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[] | 2 | The hundreds digit of a three-digit number is $$2$$ more than the units digit. The digits of the three-digit number are reversed, and the result is subtracted from the original three-digit number. What is the units digit of the result?
Options:
(A) $$0$$
(B) $$2$$
(C) $$4$$
(D) $$6$$
(E) $$8$$
Please choose an option from A-E to answer. | (E) $$8$$ |
[
"其它"
] | 4 | $$\overline{**45}$$, $$\overline{19*8}$$, $$\overline{23*1}$$, and $$\overline{3*49}$$ are four $4-$digit numbers with some unknown digits. Which number is possible to be a perfect square?
Options:
(A) $$\overline{**45}$$
(B) $$\overline{19*8}$$
(C) $$\overline{23*1}$$
(D) $$\overline{3*49}$$
(E) None
Please choose an option from A-E to answer. | (D) $$\overline{3*49}$$ |
[] | 2 | The first $2018$ integers ($1$, $2$, $3$, $\cdots$, $2017$, $2018$) are written on the blackboard. What is the minimum number of integers that should be erased from the blackboard, so that the last digit of the product of the remaining integers is $2$?
Options:
(A) $$402$$
(B) $$403$$
(C) $$404$$
(D) $$410$$
(E) None of the above
Please choose an option from A-E to answer. | (C) $$404$$ |
[
"其它"
] | 2 | Eleven members of the Middle School Math Club each paid the same integer amount for a guest speaker to talk about problem solving at their math club meeting. In all, they paid their guest speaker $$\overline{1A2}$$. What is the missing digit $A$ of this $3$-digit number? (2014 AMC 8 Problem, Question \#8)
Options:
(A) $$0$$
(B) $$1$$
(C) $$2$$
(D) $$3$$
(E) $$4$$
Please choose an option from A-E to answer. | (D) $$3$$ |
[
"其它"
] | 2 | There is a book with 650 pages. Henry tears 31 paper from the book, each paper contains two pages. Is it possible that the sum of their page number equals to 2000?
Options:
(A) $$Yes.$$
(B) $$No.$$
Please choose an option from A-E to answer. | (B) $$No.$$ |
[] | 2 | Divide 5 numbers $$2$$、$$3$$、$$12$$、$$15$$ and $$30$$ into two groups to make the product of numbers in each group the same, so the two groups are ．
Options:
(A) （$$2$$, $$3$$, $$15$$），（$$12$$, $$30$$）
(B) （$$2$$, $$12$$, $$15$$），（$$3$$, $$30$$）
(C) （$$2$$, $$3$$, $$30$$），（$$12$$, $$15$$）
(D) （$$12$$, $$3$$, $$15$$），（$$2$$, $$30$$）
Please choose an option from A-E to answer. | (C) （$$2$$, $$3$$, $$30$$），（$$12$$, $$15$$） |
[] | 2 | Mom was cooking at home with the lights on when suddenly the power went out. Dad came home and pressed the switch four times, and then Mason came home and pressed the switch three times. When the power came back on, were the lights off or on?
Options:
(A) On
(B) Off
Please choose an option from A-E to answer. | (B) Off |
[] | 2 | Salah has collected more than $$20$$ football cards. When he puts his cards in piles of four, he has three cards left over. When he puts the cards in piles of five, he has four cards left over. Which of the following could be the number of cards he has in total?
Options:
(A) $$27$$
(B) $$31$$
(C) $$35$$
(D) $$39$$
(E) $$43$$
Please choose an option from A-E to answer. | (D) $$39$$ |
[] | 2 | Weili wanted to pack $60$ apples and $75$ pears into as many bags as possible, with no remainder. She packed the same number of fruit in each bag. The number of apples in each bag was the same. How many apples were there in each bag?
Options:
(A) $$15$$
(B) $$12$$
(C) $$5$$
(D) $$4$$
Please choose an option from A-E to answer. | (D) $$4$$ |
[] | 2 | Which of the following numbers cannot be written as the sum of $$4$$ consecutive whole numbers?
Options:
(A) $$1994$$
(B) $$2042$$
(C) $$2050$$
(D) $$2060$$
Please choose an option from A-E to answer. | (D) $$2060$$ |
[] | 2 | The multiplication $$abc\times de=7632$$ uses each of the digits $$1$$ to $$9$$ exactly once. What is the value of $$b$$?
Options:
(A) $$1$$
(B) $$4$$
(C) $$5$$
(D) $$8$$
(E) $$9$$
Please choose an option from A-E to answer. | (C) $$5$$ |
[] | 2 | A $14$-digit. number $666666 XY 444444$ is a multiple of $26$. If $X$ and $Y$ are both positive, what is the smallest vaue of $X+ Y$?
Options:
(A) $$3$$
(B) $$4$$
(C) $$9$$
(D) $$14$$
(E) None of the above
Please choose an option from A-E to answer. | (B) $$4$$ |
[
"其它"
] | 2 | The $7$-digit numbers $\underline{74 A 52 B 1}$ and $\underline{326 A B 4 C}$ are each multiples of $3$ . Which of the following could be the value of $C$ ? (2014 amc 8 Problem, Question \#21)
Options:
(A) $$1$$
(B) $$2$$
(C) $$3$$
(D) $$5$$
(E) $$8$$
Please choose an option from A-E to answer. | (A) $$1$$ |
[] | 2 | A $6$-digit number starting with $18$, $18ABCD$, is a multiple of $6$, $7$, $9$ and $10$. Find $\left (A +B + C+ D\right )$ for the smallest such number?
Options:
(A) $$7$$
(B) $$12$$
(C) $$14$$
(D) $$28$$
(E) None of the above
Please choose an option from A-E to answer. | (E) None of the above |
[
"其它"
] | 2 | Among numbers like $5$, $55$, $555$, $5555$, $$\cdots$$, how many of them are perfect squares?
Options:
(A) $0$
(B) $1$
(C) $2$
(D) Countless
Please choose an option from A-E to answer. | (B) $1$ |
[
"其它"
] | 2 | Jam has some pieces of candy. He wants to share with some kids. If he shares the candy among $8$ kids on average, there will be $2$ pieces left. If he shares the candy among $9$ kids on average, there will be $3$ pieces left. If he shares the candy among $10$ kids on average, there will be $4$ pieces left. How many pieces of candy are there?
Options:
(A) $321$
(B) $354$
(C) $720$
(D) $360$
(E) $240$
Please choose an option from A-E to answer. | (B) $354$ |
[] | 2 | Chloe is working on this equation: $$475+17\times 58+990-19\times 32+33\times 111$$. Her answer is $$5681$$. Without calculating, do you think Chloe\textquotesingle s answer is correct or wrong? Explain why.
Options:
(A) Correct
(B) Wrong
Please choose an option from A-E to answer. | (B) Wrong |
[] | 2 | John loves collecting stamps! If he divides the number of stamps he has by $$32$$, then he will have $$30$$ remaining stamps; if he divides the number of stamps he has by $$9$$, he will have $$7$$ remaining stamps; if he divides the number of stamps he has by $$7$$, he will have $$5$$ remaining stamps. How many stamps, at least, does John have?
Options:
(A) $$2014$$
(B) $$2015$$
(C) $$2016$$
(D) $$2017$$
Please choose an option from A-E to answer. | (A) $$2014$$ |
[] | 2 | Prime factorise $$24\times 105$$．
Options:
(A) $${{2}^{3}}\times {{3}^{2}}\times 5\times 7$$
(B) $${{2}^{4}}\times {{3}^{2}}\times 5$$
(C) $${{2}^{4}}\times {{3}^{2}}\times 5\times 7$$
Please choose an option from A-E to answer. | (A) $${{2}^{3}}\times {{3}^{2}}\times 5\times 7$$ |
[] | 2 | $$2010$$ is divided by $$N$$ and gets a remainder of $$15$$. There are~\uline{~~~~~~~~~~}~possible values of $$N$$.
Options:
(A) $$4$$
(B) $$8$$
(C) $$9$$
(D) $$11$$
(E) $$16$$
Please choose an option from A-E to answer. | (D) $$11$$ |
[] | 3 | In the division expression $$28\div$$~\uline{~~~~~~~~~~}~$$=$$~\uline{~~~~~~~~~~}~$$\text{r}4$$, how many different pairs of number are there to fill the gaps?
Options:
(A) $$5$$
(B) $$4$$
(C) $$3$$
(D) $$2$$
(E) $$1$$
Please choose an option from A-E to answer. | (B) $$4$$ |
[] | 3 | In the division expression $$28\div$$~\uline{~~~~~~~~~~}~$$=$$~\uline{~~~~~~~~~~}~$$\text{R}4$$, how many different combinations are there for the quotient and the divisor ?
Options:
(A) $$2$$
(B) $$3$$
(C) $$4$$
(D) $$5$$
Please choose an option from A-E to answer. | (C) $$4$$ |
[] | 2 | The first $2018$ integers ($1$, $2$, $3$, $\cdots$, $2017$, $2018$) are written on the blackboard. What is the minimum number of integers that should be erased from the blackboard, so that the last digit of the product of the remaining integers is $2$?
Options:
(A) $$402$$
(B) $$403$$
(C) $$404$$
(D) $$410$$
(E) None of the above
Please choose an option from A-E to answer. | (C) $$404$$ |
[] | 2 | How many solutions that can be expressed with positive integers does the equation below have? ($$1999$$ Math kangaroo Problems, Level $$7-8$$, Question \#$$26$$) $$a^{2}b-1=1999$$
Options:
(A) $$3$$
(B) $$4$$
(C) $$5$$
(D) $$6$$
(E) $$7$$
Please choose an option from A-E to answer. | (D) $$6$$ |
[] | 2 | If you were to work out the answer to the sum $$2^{2016}+0^{2016}+1^{2016}+6^{2016}$$ you would get a number with $$1569$$ digits, starting with $$566$$ $$136$$ $$001$$ $$\cdots$$ What is the last digit of this number?
Options:
(A) $$1$$
(B) $$3$$
(C) $$5$$
(D) $$7$$
(E) $$9$$
Please choose an option from A-E to answer. | (B) $$3$$ |
[] | 2 | What is the smallest integer $$n$$ for which the number $$\left(2^{2}-1\right)\cdot \left(3^{2}-1\right)\cdot \left(4^{2}-1\right)\cdots \left(n^{2}-1\right)$$ is the square of an integer?
Options:
(A) $$6$$
(B) $$8$$
(C) $$16$$
(D) $$27$$
(E) None of these.
Please choose an option from A-E to answer. | (B) $$8$$ |
[] | 2 | The number $$95$$~\uline{~~~~~~~~~~}~$$94775998$$ is divisible by $$198$$. What is the missing digit?
Options:
(A) $$3$$
(B) $$5$$
(C) $$6$$
(D) $$8$$
(E) $$9$$
Please choose an option from A-E to answer. | (E) $$9$$ |
[
"其它"
] | 2 | What is the sum of the two smallest prime factors of $250$? (2007 AMC 8 Problems, Question \#3)
Options:
(A) $$2$$
(B) $$5$$
(C) $$7$$
(D) $$10$$
(E) $$12$$
Please choose an option from A-E to answer. | (C) $$7$$ |
[] | 2 | Lee counted by $$7$$\textquotesingle s beginning with one of the whole numbers from $$1$$ through $$7$$, until Lee passed $$1000$$. If Lee counted three of the following numbers, which number did Lee not count?
Options:
(A) $$107$$
(B) $$184$$
(C) $$534$$
(D) $$641$$
Please choose an option from A-E to answer. | (D) $$641$$ |
[] | 2 | A $14$-digit. number $666666 XY 444444$ is a multiple of $26$. If $X$ and $Y$ are both positive, what is the smallest vaue of $X+ Y$?
Options:
(A) $$3$$
(B) $$4$$
(C) $$9$$
(D) $$14$$
(E) None of the above
Please choose an option from A-E to answer. | (B) $$4$$ |
[
"其它"
] | 2 | Leo prepares more than $400$ cupcakes for a party. Now he can divided all of them equally into $5$ piles. After his pet cat eats one of the cupcakes, he finds that now he can divide the remaining cupcakes equally into $6$ piles. Then, the naughty pet cat eat another one, and Leo divides the remaining cupcakes into $7$ piles. How many cupcakes did Leo prepare at least at the beginning? Find the sum of the three digits.
Options:
(A) $$10$$
(B) $$11$$
(C) $$12$$
(D) $$13$$
(E) $$14$$
Please choose an option from A-E to answer. | (A) $$10$$ |
[] | 2 | A $6$-digit number starting with $18$, $18ABCD$, is a multiple of $6$, $7$, $9$ and $10$. Find $\left (A +B + C+ D\right )$ for the smallest such number?
Options:
(A) $$7$$
(B) $$12$$
(C) $$14$$
(D) $$28$$
(E) None of the above
Please choose an option from A-E to answer. | (E) None of the above |
[
"其它"
] | 2 | Let $N=34 \cdot 34 \cdot 63 \cdot 270$. What is the ratio of the sum of the odd divisors of $N$ to the sum of the even divisors of $N$ ?
Options:
(A) $1:16$
(B) $1:15$
(C) $1:14$
(D) $1:8$
(E) $1:3$
Please choose an option from A-E to answer. | (C) $1:14$ |
[
"其它"
] | 2 | A student wrote down a natural number. When she divided the number by $$9$$, the remainder was $$7$$. What is the~~remainder when twice that number is divided by $$9$$?
Options:
(A) $$1$$
(B) $$2$$
(C) $$5$$
(D) $$6$$
(E) $$7$$
Please choose an option from A-E to answer. | (C) $$5$$ |
[] | 2 | The hundreds digit of a three-digit number is $$2$$ more than the units digit. The digits of the three-digit number are reversed, and the result is subtracted from the original three-digit number. What is the units digit of the result?
Options:
(A) $$0$$
(B) $$2$$
(C) $$4$$
(D) $$6$$
(E) $$8$$
Please choose an option from A-E to answer. | (E) $$8$$ |
[
"其它"
] | 2 | Jam has some pieces of candy. He wants to share with some kids. If he shares the candy among $8$ kids equally, there will be $2$ pieces left. If he shares the candy among $9$ kids equally, there will be $3$ pieces left. If he shares the candy among $10$ kids equally, there will be $4$ pieces left. How many pieces of candy are there?
Options:
(A) $321$
(B) $354$
(C) $720$
(D) $360$
(E) $240$
Please choose an option from A-E to answer. | (B) $354$ |
[] | 2 | In a Fibonacci-like sequence $$1,3,4,7,11,18\cdots $$(where each term is the sum of the two previous terms, starting from the third term), what is the remainder when the $$5555^{}\text{th}$$ term is divided by $$5$$？
Options:
(A) $$0$$
(B) $$1$$
(C) $$2$$
(D) $$3$$
(E) $$4$$
Please choose an option from A-E to answer. | (E) $$4$$ |
[] | 2 | If the product of an even number and an odd number is $$840$$, what is the largest possible value of this odd number?
Options:
(A) $$21$$
(B) $$35$$
(C) $$105$$
(D) $$420$$
Please choose an option from A-E to answer. | (C) $$105$$ |
[
"其它"
] | 2 | From 202 to 2020 (including these two numbers), how many multiples of 9 are there?
Options:
(A) $$201$$
(B) $$202$$
(C) $$101$$
(D) $$102$$
Please choose an option from A-E to answer. | (B) $$202$$ |
[
"其它"
] | 2 | Amy runs a lap around the track in $4$ minutes and Pawel in $5$ minutes. Amy and Pawel start to run around the track at the same time. After how many minutes will the boys meet at the starting point again?
Options:
(A) $$4$$
(B) $$5$$
(C) $$10$$
(D) $$20$$
(E) It depends on the distance around the track
Please choose an option from A-E to answer. | (D) $$20$$ |
[
"其它"
] | 2 | The smallest number greater than $2$ that leaves a remainder of $2$ when divided by $3,4,5$, or $6$ lies between what numbers? (2012 AMC 8 Problem, Question \# 15)
Options:
(A) $40$ and $50$
(B) $51$ and $55$
(C) $56$ and $60$
(D) $61$ and $65$
(E) $66$ and $99$
Please choose an option from A-E to answer. | (D) $61$ and $65$ |
[] | 2 | Divide 8 numbers $$15$$、$$18$$、$$21$$、$$22$$、$$42$$、$$44$$、$$50$$ and $$60$$ into two groups with 4 numbers in each group to make the product of numbers in each group the same, so the two groups are ．
Options:
(A) （$$15$$, $$22$$, $$21$$, $$60$$），（$$18$$, $$44$$, $$42$$, $$50$$）
(B) （$$15$$, $$42$$, $$44$$, $$60$$），（$$18$$, $$22$$, $$21$$, $$50$$）
(C) （$$15$$, $$44$$, $$21$$, $$60$$），（$$18$$, $$22$$, $$42$$, $$50$$）
(D) （$$15$$, $$44$$, $$21$$, $$50$$），（$$18$$, $$22$$, $$42$$, $$60$$）
Please choose an option from A-E to answer. | (C) （$$15$$, $$44$$, $$21$$, $$60$$），（$$18$$, $$22$$, $$42$$, $$50$$） |
[] | 2 | The whole numbers from $$1$$ to $$2016$$ inclusive are written on a blackboard. Moritz underlines all the multiples of two in red, all the multiples of three in blue and all the multiples of four in green. How many numbers does Moritz underline exactly twice?
Options:
(A) $$1008$$
(B) $$1004$$
(C) $$504$$
(D) $$336$$
(E) $$168$$
Please choose an option from A-E to answer. | (C) $$504$$ |
[] | 2 | What is the greatest natural number $$n$$ such that $$n+27$$ and $$n-62$$ are squares of natural number?
Options:
(A) $$598$$
(B) $$1598$$
(C) $$3998$$
(D) $$1998$$
(E) Such a number does not exist
Please choose an option from A-E to answer. | (D) $$1998$$ |
[
"其它"
] | 2 | The smallest number greater than $2$ that leaves a remainder of $2$ when divided by $3,4,5$, or $6$ lies between what numbers? (2012 AMC 8 Problem, Question \# 15)
Options:
(A) $40$ and $50$
(B) $51$ and $55$
(C) $56$ and $60$
(D) $61$ and $65$
(E) $66$ and $99$
Please choose an option from A-E to answer. | (D) $61$ and $65$ |
[
"其它"
] | 2 | $\overline{392AB}$ is a multiple of $45$, and $\overline{B34}$ is a three-digit even number. What is the sum of $A$ and $B$?
Options:
(A) $$13$$
(B) $$4$$
(C) $$5$$
(D) $$7$$
(E) $4$ or $13$
Please choose an option from A-E to answer. | (A) $$13$$ |
[
"其它"
] | 2 | Two whole numbers have a least common multiple of $60$. -Each number is less than or equal to $12$. -The greatest common factor of the two number is $2$. What are the two numbers?
Options:
(A) $6$ and $10$
(B) $5$ and $12$
(C) $10$ and $12$
(D) $12$ and $16$
Please choose an option from A-E to answer. | (C) $10$ and $12$ |
[] | 2 | There are some books in the central library. If Adam divides the number of the books in the library by $32$, there will be $30$ books remained; if he divides the number of books in the library by $9$, there will be $7$ books remained; if he divides the number of books in the library by $7$, there will be $5$ books remained. How many books, at least, are there in the central library?
Options:
(A) $$2014$$
(B) $$2015$$
(C) $$2016$$
(D) $$2017$$
Please choose an option from A-E to answer. | (A) $$2014$$ |
[
"其它"
] | 2 | When Ringo places his marbles into bags with $6$ marbles per bag, he has $4$ marbles left over. When Paul does the same with his marbles, he has $3$ marbles left over. Ringo and Paul pool their marbles and place them into as many bags as possible, with $6$ marbles per bag. How many marbles will be leftover? (2012 AMC 10B Problems, Question \#4)
Options:
(A) $$1$$
(B) $$2$$
(C) $$3$$
(D) $$4$$
(E) $$5$$
Please choose an option from A-E to answer. | (A) $$1$$ |
[
"其它"
] | 2 | Leo prepares more than $400$ cupcakes for a party. Now he can divided all of them equally into $5$ piles. After his pet cat eats one of the cupcakes, he finds that now he can divide the remaining cupcakes equally into $6$ piles. Then, the naughty pet cat eat another one, and Leo divides the remaining cupcakes into $7$ piles. How many cupcakes did Leo make at least at the beginning? Find the sum of the three digits.
Options:
(A) $$10$$
(B) $$11$$
(C) $$12$$
(D) $$13$$
(E) $$14$$
Please choose an option from A-E to answer. | (A) $$10$$ |
[] | 2 | What are the last three digits of the answer to the calculation below? $$123\times 124\times 125\times 126\times 127$$
Options:
(A) $$000$$
(B) $$222$$
(C) $$444$$
(D) $$666$$
(E) $$888$$
Please choose an option from A-E to answer. | (A) $$000$$ |
[
"其它"
] | 2 | Malcolm wants to visit Isabella after school today and he knows the street where she lives but does not know her house number. She tells him,~"My house number has two digits, and all of the following four statements about it are true." $(1)$ It is a prime number. $(2)$ It is less than $40$. $(3)$ One of its digits is $3$. $(4)$ Another digit is an even number. This information allows Malcolm to determine Isabella\textquotesingle s house number. What is the house number? (adapted from 2017 AMC 8 problem, Question \#8)
Options:
(A) $$43$$
(B) $$13$$
(C) $$23$$
(D) $$32$$
(E) $$3$$
Please choose an option from A-E to answer. | (C) $$23$$ |
[
"其它"
] | 2 | Malcolm wants to visit Isabella after school today and he knows the street where she lives but doesn't know her house number. She tells him, ``My house number has two digits, and all of the following four statements about it are true.'' $(1)$ It is a prime number. $(2)$ It is less than $40$. $(3)$ One of its digits is $3$. $(4)$ Another digit is an even number. This information allows Malcolm to determine Isabella's house number. What is the house number? (adapted from 2017 AMC 8 problem, Question \#8)
Options:
(A) $$43$$
(B) $$13$$
(C) $$23$$
(D) $$32$$
(E) $$3$$
Please choose an option from A-E to answer. | (C) $$23$$ |
[
"其它"
] | 2 | There is a book with 650 pages. Henry tears 31 paper from the book, each paper contains two pages. Is it possible that the sum of their page number equals to 953?
Options:
(A) $$Yes.$$
(B) $$No.$$
Please choose an option from A-E to answer. | (A) $$Yes.$$ |
[
"其它"
] | 2 | Vivian bakes a cuboid cake with a dimension of $6\times8\times10$ and cuts it into many small cubical cakes with a dimension of $2\times2\times2$. She wants to equally divide the cake without remainder among $x$ people so that each person can get at least one small cake. How many possible values of $x$ are there?
Options:
(A) $$6$$
(B) $$8$$
(C) $$12$$
(D) $$16$$
(E) $$18$$
Please choose an option from A-E to answer. | (C) $$12$$ |
[] | 2 | The positive integers from $$1$$ to $$150$$ inclusive are placed in a $$10$$ by $$15$$ grid so that each cell contains exactly one integer. Then the multiples of $$3$$ are given a red mark, the multiples of $$5$$ are given a blue mark, and the multiples of $$7$$ are given a green mark. How many cells have more than $$1$$ mark?
Options:
(A) $$10$$
(B) $$12$$
(C) $$15$$
(D) $$18$$
(E) $$19$$
Please choose an option from A-E to answer. | (E) $$19$$ |
[
"其它"
] | 2 | Allen has some apples, and the number of apples is more than $2200$ but less than $2300$. If he distributes them among $12$ children evenly, there will be $11$ apples left. If he distributes them among $13$ children evenly, there will be $7$ apples left.~ If he distributes them among $14$ children evenly, there will be $3$ apples left. Which is the correct range of the number of pens?
Options:
(A) $2530\sim2540$
(B) $2540\sim2550$
(C) $2550\sim2560$
(D) $2570\sim2590$
(E) $2580\sim2600$
Please choose an option from A-E to answer. | (A) $2530\sim2540$ |
[
"其它"
] | 2 | One day Randy was bored and he wrotre all the whole numbers from $49$ to $97$ on his paper. How many times did he write the digit \textquotesingle\textquotesingle$8$\textquotesingle\textquotesingle{} on his paper?
Options:
(A) $$4$$
(B) $$8$$
(C) $$11$$
(D) $$13$$
(E) None of the above
Please choose an option from A-E to answer. | (E) None of the above |
[
"其它"
] | 2 | What is the sum of the two smallest prime factors of $250$? (2007 AMC 8 Problems, Question \#3)
Options:
(A) $$2$$
(B) $$5$$
(C) $$7$$
(D) $$10$$
(E) $$12$$
Please choose an option from A-E to answer. | (C) $$7$$ |
[] | 2 | When $$1001$$ is divided by a certain one-digit number, the remainder is $$5$$. What is the remainder when the same one-digit number divides $$2006$$? ．
Options:
(A) $$2$$
(B) $$3$$
(C) $$4$$
(D) $$5$$
(E) $$6$$
Please choose an option from A-E to answer. | (A) $$2$$ |
[
"其它"
] | 4 | How many perfect cubes lie between $2^{8}+1$ and $2^{18}+1$, inclusive? (2018 AMC 8 Problem, Question \#25)
Options:
(A) $$4$$
(B) $$9$$
(C) $$10$$
(D) $$57$$
(E) $$58$$
Please choose an option from A-E to answer. | (E) $$58$$ |
[
"其它"
] | 2 | Let $N=34 \cdot 34 \cdot 63 \cdot 270$. What is the ratio of the sum of the odd divisors of $N$ to the sum of the even divisors of $N$ ?
Options:
(A) 1:16
(B) 1:15
(C) 1:14
(D) 1:8
(E) 1:3
Please choose an option from A-E to answer. | (C) 1:14 |
[
"其它"
] | 4 | Every positive integer is congruent modulo $9$ to the sum of its decimal digits. Now, let $S(n)$ equal the sum of the digits of positive integer $n$. For example, $S(1507)=13$. For a particular positive integer $n, S(n)=691$. Which of the following could be the value of $S(n+2)$? (Adapted From 2017 AMC 12A Problems, Question \#18)
Options:
(A) $$9$$
(B) $$17$$
(C) $$143$$
(D) $$116$$
(E) $$6$$
Please choose an option from A-E to answer. | (A) $$9$$ |
[] | 2 | $$(2345678+3456782+4567823+5678234+6782345+7823456+8234567)\div5$$=~\uline{~~~~~~~~~~}~
Options:
(A) $$5555555$$
(B) $$6666666$$
(C) $$7777777$$
(D) $$8888888$$
(E) $$9999999$$
Please choose an option from A-E to answer. | (C) $$7777777$$ |
[
"其它"
] | 2 | How many positive integer factors of $2020$ have more than $3$ factors? (2020 AMC 8 Problems, Question \#17)
Options:
(A) $$6$$
(B) $$7$$
(C) $$8$$
(D) $$9$$
(E) $$10$$
Please choose an option from A-E to answer. | (B) $$7$$ |
[] | 2 | How many whole numbers between $$1$$ and $$100$$ are $$3$$ times a prime?
Options:
(A) $$9$$
(B) $$10$$
(C) $$11$$
(D) $$12$$
Please choose an option from A-E to answer. | (C) $$11$$ |
[] | 2 | Divide $$4$$、$$9$$、$$10$$、$$14$$、$$15$$ and $$21$$ into 2 groups with 3 numbers in each group to make the product of numbers in each group the same. How can we divide the numbers?
Options:
(A) $$(14,9,10), (21,15,4)$$
(B) $$(14,21,10), (9,15,4)$$
(C) $$(14,4,10), (21,15,9)$$
(D) $$(14,15,9), (21,10,4)$$
Please choose an option from A-E to answer. | (A) $$(14,9,10), (21,15,4)$$ |
[] | 2 | What are the last three digits of the answer to the calculation below? $$123\times 124\times 125\times 126\times 127$$
Options:
(A) $$000$$
(B) $$222$$
(C) $$444$$
(D) $$666$$
Please choose an option from A-E to answer. | (A) $$000$$ |
[] | 2 | What are the last two digits of the result of $$1\times 3\times 5\times 7\times \cdots \times 101$$?
Options:
(A) $$05$$
(B) $$25$$
(C) $$50$$
(D) $$55$$
(E) $$75$$
Please choose an option from A-E to answer. | (E) $$75$$ |
[] | 2 | The multiplication $$abc\times de=7632$$ uses each of the digits $$1$$ to $$9$$ exactly once. What is the value of $$b$$?
Options:
(A) $$1$$
(B) $$4$$
(C) $$5$$
(D) $$9$$
Please choose an option from A-E to answer. | (C) $$5$$ |
[
"其它"
] | 2 | Vivian has many barbie cards. If she puts $8$ cards in each group, there will be $5$ cards left. If she puts $9$ cards in each group, there will be $3$ cards left. If she puts $10$ cards in each group, there will be $1$ card left. How many cards at least should Vivian take away, so that the remaining number of cards can be divisible by $8,$ $9,$ and $10$?
Options:
(A) $$36$$
(B) $$15$$
(C) $$23$$
(D) $$21$$
(E) $$9$$
Please choose an option from A-E to answer. | (D) $$21$$ |
[] | 2 | $$(14\times 9\times 8)\div \left( 9\times 7\times 8 \right)=$$．
Options:
(A) $$2$$
(B) $$1$$
(C) $$0$$
(D) $$3$$
Please choose an option from A-E to answer. | (A) $$2$$ |
[] | 2 | Two(different) numbers are selected from $$0$$，$$1$$，$$3$$，$$5$$，$$8$$ and $$9$$. How many two-digit even mumbers can be formed？
Options:
(A) $$9$$
(B) $$10$$
(C) $$19$$
(D) $$20$$
(E) $$30$$
Please choose an option from A-E to answer. | (A) $$9$$ |
[
"其它"
] | 2 | Students guess that Norb's age is $28$, $30$, $34$, $36$, $38$, and $41$. Norb says, "At least half of you guessed too low, two of your guesses are off by one, and my age is a prime number."~How old is Norb? (adapted from 2011 AMC 8 Problem, Question \#21)
Options:
(A) $$25$$
(B) $$29$$
(C) $$31$$
(D) $$37$$
(E) $$14$$
Please choose an option from A-E to answer. | (D) $$37$$ |
[
"其它"
] | 2 | Among numbers like $5$, $55$, $555$, $5555$, $$\cdots$$, how many of them are perfect squares?
Options:
(A) $0$
(B) $1$
(C) $2$
(D) Countless
Please choose an option from A-E to answer. | (A) $0$ |
[] | 2 | If the sum of two prime numbers is $$39$$, the difference between these two prime numbers will be ．
Options:
(A) $$29$$
(B) $$31$$
(C) $$33$$
(D) $$35$$
(E) $$37$$
Please choose an option from A-E to answer. | (D) $$35$$ |
[] | 2 | There are two reading rooms at Think Town\textquotesingle s Library: Tulip\textquotesingle s and Lily\textquotesingle s. There are two lamps on every table in Tulip\textquotesingle s Reading Room. As for Lily\textquotesingle s Reading Room, there are three lamps on every table. Nini knows that the total number of lamps in the two reading rooms is an odd number, and the total number of tables in the two reading rooms is also an odd number. Which reading room has an odd number of tables?
Options:
(A) Tulip\textquotesingle s Reading Room
(B) Lily\textquotesingle s Reading Room
(C) Both rooms
(D) None of the rooms
Please choose an option from A-E to answer. | (B) Lily\textquotesingle s Reading Room |
[] | 3 | In the division expression $$28\div$$~\uline{~~~~~~~~~~}~$$=$$~\uline{~~~~~~~~~~}~$$\text{R}4$$, how many different combinations are there for the quotient and the divisor?
Options:
(A) $$1$$
(B) $$2$$
(C) $$3$$
(D) $$4$$
(E) $$5$$
Please choose an option from A-E to answer. | (D) $$4$$ |
[
"其它"
] | 4 | Every positive integer is congruent modulo $9$ to the sum of its decimal digits. Now, let $S(n)$ equal the sum of the digits of positive integer $n$. For example, $S(1507)=13$. For a particular positive integer $n, S(n)=1274$. Which of the following could be the value of $S(n+1)$? (Adapted From 2017 AMC 12A Problems, Question \#18)
Options:
(A) $$1$$
(B) $$3$$
(C) $$12$$
(D) $$1239$$
(E) $$1265$$
Please choose an option from A-E to answer. | (D) $$1239$$ |
[] | 2 | Of the following, which has an odd quotient when divided by $$2$$?
Options:
(A) $$456456456456456$$
(B) $$678 678678678678$$
(C) $$432432432432432$$
(D) $$876876876 876876$$
Please choose an option from A-E to answer. | (B) $$678 678678678678$$ |
[
"其它"
] | 3 | A robot is facing south-east. It makes 58 quarter-turns clockwise, then 93 quarter-turns anti-clockwise. In which direction is the robot now facing?
Options:
(A) north
(B) north-east
(C) north-west
(D) south-east
(E) south-west
Please choose an option from A-E to answer. | (E) south-west |
[] | 2 | $$2006$$ students participated in a survey. The survey stated that $$1500$$ of them participated in the Math Kangaroo contest, and $$1200$$ of them participated in an English Language contest. Out of the students who participated in the survey, how many participated in both contests if it is known that $$6$$ people did not take part in either of the competitions? ($$2006$$ Math Kangaroo Problems, Level $$7-8$$, Question \#$$5$$)
Options:
(A) $$300$$
(B) $$500$$
(C) $$600$$
(D) $$700$$
(E) $$1000$$
Please choose an option from A-E to answer. | (D) $$700$$ |
[
"其它"
] | 2 | In how many ways can the letters in $BEEKBBPERPP$ be rearranged so that two or more $E$s do not appear together?
Options:
(A) $$49200$$
(B) $$94080$$
(C) $$564480$$
(D) $$1800$$
(E) $$98400$$
Please choose an option from A-E to answer. | (B) $$94080$$ |
[] | 2 | I have $$11$$ pieces of candy in each of three baskets. From each basket I take out one piece of candy in the following order: from the left, from the middle, from the right, from the middle, from the left, from the middle, from the right, and so on. What is the largest number of pieces of candy left in one of the baskets when the middle basket is empty? (2001 Math Kangaroo Problem, Level 3-4, Question \#23)
Options:
(A) $$1$$
(B) $$2$$
(C) $$5$$
(D) $$6$$
(E) $$11$$
Please choose an option from A-E to answer. | (D) $$6$$ |
[
"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 $m+n$?~ (2020 AMC 10A Problem, Question \#15)
Options:
(A) $$3$$
(B) $$5$$
(C) $$12$$
(D) $$18$$
(E) $$23$$
Please choose an option from A-E to answer. | (E) $$23$$ |
[] | 2 | A $$3$$-digit integer is called a \textquotesingle V-number\textquotesingle{} if the digits go \textquotesingle high-low-high\textquotesingle{} $$-$$ that is, if the tens digit is smaller than both the hundreds digit and the units (or \textquotesingle ones\textquotesingle) digit. How many $$3$$-digit \textquotesingle V-numbers\textquotesingle{} are there?
Options:
(A) $$120$$
(B) $$240$$
(C) $$285$$
(D) $$320$$
(E) $$400$$
Please choose an option from A-E to answer. | (C) $$285$$ |
[
"其它"
] | 2 | On $2021$ December $31$\textsuperscript{st}, Lucas, Jeremy, and Irene visited their grandpa together. Then Lucas visited him every $4$ days, Jeremy visited him every $5$ days, and Irene visited him every $6$ days. In the first three months of $2022$, how many days could the grandpa be visited by at least one person?
Options:
(A) $$42$$
(B) $$52$$
(C) $$45$$
(D) $$46$$
(E) $$56$$
Please choose an option from A-E to answer. | (A) $$42$$ |
[
"其它"
] | 2 | Find the number of positive integers from $100$ to $300$ which is divisible by $6$, $8$ and $10$.
Options:
(A) $$45$$
(B) $$55$$
(C) $$65$$
(D) $$75$$
(E) None of the above
Please choose an option from A-E to answer. | (E) None of the above |
[
"其它"
] | 3 | Professor Chang has ten different language books lined up on a bookshelf: three Arabic, three German, and four Spanish. How many ways are there to arrange the ten books on the shelf keeping the Arabic books together and keeping the Spanish books together? (Adapted from $2018$ AMC $8$ Problem, Question \#$16$)
Options:
(A) $$1440$$
(B) $$2880$$
(C) $$5760$$
(D) $$17280$$
(E) $$34560$$
Please choose an option from A-E to answer. | (D) $$17280$$ |
[
"其它"
] | 2 | Annie has four cards of different colors. She writes letter $B$ on the red card and blue card, and writes letter $O$ on the yellow card and green card. Now Annie puts the four cards in a box. Bob is going to draw three of them from the box randomly. How many different possible results can Bob get? Among them, how many can Bob get his name?
Options:
(A) $6$; $3$
(B) $4$; $3$
(C) $6$; $2$
(D) $4$; $2$
(E) $6$; $1$
Please choose an option from A-E to answer. | (D) $4$; $2$ |
[
"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 ways can he do this?
Options:
(A) $$288$$
(B) $$72$$
(C) $$144$$
(D) $$96$$
(E) $$252$$
Please choose an option from A-E to answer. | (C) $$144$$ |
[] | 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 to her. Who is sitting at the far right end?
Options:
(A) Molly
(B) Dolly
(C) Sally
(D) Kelly
(E) Elly
Please choose an option from A-E to answer. | (E) Elly |
[
"其它"
] | 2 | In how many ways can the letters in $BEEKEEPER$ be rearranged so that two or more $E$s do not appear together?
Options:
(A) $$1$$
(B) $$4$$
(C) $$12$$
(D) $$24$$
(E) $$120$$
Please choose an option from A-E to answer. | (D) $$24$$ |
[
"其它"
] | 2 | The mean, median, and unique mode of the positive integers $3,4,5,6,6,7$, and $x$ are all equal. What is the value of $x$ ? (2012 AMC8, Question \#11)
Options:
(A) $$5$$
(B) $$6$$
(C) $$7$$
(D) $$11$$
(E) $$12$$
Please choose an option from A-E to answer. | (D) $$11$$ |
[
"其它"
] | 3 | 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. For example if Frieda begins in the center square and makes two hops "up", the first hop would place her in the top row middle square, and the second hop would cause Frieda to jump to the opposite edge, landing in the bottom row middle square. Suppose Frieda starts from the center square, makes at most four hops at random, and stops hopping if she lands on a corner square. What is the probability that she reaches a corner square on one of the four hops?
Options:
(A) $\frac{9}{16}$
(B) $\frac{5}{8}$
(C) $\frac{3}{4}$
(D) $\frac{25}{32}$
(E) $\frac{13}{16}$
Please choose an option from A-E to answer. | (D) $\frac{25}{32}$ |
[] | 2 | A dataset of $9$ numbers has an average of $72$. After removing one of the numbers, the average of the remaining numbers becomes $78$. The number that gets removed is~\uline{~~~~~~~~~~}~.
Options:
(A) $$6$$
(B) $$24$$
(C) $$48$$
(D) $$60$$
Please choose an option from A-E to answer. | (B) $$24$$ |
[] | 2 | A win, a loss and a draw are three outcomes of a football game: a win scores $$2$$ points, a draw scores $$1$$ point for each of two teams and a loss scores $$0$$ points. Now, $15$ teams run a single round-robin tournament. How many scores in total will all the $15$ teams get?
Options:
(A) $$150$$
(B) $$420$$
(C) $$105$$
(D) $$225$$
(E) $$210$$
Please choose an option from A-E to answer. | (E) $$210$$ |
[] | 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 to her. Who is sitting at the far right end?
Options:
(A) Molly
(B) Dolly
(C) Sally
(D) Kelly
(E) Elly
Please choose an option from A-E to answer. | (E) Elly |
[] | 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? ．
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 answer. | (C) $\dfrac{5}{9}$ |
[
"其它"
] | 2 | In how many ways can the letters in $BEEKBBPERPP$ be rearranged so that two or more $E$s do not appear together?
Options:
(A) $$49200$$
(B) $$94080$$
(C) $$564480$$
(D) $$1800$$
(E) $$98400$$
Please choose an option from A-E to answer. | (B) $$94080$$ |
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