competition_source_list listlengths 0 1 | difficulty stringclasses 3
values | problem stringlengths 115 1.42k | solution stringlengths 7 165 |
|---|---|---|---|
[
"其它"
] | 3 | How many whole numbers between $$1$$ and $$1000$$ do not contain the digit $$1$$? ($2009$ AMC $8$ Problems, Question \#$22$)
Options:
(A) $$512$$
(B) $$648$$
(C) $$720$$
(D) $$728$$
(E) $$800$$
Please choose an option from A-E to answer. | (D) $$728$$ |
[] | 2 | In Carl\textquotesingle s pencil case there are nine pencils. At least one of the pencils is blue. In any group of four pencils, at least two have the same colour. In any group of five pencils, at most three have the same colour. How many pencils are blue?
Options:
(A) $$1$$
(B) $$2$$
(C) $$3$$
(D) $$4$$
(E) More info... | (C) $$3$$ |
[] | 2 | There are some pieces of candy on a table. You are challenged by your friend to play the following game: The two players take turns taking some candy. Every turn, you can take away either $$1$$, $$2$$, $$3$$, $$4$$ or $$5$$ pieces from the table. The person who takes away the final piece of candy from the table wins. I... | (C) $$18$$ |
[] | 2 | Between them, the two four-digit integers $$M$$ and $$N$$ contain all ten digits from $$1$$ to $$8$$. What is the least possible difference between $$M$$ and $$N$$?
Options:
(A) $$123$$
(B) $$247$$
(C) $$427$$
(D) $$472$$
(E) $$742$$
Please choose an option from A-E to answer. | (B) $$247$$ |
[] | 2 | A chess singles tournament had $10$ players. Each player played with every other player only once. $2$ points are earned for winning a game, $0$ points are earned for losing a game, and $1$ point is earned by each player in a tie. After the tournament, the judge finds that the sum of these $10$ players\textquotesingle{... | (E) $$90$$ |
[] | 2 | 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:
(A) all $4$ are boys
(B) all $4$ are girls
(C) $2$ are girls and $2$ are boys
(D) $3$ are of one gender and $1$ is of the other gender
(E) all of these... | (D) $3$ are of one gender and $1$ is of the other gender |
[
"其它"
] | 2 | How many positive integers from $1$ to $100$ do not have $2,3$ or $5$ as its factors?
Options:
(A) $$23$$
(B) $$25$$
(C) $$26$$
(D) $$28$$
(E) $$30$$
Please choose an option from A-E to answer. | (C) $$26$$ |
[] | 2 | Molly, Dolly, Sally, Elly and Kelly are sitting on a park bench. Molly is not sitting on the far right and Dolly is not sitting on the far left. Sally is not sitting at either end. Kelly is not sitting next to Sally and Sally is not sitting next to Dolly. Elly is sitting to the right of Dolly but not necessarily next t... | (E) Elly |
[] | 2 | If $$a⊕b= \frac{1}{ \dfrac{1}{a}+ \dfrac{1}{b}}$$, then what is the value of $$ (1\times2)⊕(2\times3)⊕(3 \times4)⊕\ldots⊕(2013\times2014)$$?
Options:
(A) $$\frac {2013}{2014}$$
(B) $$\frac{2014}{2013}$$
(C) $$\frac{2014}{2015}$$
(D) $$\frac{2015}{2014}$$
(E) None of the above
Please choose an option from A-E to answe... | (B) $$\frac{2014}{2013}$$ |
[
"其它"
] | 2 | Josip has 4 toys - a car, a doll, a ball and a ship. He wants to put them on a line on a shelf. The ship has to be next to the car and the doll has to be next to the car. In how many ways can he arrange them so all the conditions would be fulfilled?
Options:
(A) $$2$$
(B) $$4$$
(C) $$5$$
(D) $$6$$
(E) $$8$$
Please ch... | (B) $$4$$ |
[] | 3 | A box contains $5$ red balls and $3$ white balls that are identical in all aspects except color. One ball is drawn at random from the box and then replaced. The box is then thoroughly shaken so that the balls are arranged at random again and a second ball is drawn randomly from the box. What is the probability of drawi... | (D) $$\frac{9}{64}$$ |
[
"其它"
] | 2 | 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? (2019 AMC 8 Problems, Question \#18)
Options:
(A) $\dfrac{4}{9}$
(B) $\dfrac{1}{2}$
(C) $\dfrac{5}{9}$
(D) $\dfrac{3}{5}$
(E) $\dfrac{2}{3}$
Pl... | (C) $\dfrac{5}{9}$ |
[
"其它"
] | 2 | Five balls are arranged around a circle. Chris chooses two adjacent balls at random and interchanges them. Then Silva does the same, with her choice of adjacent balls to interchange being independent of Chris\textquotesingle s. What is the expected number of balls that occupy their original positions after these two su... | (D) $$2.2$$ |
[
"其它"
] | 2 | Rabbit Borya likes cabbages and carrots very much. In a day he eats either 9 carrots, or 2 cabbages, or 1 cabbage and 4 carrots. During one week Borya has eaten 30 carrots. How mnay cabbages has he eaten during this week?
Options:
(A) $$6$$
(B) $$7$$
(C) $$8$$
(D) $$9$$
(E) $$10$$
Please choose an option from A-E to ... | (B) $$7$$ |
[] | 2 | What is the average (mean) of all $$5-$$digit numbers that can be formed by using each of the digits $$1$$, $$3$$, $$5$$, $$7$$, and $$8$$ exactly once? ($$2005$$ AMC $$10B$$ Problem, Question \#$$20$$)
Options:
(A) $$48000$$
(B) $$49999.5$$
(C) $$53332.8$$
(D) $$55555$$
(E) $$56432.8$$
Please choose an option from A... | (C) $$53332.8$$ |
[
"其它"
] | 2 | Timi has $8$ paintings: $3$ of them are drawing landscape, and $5$ of them are drawing figure. Among the $5$ figure paintings, there are $3$ drawing the whole family of Timi, and the other $2$ are drawing himself. Now, Timi wants to put those painting in a line. The $3$ landscape paintings cannot be adjacent. How many ... | (C) $$144$$ |
[] | 2 | A singles tournament had six players. Each player played every other player only once, with no ties. If Helen won $$4$$ games, Ines won $$3$$ games, Janet won $$2$$ games, Kendra won $$2$$ games and Lara won $2$ games, how many games did Monica (the sixth player) win? ($$2006 \text{ AMC } 8$$ Problem, Question \#$$20$$... | (C) $$2$$ |
[
"其它"
] | 2 | Frieda the frog begins a sequence of hops on a $3 \times 3$ grid of squares, moving one square on each hop and choosing at random the direction of each hop-up, down, left, or right. She does not hop diagonally. When the direction of a hop would take Frieda off the grid, she "wraps around" and jumps to the opposite edge... | (D) $\frac{25}{32}$ |
[
"其它"
] | 2 | Hansel wants to buy 2 dice of different colours. If the available colours in a store are red, blue, green, yellow, pink and white, how many different combinations of 2 dice are there in the store? (Example: 1 combination is yellow and white)
Options:
(A) $$5$$
(B) $$10$$
(C) $$15$$
(D) $$20$$
(E) None of the above
Pl... | (C) $$15$$ |
[
"其它"
] | 2 | There is a cuboid with a dimension of $3\times4\times5$. Now paint all the surfaces red and cut it into many $1\times1\times1$ cubes. How many cubes that have two faces painted red are there?
Options:
(A) $$24$$
(B) $$6$$
(C) $$8$$
(D) $$11$$
(E) $$22$$
Please choose an option from A-E to answer. | (A) $$24$$ |
[
"其它"
] | 2 | SASMO 2015 P2 Q7 Study the figures made with matchsticks below. How many matchsticks are needed to make figure 5?
Options:
(A) $$30$$
(B) $$33$$
(C) $$39$$
(D) $$45$$
(E) $$51$$
Please choose an option from A-E to answer. | (D) $$45$$ |
[] | 2 | The product of three consecutive numbers is $$15600$$. What is their sum?
Options:
(A) $$75$$
(B) $$78$$
(C) $$81$$
(D) $$84$$
(E) $$87$$
Please choose an option from A-E to answer. | (A) $$75$$ |
[
"其它"
] | 2 | A school has 100 students and 5 teachers. In the first period, each student is taking one class, and each teacher is teaching one class. The enrollments in the classes are $50,20,20,5$, and 5 . Let $l$ be the average value obtained if a teacher is picked at random and the number of students in their class is noted. Let... | (B) $$-13.5$$ |
[
"其它"
] | 2 | 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? (2019 AMC 8 Problems, Question \#18)
Options:
(A) $\dfrac{4}{9}$
(B) $\dfrac{1}{2}$
(C) $\dfrac{5}{9}$
(D) $\dfrac{3}{5}$
(E) $\dfrac{2}{3}$
Pl... | (C) $\dfrac{5}{9}$ |
[] | 3 | Moon and Archie played chess competitively. Both of them had same levels of skill. They agreed to play seven games, and the one that win four games first would be the ultimate winner. Now, they have already played three games, and Moon won two games while Archie won one game. What is the probability that Mon be the ult... | (B) $$\frac{11}{16}$$ |
[
"其它"
] | 2 | In how many ways can the letters in $CPCCKBY$ be rearranged so that $C$ cannot be put in both ends and two or more $C$s do not appear together?
Options:
(A) $$24$$
(B) $$18$$
(C) $$64$$
(D) $$9$$
(E) $$14$$
Please choose an option from A-E to answer. | (A) $$24$$ |
[] | 2 | A drawer contains ten identical yellow socks, eight identical blue socks and one hundred identical pink socks. Amrita picks socks from the drawer without looking. What is the smallest number of socks she must pick to be sure that she has at least two pairs of matching socks?
Options:
(A) $$5$$
(B) $$6$$
(C) $$8$$
(D)... | (B) $$6$$ |
[
"其它"
] | 2 | Let $(a, b, c, d)$ be integers where they are not necessarily different. If each one of them is in the set ($0$, $1$, $2$, $3$), what is the probability that $a \cdot d-b \cdot c$ is odd? (For example, ($0$, $3$, $1$, $1$) meet the condition, because $0 \cdot 1-3 \cdot 1=-3$ is odd.)
Options:
(A) $\frac3{16}$
(B) $\fr... | (C) $\frac38$ |
[
"其它"
] | 2 | A positive integer divisor of $12 !$ is chosen at random. The probability that the divisor chosen is a perfect square can be expressed as $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. What is $m+n$?
Options:
(A) $$3$$
(B) $$5$$
(C) $$12$$
(D) $$18$$
(E) $$23$$
Please choose an option from A... | (E) $$23$$ |
[] | 2 | There are some pieces of candy on a table.You are challenged by your friend to play the following game: you both have to altemate moves, and in each move, you can take away either $$1$$, $$2$$, $$3$$,~ $$4$$ or $$5$$ pieces from the table. The person who takes away the final piece from the table wins. If you go second... | (C) $$18$$ |
[] | 2 | The faces of two identical 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:
(A) $\dfrac{4}{9}$
(B) $\dfrac{1}{2}$
(C) $\dfrac{5}{9}$
(D) $\dfrac{3}{5}$
(E) $\dfrac{2}{3}$
Please choose an option from A-E to a... | (C) $\dfrac{5}{9}$ |
[] | 2 | There are many red balls, yellow balls, and blue balls of identical shape in a bag. Many students are playing a game in which each of them can take $$2$$ balls from the bag without observing the color of the balls. (After each student takes the balls, they should put them back in the bag.) The teacher finds that no mat... | (C) $$7$$ |
[
"其它"
] | 2 | Let $(a, b, c, d)$ be an ordered quadruple of not necessarily distinct integers, each one of them is in the set ($0$, $1$, $2$, $3$). What is the probability that $a \cdot d-b \cdot c$ is odd? (For example, ($0$, $3$, $1$, $1$) meet the condition, because $0 \cdot 1-3 \cdot 1=-3$ is odd.) (Adapted from 2020 AMC 10A Pro... | (C) $\frac38$ |
[
"其它"
] | 3 | Professor Chang has nine language books lined up on a bookshelf: two different Arabic books, three different German books, and four different Spanish books. How many ways are there to arrange the nine books on the shelf keeping the Arabic books together and keeping the Spanish books together? ($2018$ AMC $8$ Problem, Q... | (C) $$5760$$ |
[] | 2 | There are $$12$$ gold coins with exactly the same appearance, including $$11$$ real coins and $$1$$ fake coin. The weight of the fake coin is different from that of the real coin, and whether the fake coin is lighter or heavier than the real coin is unknown. How many times at least do you need to weigh the coins using ... | (C) $$3$$ |
[
"其它"
] | 2 | In how many ways can the letters in $CPCCKBY$ be rearranged so that two or more $C$s do not appear together?
Options:
(A) $$240$$
(B) $$180$$
(C) $$64$$
(D) $$96$$
(E) $$140$$
Please choose an option from A-E to answer. | (A) $$240$$ |
[
"其它"
] | 2 | In how many ways can the letters in $AAABCDA$ be rearranged so that two or more $A$s do not appear together?
Options:
(A) $$4$$
(B) $$6$$
(C) $$8$$
(D) $$12$$
(E) $$18$$
Please choose an option from A-E to answer. | (B) $$6$$ |
[
"其它"
] | 2 | Two distinct numbers from $$1$$ to $$100$$ inclusive will form a pair if the sum of these two is a multiple of $$5$$. How many different pairs are there?
Options:
(A) $$50$$
(B) $$150$$
(C) $$800$$
(D) $$990$$
(E) $$1200$$
Please choose an option from A-E to answer. | (D) $$990$$ |
[
"其它"
] | 2 | In how many ways can the digits in $3433256337$ be rearranged so that two or more $3$s do not appear together?
Options:
(A) $$1800$$
(B) $$1200$$
(C) $$1000$$
(D) $$720$$
(E) $$120$$
Please choose an option from A-E to answer. | (D) $$720$$ |
[] | 2 | Eight cards are numbered from $$1$$ to $$8$$. The cards are placed in two boxes $$P$$ and $$Q$$ so that the sum of the numbers on the three cards in box $$P$$ is equal to the sum of the numbers on the five cards in box $$Q$$. Which of the following statements must be true?
Options:
(A) The card numbered $$1$$ is not i... | (D) The card numbered $$2$$ is in box $$Q$$ |
[] | 2 | A palindromic number is a number that reads the same when the order of its digits is reversed. What is the difference between the largest and smallest five-digit palindromic numbers that are both multiples of $$45$$?
Options:
(A) $$9180$$
(B) $$9090$$
(C) $$9000$$
(D) $$8910$$
(E) $$8190$$
Please choose an option fro... | (B) $$9090$$ |
[] | 3 | A box contains $5$ red balls and $3$ white balls that are identical in all aspects except color. One ball is drawn at random from the box and then replaced. The box is then thoroughly shaken so that the balls are arranged at random again and a second ball is drawn randomly from the box. What is the probability of drawi... | (D) $$\frac{9}{64}$$ |
[
"其它"
] | 2 | How many $$4$$-digit numbers greater than $$1000$$ are there that use the four digits of $$2012$$? ($$2012$$ AMC $$8$$ Problems, Question \#$10$)
Options:
(A) $$6$$
(B) $$7$$
(C) $$8$$
(D) $$9$$
(E) $$12$$
Please choose an option from A-E to answer. | (D) $$9$$ |
[
"其它"
] | 2 | In how many ways can the letters in $CPCCKBY$ be rearranged so that two or more $C$s are not adjacent to each other?
Options:
(A) $$240$$
(B) $$180$$
(C) $$64$$
(D) $$96$$
(E) $$140$$
Please choose an option from A-E to answer. | (A) $$240$$ |
[] | 2 | The room numbers of a hotel are all three-digit numbers. The first digit represents the floor and the last two digits represent the room number. The hotel has rooms on five floors, numbered $$1$$ to $$5$$. It has $$35$$ rooms on each floor, numbered $$n01$$ to $$n35$$ where $$n$$ is the number of the floor. In numberin... | (E) $$105$$ |
[
"其它"
] | 2 | 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? (20... | (B) $\dfrac{1}{6}$ |
[] | 2 | How many different cubes are there with three faces coloured red and three faces coloured blue?
Options:
(A) $$1$$
(B) $$2$$
(C) $$3$$
(D) $$4$$
(E) $$5$$
Please choose an option from A-E to answer. | (B) $$2$$ |
[] | 2 | Molly, Dolly, Sally, Elly and Kelly are sitting on a park bench. Molly is not sitting on the far right and Dolly is not sitting on the far left. Sally is not sitting at either end. Kelly is not sitting next to Sally and Sally is not sitting next to Dolly. Elly is sitting to the right of Dolly but not necessarily next t... | (E) Elly |
[
"其它"
] | 3 | 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? ($2018$ AMC $8$ Problem, Question \#$16$)
Options:
(A) $$1440$$... | (C) $$5760$$ |
[
"其它"
] | 2 | A school has $100$ students and $5$ teachers. In the first period, each student is taking one class, and each teacher is teaching one class. The enrollments in the classes are $50,20,20,5$, and $5$. Let $l$ be the average value obtained if a teacher is picked at random and the number of students in their class is noted... | (B) $$-13.5$$ |
[
"其它"
] | 2 | How many different $3-$digit numbers are there with the sum of digits as $15$ ?
Options:
(A) $$69$$
(B) $$78$$
(C) $$60$$
(D) $$51$$
(E) $$49$$
Please choose an option from A-E to answer. | (A) $$69$$ |
[] | 2 | Gregor, the mathematician, forms two numbers with the digits $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, and $$5$$. Both numbers have three digits, and each digit is used only once. He adds these two numbers. What is the greatest sum Gregor can get? (adapted from 2012 Math Kangaroo Problem, Level 3 - 4, Question \#19)
Options:... | (C) $$951$$ |
[
"其它"
] | 2 | In how many ways can the digits in $3433256337$ be rearranged so that two or more $3$s are not adjacent to each other?
Options:
(A) $$1800$$
(B) $$1200$$
(C) $$1000$$
(D) $$720$$
(E) $$120$$
Please choose an option from A-E to answer. | (D) $$720$$ |
[
"其它"
] | 2 | In a regular hexagonal prism, how many pairs of parallel edges can you find?
Options:
(A) $$33$$
(B) $$9$$
(C) $$24$$
(D) $$18$$
(E) $$36$$
Please choose an option from A-E to answer. | (A) $$33$$ |
[] | 2 | A drawer contains ten identical yellow socks, eight identical blue socks and four identical pink socks. Amrita picks socks from the drawer without looking. What is the smallest number of socks she must pick to be sure that she has at least two pairs of matching socks?
Options:
(A) $$5$$
(B) $$6$$
(C) $$8$$
(D) $$11$$... | (B) $$6$$ |
[
"其它"
] | 3 | Peter bought a carpet 36dm wide and 60dm long. The figure shows part of this carpet. As seen, the carpet has a small squares contianing either a sun or a moon. You can count that along the width there are nine squares. When the carpet is fully unrolled, how many moons will be seen? [Insert pic]
Options:
(A) $$68$$
(B... | (B) $$67$$ |
[] | 2 | There are $$12$$ gold coins with exactly the same appearance, including $$11$$ real coins and $$1$$ fake coin. The weight of the fake coin is different from that of the real coin, and whether the fake coin is lighter or heavier than the real coin is unknown. How many times at least do you need to weigh the coins using ... | (C) $$3$$ |
[
"其它"
] | 2 | Mary, Nancy, and Peter are playing archery. They have $$7$$ identical arrows in total. Each of them must shoot at least once. How many different ways can they shoot the arrows?
Options:
(A) $$2$$
(B) $$4$$
(C) $$12$$
(D) $$15$$
Please choose an option from A-E to answer. | (D) $$15$$ |
[] | 2 | Betty and Abby are playing a game. They take turns writing numbers from $$1$$ to $$52 $$ on a blackboard. Each person can only write $$1$$, $$2$$, $$3$$ or $$4$$ numbers at a time, and each number can only be written once. The person who has no more numbers to write loses. Should Betty go first or second in order to wi... | (A) First |
[] | 2 | Ashley and Elvis are playing a game that requires them to drink a total of $$12$$ cups of coffee. They take turns drinking and each can drink either $$1$$ or $$2$$ cups at a time. The person who finishes the last cup of coffee wins this game. Should Elvis go first or second to ensure victory?
Options:
(A) Go first
(B)... | (B) Go second |
[] | 3 | Moon and Archie played chess competitively. Both of them are of the same level in terms of skill. They agreed to play in a best-of-seven games, where the one who wins four games first would be the ultimate winner. They have already played three games, with Moon winning two games and Archie winning just one game. What i... | (B) $$\frac{11}{16}$$ |
[
"其它"
] | 2 | How many different four-digit numbers can be formed by rearranging the four digits in $2004$?~
Options:
(A) $$4$$
(B) $$6$$
(C) $$16$$
(D) $$24$$
(E) $$81$$
Please choose an option from A-E to answer. | (B) $$6$$ |
[
"其它"
] | 2 | In how many ways can the letters in $BEEKBBPER$ be rearranged so that two or more $E$s do not appear together?
Options:
(A) $$4200$$
(B) $$900$$
(C) $$800$$
(D) $$720$$
(E) $$700$$
Please choose an option from A-E to answer. | (A) $$4200$$ |
[] | 3 | Linda picks $3$ different numbers from $$1-15$$. To make the sum of the three numbers divisible by $3$, how many different groups are there for Linda to pick?
Options:
(A) $$100$$
(B) $$910$$
(C) $$91$$
(D) $$155$$
(E) $$30$$
Please choose an option from A-E to answer. | (D) $$155$$ |
[
"其它"
] | 2 | Each of the 20 balls is tossed independently and at random into one of the 5 bins. Let $p$ be the probability that some bin ends up with 3 balls, another with 5 balls, and the other three with 4 balls each. Let $q$ be the probability that every bin ends up with 4 balls. What is $\frac{p}{q}$ ?
Options:
(A) $$1$$
(B) $... | (E) $$16$$ |
[
"其它"
] | 2 | In the Coin Game, you toss three coins at the same time. You win only if the 3 coins are all showing heads, or if the 3 coins are all showing tails. If you play the game once only, what is the probability of winning?
Options:
(A) $\frac{1}{6}$
(B) $\frac{1}{3}$
(C) $\frac{2}{27}$
(D) $\frac{2}{3}$
(E) $\frac{1}{4}$
P... | (E) $\frac{1}{4}$ |
[
"其它"
] | 2 | How many different four-digit numbers can be formed by rearranging the four digits in $2021$?~(Adapted from $2004$ AMC $8$ Problem, Question \#2)
Options:
(A) $$4$$
(B) $$6$$
(C) $$9$$
(D) $$18$$
(E) $$24$$
Please choose an option from A-E to answer. | (C) $$9$$ |
[] | 2 | Three kids $$A$$、$$B$$、$$C$$ are playing the game "pass the ball". If it starts with $$A$$, he can pass the ball to~\uline{~~~~~~~~~~}~.
Options:
(A) $$A$$ or $$B$$ or $$C$$
(B) $$B$$ or $$C$$
(C) $$A$$ or $$C$$
Please choose an option from A-E to answer. | (B) $$B$$ or $$C$$ |
[] | 2 | Gregor forms two numbers with digits $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, and $$6$$. Both numbers have three digits, and each digit is used only once. He adds these two numbers. What is the greatest sum Gregor can get?
Options:
(A) $$975$$
(B) $$999$$
(C) $$1083$$
(D) $$1173$$
(E) $$1221$$
Please choose an option from ... | (D) $$1173$$ |
[
"其它"
] | 2 | 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? (2019 AMC 8 Problems, Question \#18)
Options:
(A) $\dfrac{4}{9}$
(B) $\dfrac{1}{2}$
(C) $\dfrac{5}{9}$
(D) $\dfrac{3}{5}$
(E) $\dfrac{2}{3}$
Pl... | (C) $\dfrac{5}{9}$ |
[
"其它"
] | 2 | How many ways are there of making a total of 10 using three different positive numbers?
Options:
(A) $$4$$
(B) $$3$$
(C) $$2$$
(D) $$1$$
(E) $$0$$
Please choose an option from A-E to answer. | (A) $$4$$ |
[] | 2 | Given that only one of the following statement is corect, which one is correct? ($$1$$) All of the statements below are correct. ($$2$$) None of the statement below is corect. ($$3$$) One of the statements above is corect. ($$4$$) All the statements above are correct. ($$5$$) None of the statement above is corect.... | (E) (5) |
[
"其它"
] | 2 | \textbf{Megan wonders how the size of her beagle Herbie compares with other beagles. Herbie is 40.6cm tall. Megan learned on the internet that beagle heights are approximately normally distributed with a mean of 38.5 cm and a standard deviation of 1.25 cm. What is the percentile rank of Herbie's height?}
Options:
(A) ... | (E) $$95$$ |
[
"其它"
] | 2 | Free-response questions on the AP Statistics Exam are graded 4, 3, 2, 1, or~ 0. Question 2 on the exam was of moderate difficulty. The average score on question 2 was 2.05 with a standard deviation of 1. To the nearest tenth, what score was achieved by a student who was at the 90th percentile of all students on the tes... | (B) $$3.3$$ |
[
"其它"
] | 2 | A bakery sells cakes in three different sizes: small ($S$), medium ($M$), and large ($L$). The medium size costs $40\textbackslash\%$ more than the small size and contains $25\textbackslash\%$ less cake than the large size. The large size contains twice as much cake as the small size and costs $60\textbackslash\%$ more... | (A) $MSL$ |
[
"其它"
] | 2 | For $\triangle ABC$, all of its side lengths are integers. The primeter of $\triangle ABC$ with a side of length $12$ and a side length of $7$ is at least ．
Options:
(A) $$24$$
(B) $$25$$
(C) $$26$$
(D) $$27$$
(E) $$28$$
Please choose an option from A-E to answer. | (B) $$25$$ |
[
"其它"
] | 2 | \textbf{A copy machine dealer has data on the number x of copy machines at each of 89 customer locations and the number y of service calls in a month at each location. Summary calculations give $$\bar{}x$$ = 8.4, $$S\_x$$ = 2.1, ȳ = 14.2, $$S\_y$$ = 3.8, and r = 0.86. What is the slope of the least squares regression l... | (B) $$1.56$$ |
[
"其它"
] | 2 | 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 st... | (A) $$45$$ |
[
"其它"
] | 2 | \textbf{In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was y = 10 + .9x where y is the final exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on t... | (D) $$95.5$$ |
[
"其它"
] | 2 | For how many values of $a$ is it true that the line $y=x+a^{2}-a-3$ passes through the vertex of the parabola $y=x^{2}-6x+a^{2}$? (Adapted From 2005 AMC 12B Problem, Question \#8)
Options:
(A) $$0$$
(B) $$1$$
(C) $$2$$
(D) $$10$$
(E) infinitely many
Please choose an option from A-E to answer. | (B) $$1$$ |
[
"其它"
] | 2 | For how many values of $a$ is it true that the line $y=x+a$ passes through the vertex of the parabola $y=x^{2}+a^{2}$? (2005 AMC 12B Problem, Question \#8)
Options:
(A) $$0$$
(B) $$1$$
(C) $$2$$
(D) $$10$$
(E) infinitely many
Please choose an option from A-E to answer. | (C) $$2$$ |
[] | 2 | What is the value of $$1+3+5+\cdots +2017+2019-2-4-6-\cdots -2016-2018$$?
Options:
(A) $$-1010$$
(B) $$-1009$$
(C) $$1008$$
(D) $$1009$$
(E) $$1010$$
Please choose an option from A-E to answer. | (E) $$1010$$ |
[
"其它"
] | 2 | How many even numbers are there? 2, 3, 5, 6, 7, 9, 10.
Options:
(A) $$3$$
(B) $$4$$
(C) $$5$$
Please choose an option from A-E to answer. | (A) $$3$$ |
[
"其它"
] | 2 | \textbf{If I toss a fair coin 5000 times}
Options:
(A) \textbf{and I get anything other than 2500 heads, then something is wrong with the way I flip coins.}
(B) \textbf{the proportion of heads will be close to 0.5}
(C) \textbf{a run of 10 heads in a row will increase the probability of getting a run of 10 tails in a r... | (B) \textbf{the proportion of heads will be close to 0.5} |
[
"其它"
] | 2 | For certain real numbers $a, b$, and $c$, the polynomial $$ g(x)=x^{3}+a x^{2}+x+10 $$ has three distinct roots, and each root of $g(x)$ is also a root of the polynomial $$ f(x)=x^{4}+x^{3}+b x^{2}+100 x+c . $$ What is $f(1)$?
Options:
(A) $$-9009$$
(B) $$-8008$$
(C) $$-7007$$
(D) $$-6006$$
(E) $$-5005$$
Please choos... | (C) $$-7007$$ |
[
"其它"
] | 2 | Find the value of $$\left\textbackslash{ \frac{2018+1}{5} \right\textbackslash} + \left\textbackslash{ \frac{2018+2}{5} \right\textbackslash} + \cdots \cdots + \left\textbackslash{ \frac{2018+2017}{5} \right\textbackslash} + \left\textbackslash{ \frac{2018+2018}{5} \right\textbackslash}$$.
Options:
(A) $$1$$
(B) $$751... | (E) None of the above |
[
"其它"
] | 2 | \textbf{According to data from the United States Elections Project, only 36 percent of eligible voters voted in the 2014 elections. For random samples of size 40, which of the following best describes the sampling distribution of pˆ, the sample proportion of people who voted in the 2014 elections?}
Options:
(A) \textb... | (C) \textbf{The sampling distribution is approximately normal, with mean 0.36 and standard deviation 0.076.~} |
[
"其它"
] | 3 | Two integers are inserted into the list $3,3,8,11,28$ to double its range. The mode and median remain unchanged. What is the maximum possible sum of the two additional numbers?
Options:
(A) $$56$$
(B) $$57$$
(C) $$58$$
(D) $$60$$
(E) $$61$$
Please choose an option from A-E to answer. | (D) $$60$$ |
[
"其它"
] | 2 | If $3^{}p+3^{4}=90$, $2^{}r+44=76$, and $5^{3}+6^{}s=1421$, what is the product of $p$, $r$, and $s$? (2013 AMC 8 Problem, Question \#15)
Options:
(A) $$27$$
(B) $$40$$
(C) $$50$$
(D) $$70$$
(E) $$90$$
Please choose an option from A-E to answer. | (B) $$40$$ |
[
"其它"
] | 2 | For $\triangle ABC$, all its side lengths are integers. The primeter of $\triangle ABC$ with a side of length $14$ and a side length of $8$ is at least ．
Options:
(A) $$25$$
(B) $$26$$
(C) $$27$$
(D) $$28$$
(E) $$29$$
Please choose an option from A-E to answer. | (E) $$29$$ |
[
"其它"
] | 2 | For $\triangle ABC$, all its side lengths are integers. The perimeter of $\triangle ABC$ with a side of length $14$ and a side length of $8$ is at least ．
Options:
(A) $$25$$
(B) $$26$$
(C) $$27$$
(D) $$28$$
(E) $$29$$
Please choose an option from A-E to answer. | (E) $$29$$ |
[
"其它"
] | 3 | What is the remainder when $2^{2023}+2023$ is divided by $2^{20}+1$? (Adapted From 2020 AMC 10B Problems, Question \#22)
Options:
(A) $$2015$$
(B) $$2^{5}$$
(C) $$2023$$
(D) $$2048$$
(E) $$20$$
Please choose an option from A-E to answer. | (A) $$2015$$ |
[
"其它"
] | 2 | Find all values of $x$ such that $\textbar3 x+12\textbar\textless9$ and $\textbar x+2\textbar\textless\textbar-3 x-6\textbar$.~\uline{~~~~~~~~~~}~
Options:
(A) $x\textless-2$
(B) $-7\textless x\textless-1$
(C) $-7\textless x\textless-2$
(D) $-7\textless x\textless-1 ; x \neq-2$
Please choose an option from A-E to ans... | (D) $-7\textless x\textless-1 ; x \neq-2$ |
[
"其它"
] | 2 | For $\triangle ABC$, all its side lengths are integers. The perimeter of $\triangle ABC$ with a side of length $3$ and a side length of $4$ is at least ．
Options:
(A) $$7$$
(B) $$8$$
(C) $$9$$
(D) $$12$$
Please choose an option from A-E to answer. | (C) $$9$$ |
[
"其它"
] | 3 | (2) Eddie had 120 dollars as his pocket money, and spent $$ \frac{3}{4} $$of it. How much money is left?
Options:
(A) $$30$$
(B) $$60$$
(C) $$90$$
(D) $$120$$
Please choose an option from A-E to answer. | (A) $$30$$ |
[
"其它"
] | 2 | For $\triangle ABC$, all its side lengths are integers. The primeter of $\triangle ABC$ with a side of length $3$ and a side length of $4$ is at least ．
Options:
(A) $$7$$
(B) $$8$$
(C) $$9$$
(D) $$12$$
Please choose an option from A-E to answer. | (C) $$9$$ |
[
"其它"
] | 2 | For $\triangle ABC$, all its side lengths are integer. The primeter of $\triangle ABC$ with a side of length $12$ and a side length of $7$ is at least ．
Options:
(A) $$24$$
(B) $$25$$
(C) $$26$$
(D) $$27$$
(E) $$28$$
Please choose an option from A-E to answer. | (B) $$25$$ |
[
"其它"
] | 2 | What is the correct ordering of the three answers from $\frac5{19}\div \frac{25}{38}$, $1\frac12 \div \frac{15}8$, and $\frac74 \div \frac{35}{12}$, in increasing order? (adapted from 2012 AMC 8 Problems, Question \#20)
Options:
(A) $\frac5{19}\div \frac{25}{38}$ \textless~$1\frac12 \div \frac{15}8$ \textless{} $\frac... | (D) $\frac5{19}\div \frac{25}{38}$ \textless{} $\frac74 \div \frac{35}{12}$ \textless~$1\frac12 \div \frac{15}8$ |
[
"其它"
] | 2 | For $\triangle ABC$, all its side lengths are integer. The primeter of $\triangle ABC$ with a side of length $12$ and a side length of $7$ is at least ．
Options:
(A) $$24$$
(B) $$25$$
(C) $$26$$
(D) $$27$$
Please choose an option from A-E to answer. | (B) $$25$$ |
[
"其它"
] | 4 | How many perfect cubes lie between $2^{2}+1$ and $2^{8}+1$, inclusive? (Adapted from 2018 AMC 8 Problem, Question \#25)
Options:
(A) $$2$$
(B) $$3$$
(C) $$4$$
(D) $$5$$
(E) $$6$$
Please choose an option from A-E to answer. | (D) $$5$$ |
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