each of the top three teams?", "options": ["30", "26", "24", "23"], "answer": "C", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "How many different real numbers $x$ satisfy the equation $(x^{2}-5)^{2}=16?$", "options": ["0", "4", "1", "8"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} | |
| {"question": "What is the area of the triangle formed by the lines $y=5$ , $y=1+x$ , and $y=1-x$ ?", "options": ["8", "16", "12", "4"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "A store increased the original price of a shirt by a certain percent and then lowered the new price by the same amount. Given that the resulting price was $84\\%$ of the original price, by what percent was the price increased and decreased $?$", "options": ["36", "40", "28", "16"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "After Euclid High School's last basketball game, it was determined that $\\frac{1}{4}$ of the team's points were scored by Alexa and $\\frac{2}{7}$ were scored by Brittany. Chelsea scored $15$ points. None of the other $7$ team members scored more than $2$ points. What was the total number of points scored by the other $7$ team members?", "options": ["12", "11", "14", "10"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "Alice has $24$ apples. In how many ways can she share them with Becky and Chris so that each of the three people has at least two apples?", "options": ["105", "380", "114", "190"], "answer": "D", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} | |
| {"question": "Which of the following is the correct order of the fractions $\\frac{15}{11},\\frac{19}{15},$ and $\\frac{17}{13},$ from least to greatest?", "options": ["\\frac{15}{11}< \\frac{19}{15}<\\frac{17}{13} ", "\\frac{15}{11}< \\frac{17}{13}< \\frac{19}{15} ", " \\frac{19}{15}<\\frac{17}{13}<\\frac{15}{11}", "\\frac{17}{13}<\\frac{19}{15}<\\frac{15}{11} "], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "Shauna takes five tests, each worth a maximum of $100$ points. Her scores on the first three tests are $76$ , $94$ , and $87$ . In order to average $81$ for all five tests, what is the lowest score she could earn on one of the other two tests?", "options": ["66", "52", "48", "74"], "answer": "C", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "Gilda has a bag of marbles. She gives $20\\%$ of them to her friend Pedro. Then Gilda gives $10\\%$ of what is left to another friend, Ebony. Finally, Gilda gives $25\\%$ of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself?", "options": ["54", "38", "33\\frac{1}{3}", "20"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are $6$ cm in diameter and $12$ cm high. Felicia buys cat food in cylindrical cans that are $12$ cm in diameter and $6$ cm high. What is the ratio of the volume of one of Alex's cans to the volume of one of Felicia's cans?", "options": ["4:1", "1:2", "1:4", "2:1"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "Luka is making lemonade to sell at a school fundraiser. His recipe requires $4$ times as much water as sugar and twice as much sugar as lemon juice. He uses $3$ cups of lemon juice. How many cups of water does he need?", "options": ["18 ", "12 ", "6 ", "24"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "Zara has a collection of $4$ marbles: an Aggie, a Bumblebee, a Steelie, and a Tiger. She wants to display them in a row on a shelf, but does not want to put the Steelie and the Tiger next to one another. In how many ways can she do this?", "options": ["6 ", "12 ", "24", "18 "], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "For a positive integer $n$ , the factorial notation $n!$ represents the product of the integers from $n$ to $1$ . What value of $N$ satisfies the following equation? $5!\\cdot 9!=12\\cdot N!$", "options": ["11", "10", "13", "12"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Jamal has a drawer containing $6$ green socks, $18$ purple socks, and $12$ orange socks. After adding more purple socks, Jamal noticed that there is now a $60\\%$ chance that a sock randomly selected from the drawer is purple. How many purple socks did Jamal add?", "options": ["9 ", "12 ", "6 ", "18 "], "answer": "A", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "Suppose $15\\%$ of $x$ equals $20\\%$ of $y.$ What percentage of $x$ is $y?$", "options": ["75 ", "5 ", "35 ", "300"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "How many positive integer factors of $2020$ have more than $3$ factors? (As an example, $12$ has $6$ factors, namely $1,2,3,4,6,$ and $12.$ )", "options": ["9 ", "7 ", "10", "8 "], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "A number is called flippy if its digits alternate between two distinct digits. For example, $2020$ and $37373$ are flippy, but $3883$ and $123123$ are not. How many five-digit flippy numbers are divisible by $15?$", "options": ["5 ", "8", "3 ", "4 "], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Four friends do yardwork for their neighbors over the weekend, earning $\\$15, \\$20, \\$25,$ and $\\$40,$ respectively. They decide to split their earnings equally among themselves. In total how much will the friend who earned $\\$40$ give to the others?", "options": ["25", "20 ", "15 ", "10 "], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "A scientist walking through a forest recorded as integers the heights of $5$ trees standing in a row. She observed that each tree was either twice as tall or half as tall as the one to its right. Unfortunately some of her data was lost when rain fell on her notebook. Her notes are shown below, with blanks indicating the missing numbers. Based on her observations, the scientist was able to reconstruct the lost data. What was the average height of the trees, in meters?\n\n $\\begingroup \\setlength{\\tabcolsep}{10pt} \\renewcommand{\\arraystretch}{1.5} \\begin{array}{|c|c|} \\hline Tree 1 & \\rule{0.4cm}{0.15mm} meters \\\\ Tree 2 & 11 meters \\\\ Tree 3 & \\rule{0.5cm}{0.15mm} meters \\\\ Tree 4 & \\rule{0.5cm}{0.15mm} meters \\\\ Tree 5 & \\rule{0.5cm}{0.15mm} meters \\\\ \\hline Average height & \\rule{0.5cm}{0.15mm}\\text{ .}2 meters \\\\ \\hline \\end{array} \\endgroup$", "options": ["22.2 ", "24.2 ", "37.2", "35.2 "], "answer": "B", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "Five different awards are to be given to three students. Each student will receive at least one award. In how many different ways can the awards be distributed?", "options": ["240", "150 ", "180 ", "120 "], "answer": "B", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "Carrie has a rectangular garden that measures $6$ feet by $8$ feet. She plants the entire garden with strawberry plants. Carrie is able to plant $4$ strawberry plants per square foot, and she harvests an average of $10$ strawberries per plant. How many strawberries can she expect to harvest?", "options": ["3840", "1120 ", "1920 ", "960 "], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "Three fourths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of $5$ cups. What percent of the total capacity of the pitcher did each cup receive?", "options": ["5 ", "10 ", "15 ", "20 "], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Aaron, Darren, Karen, Maren, and Sharon rode on a small train that has five cars that seat one person each. Maren sat in the last car. Aaron sat directly behind Sharon. Darren sat in one of the cars in front of Aaron. At least one person sat between Karen and Darren. Who sat in the middle car?", "options": ["\\text{Darren} ", "\\text{Aaron} ", "\\text{Maren}", "\\text{Karen} "], "answer": "B", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "How many integers between $2020$ and $2400$ have four distinct digits arranged in increasing order? (For example, $2347$ is one integer.)", "options": ["\\text{28}", "\\text{21}", "\\text{15} ", "\\text{9} "], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Ricardo has $2020$ coins, some of which are pennies ( $1$ -cent coins) and the rest of which are nickels ( $5$ -cent coins). He has at least one penny and at least one nickel. What is the difference in cents between the greatest possible and least amounts of money that Ricardo can have?", "options": ["\\text{8072} ", "\\text{806} ", "\\text{8068} ", "\\text{8076}"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Basic Concepts of Inequalities"} | |
| {"question": "Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating $3$ inches of pasta from the middle of one piece. In the end, he has $10$ pieces of pasta whose total length is $17$ inches. How long, in inches, was the piece of pasta he started with?", "options": [" 41", " 38", " 34", " 44"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "How many positive integers can fill the blank in the sentence below?\n\n“One positive integer is _____ more than twice another, and the sum of the two numbers is $28$ .”", "options": [" 7 ", " 9 ", " 10", " 6 "], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} | |
| {"question": "In how many ways can the letters in $\\textbf{BEEKEEPER}$ be rearranged so that two or more $\\textbf{E}$ s do not appear together?", "options": [" 12 ", " 24 ", " 4 ", " 120"], "answer": "B", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "Four numbers are written in a row. The average of the first two is $21,$ the average of the middle two is $26,$ and the average of the last two is $30.$ What is the average of the first and last of the numbers?", "options": [" 28", " 24 ", " 26 ", " 25 "], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "If $n$ is an even positive integer, the $\\emph{double factorial}$ notation $n!!$ represents the product of all the even integers from $2$ to $n$ . For example, $8!! = 2 \\cdot 4 \\cdot 6 \\cdot 8$ . What is the units digit of the following sum? $2!! + 4!! + 6!! + \\cdots + 2018!! + 2020!! + 2022!!$", "options": [" 4", " 2", " 6", " 8"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "The midpoints of the four sides of a rectangle are $(-3,0), (2,0), (5,4),$ and $(0,4).$ What is the\narea of the rectangle?", "options": [" 20 ", " 80", " 40 ", " 25 "], "answer": "C", "topic": "Middle--Basic Geometry--Quadrilaterals"} | |
| {"question": "Consider these two operations:\n\n$$\n\\begin{align*} a \\, \\blacklozenge \\, b &= a^2 - b^2\\\\ a \\, \\bigstar \\, b &= (a - b)^2 \\end{align*}\n$$\n\nWhat is the output of $(5 \\, \\blacklozenge \\, 3) \\, \\bigstar \\, 6?$", "options": [" 4 ", " 100 ", " 16 ", " {-}20 "], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "When three positive integers $a$ , $b$ , and $c$ are multiplied together, their product is $100$ . Suppose $a < b < c$ . In how many ways can the numbers be chosen?", "options": [" 2", " 0 ", " 3", " 4"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned $6$ years old, she received a newborn kitten as a birthday present. Today the sum of the ages of the two children and the kitten is $30$ years. How many years older than Bella is Anna?", "options": [" 2 ", " 3 ", " 1 ", " 4 "], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "Three positive integers are equally spaced on a number line. The middle number is $15,$ and the largest number is $4$ times the smallest number. What is the smallest of these three numbers?", "options": [" 4 ", " 7 ", " 5 ", " 6 "], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "When the World Wide Web first became popular in the $1990$ s, download speeds reached a maximum of about $56$ kilobits per second. Approximately how many minutes would the download of a $4.2$ -megabyte song have taken at that speed? (Note that there are $8000$ kilobits in a megabyte.)", "options": [" 36000", " 10 ", " 1800 ", " 7200 "], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "What is the value of $\\frac{1}{3}\\cdot\\frac{2}{4}\\cdot\\frac{3}{5}\\cdots\\frac{18}{20}\\cdot\\frac{19}{21}\\cdot\\frac{20}{22}?$", "options": [" \\frac{1}{132} ", " \\frac{2}{213} ", " \\frac{1}{462} ", " \\frac{1}{231} "], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "A cup of boiling water ( $212^{\\circ}\\text{F}$ ) is placed to cool in a room whose temperature remains constant at $68^{\\circ}\\text{F}$ . Suppose the difference between the water temperature and the room temperature is halved every $5$ minutes. What is the water temperature, in degrees Fahrenheit, after $15$ minutes?", "options": [" 77 ", " 86 ", " 92 ", " 98 "], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} | |
| {"question": "What is the value of $(8 \\times 4 + 2) - (8 + 4 \\times 2)$ ?\n\n $", "options": [" 10 ", "0 ", " 18 ", " 6 "], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Harold made a plum pie to take on a picnic. He was able to eat only $\\frac{1}{4}$ of the pie, and he left the rest for his friends. A moose came by and ate $\\frac{1}{3}$ of what Harold left behind. After that, a porcupine ate $\\frac{1}{3}$ of what the moose left behind. How much of the original pie still remained after the porcupine left?\n\n $", "options": [" \\frac{1}{6} ", " \\frac{1}{4} ", " \\frac{1}{3} ", "\\frac{1}{12} "], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "NASA’s Perseverance Rover was launched on July $30,$ $2020.$ After traveling $292{,}526{,}838$ miles, it landed on Mars in Jezero Crater about $6.5$ months later. Which of the following is closest to the Rover’s average interplanetary speed in miles per hour?\n\n $", "options": [" 120{,}000 ", " 600{,}000", " 12{,}000 ", " 60{,}000 "], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} | |
| {"question": "Nicolas is planning to send a package to his friend Anton, who is a stamp collector. To pay for the postage, Nicolas would like to cover the package with a large number of stamps. Suppose he has a collection of $5$ -cent, $10$ -cent, and $25$ -cent stamps, with exactly $20$ of each type. What is the greatest number of stamps Nicolas can use to make exactly $\\$7.10$ in postage?\n(Note: The amount $\\$7.10$ corresponds to $7$ dollars and $10$ cents. One dollar is worth $100$ cents.)\n\n $", "options": [" 55", " 54", " 51 ", "45 "], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Greta Grasshopper sits on a long line of lily pads in a pond. From any lily pad, Greta can jump 5 pads to the right or 3 pads to the left. What is the fewest number of jumps Greta must make to reach the lilly pad located 2023 pads to the right of her starting position?", "options": [" 411 ", " 409 ", " 413", " 407 "], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "Two integers are inserted into the list $3, 3, 8, 11, 28$ to double its range. The mode and median remain unchanged. What is the maximum possible sum of the two additional numbers?", "options": [" 58 ", " 61", " 60 ", " 56 "], "answer": "C", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "Alina writes the numbers $1, 2, \\dots , 9$ on separate cards, one number per card. She wishes to divide the cards into $3$ groups of $3$ cards so that the sum of the numbers in each group will be the same. In how many ways can this be done?", "options": [" 4", " 2 ", " 0 ", " 1 "], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term is $4000$ . What is the first term?\n\n $", "options": [" 10", " 5 ", "1 ", " 4 "], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "Fifteen integers $a_1, a_2, a_3, \\dots, a_{15}$ are arranged in order on a number line. The integers are equally spaced and have the property that\n $1 \\le a_1 \\le 10, \\thickspace 13 \\le a_2 \\le 20, \\thickspace \\text{ and } \\thickspace 241 \\le a_{15}\\le 250.$ \nWhat is the sum of digits of $a_{14}?$ \n\n $", "options": [" 10 ", "8 ", " 9 ", " 12"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "Wind chill is a measure of how cold people feel when exposed to wind outside. A good estimate for wind chill can be found using this calculation\n $(\\text{wind chill}) = (\\text{air temperature}) - 0.7 \\times (\\text{wind speed}),$ \nwhere temperature is measured in degrees Fahrenheit $(^{\\circ}\\text{F})$ and the wind speed is measured in miles per hour (mph). Suppose the air temperature is $36^{\\circ}\\text{F}$ and the wind speed is $18$ mph. Which of the following is closest to the approximate wind chill?\n\n $", "options": ["18 ", " 32 ", " 28 ", " 23 "], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "A lake contains $250$ trout, along with a variety of other fish. When a marine biologist catches and releases a sample of $180$ fish from the lake, $30$ are identified as trout. Assume that the ratio of trout to the total number of fish is the same in both the sample and the lake. How many fish are there in the lake?\n\n $", "options": [" 2000", " 1750 ", "1250 ", " 1500 "], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Lola, Lolo, Tiya, and Tiyo participated in a ping pong tournament. Each player competed against each of the other three players exactly twice. Shown below are the win-loss records for the players. The numbers $1$ and $0$ represent a win or loss, respectively. For example, Lola won five matches and lost the fourth match. What was Tiyo’s win-loss record?\n\n $\\begin{array}{c | c} Player & Result \\\\ \\hline Lola & \\texttt{111011}\\\\ Lolo & \\texttt{101010}\\\\ Tiya & \\texttt{010100}\\\\ Tiyo & \\texttt{??????} \\end{array}$ \n $", "options": [" \\texttt{001001} ", " \\texttt{010000} ", "\\texttt{000101} ", " \\texttt{011000}"], "answer": "C", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |