watermelonhjg/TAL-SCQ5K-EN-level-Low · Datasets at Hugging Face

competition_source_list sequencelengths 0 2	difficulty stringclasses 2 values	problem stringlengths 102 1.61k	solution stringlengths 5 101
[]	1	If a four-digit number $$5A2A$$ can be divisible by $20$, the digit that $$A$$ represents is . Options: (A) $$0$$ (B) $$1$$ (C) $$2$$ (D) $$5$$ (E) $$8$$ Please choose an option from A-E to answer.	(A) $$0$$
[]	1	If $$1994$$ is added to any odd number, the sum will always be． Options: (A) odd (B) even (C) $$1995$$ (D) $$0$$ Please choose an option from A-E to answer.	(A) odd
[]	1	How many whole numbers are greater than $$9$$ and less than $$60$$? Options: (A) $$49$$ (B) $$50$$ (C) $$51$$ (D) $$59$$ Please choose an option from A-E to answer.	(B) $$50$$
[]	1	If $$a$$, $$b$$ are prime numbers, and $$3a+7b=41$$, then $$a+b=$$． Options: (A) $$6$$ (B) $$7$$ (C) $$8$$ (D) $$9$$ Please choose an option from A-E to answer.	(B) $$7$$
[ "其它" ]	1	Cindy prepares burgers with two slices of beef each. A box of beef has $20$ slices. How many burgers can she prepare with all the three and a half box of beef? (Adapted from 2013 Math Kangaroo Problem, Level 3-4, Question \#7) Options: (A) $$10$$ (B) $$35$$ (C) $$45$$ (D) $$25$$ (E) $$30$$ Please choose an option from A-E to answer.	(B) $$35$$
[ "其它" ]	1	Today is $$1^{st}$$ January $$2023$$, which is a Sunday. Teacher Angel has $$5$$ candies in her bag. Every time she completed her Tuesday and Thursday class, she will award herself with $$2$$ candies. On which date would she have $$15$$ candies in her bag? Options: (A) $$15^{th}$$ January $$2023$$ (B) $$16^{th}$$ January $$2023$$ (C) $$17^{th}$$ January $$2023$$ (D) $$18^{th}$$ January $$2023$$ (E) $$19^{th}$$ January $$2023$$ Please choose an option from A-E to answer.	(C) $$17^{th}$$ January $$2023$$
[]	1	$$N$$ is a two$$-$$digit number. When $$N$$ is divided by $$5$$, the remainder is $$1$$. When $$N$$ is divided by $$11$$, the remainder is $$1$$. The smallest possible value of $N$ is~\uline{~~~~~~~~~~}~.(Adapted from $$2016$$ AMC $$8$$ Problem, Question \#$$5$$) Options: (A) $$51$$ (B) $$54$$ (C) $$56$$ (D) $$61$$ (E) $$67$$ Please choose an option from A-E to answer.	(C) $$56$$
[]	1	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: (A) $$15$$ (B) $$16$$ (C) $$17$$ (D) $$18$$ (E) $$20$$ Please choose an option from A-E to answer.	(D) $$18$$
[]	1	Summer has some nuts and wants to divide them equally to $5$ kids. Everyone can get $7$ nuts at most. How many nuts does Summer have at most? Options: (A) $$34$$ (B) $$35$$ (C) $$30$$ (D) $$39$$ (E) $$40$$ Please choose an option from A-E to answer.	(D) $$39$$
[]	1	The ones digit of $$9\times 8\times 7\times 6\times 5\times 4\times 3\times 3\times 4\times 5\times 6\times 7\times 8\times 9$$ is． Options: (A) $$0$$ (B) $$4$$ (C) $$6$$ (D) $$9$$ Please choose an option from A-E to answer.	(A) $$0$$
[]	1	How many 0s are there at the end of the product $$2\times3\times5\times7\times8\times12\times25$$. ． Options: (A) $$0$$ (B) $$1$$ (C) $$2$$ (D) $$3$$ Please choose an option from A-E to answer.	(D) $$3$$
[]	1	What is the sum of the ten-thousands\textquotesingle{} digit and the millions\textquotesingle{} digit of $$1234567890$$? Options: (A) $$7$$ (B) $$9$$ (C) $$10$$ (D) $$11$$ Please choose an option from A-E to answer.	(C) $$10$$
[]	1	Which of the following numbers is the odd one out? Options: (A) $$1138$$ (B) $$1226$$ (C) $$1324$$ (D) $$1416$$ (E) $$1854$$ Please choose an option from A-E to answer.	(E) $$1854$$
[]	1	The greatest odd factor of the product $$1\times 2\times 3\times 4\times 5\times 6$$ is． Options: (A) $$5$$ (B) $$15$$ (C) $$45$$ (D) $$75$$ Please choose an option from A-E to answer.	(C) $$45$$
[]	1	The product of any two multiples of $$3$$ must be a multiple of． Options: (A) $$6$$ (B) $$9$$ (C) $$12$$ (D) $$15$$ Please choose an option from A-E to answer.	(B) $$9$$
[ "其它" ]	1	There are three whole numbers $A$, $B$ and $C$. $A\times B=35$, $B\times C=84$. $A+B+C=$~\uline{~~~~~~~~~~}~. Options: (A) $$20$$ (B) $$23$$ (C) $$24$$ (D) $$29$$ Please choose an option from A-E to answer.	(C) $$24$$
[ "其它" ]	1	Determine whether the following calculations give odd or even numbers. (a) $$14327+21462-3583$$ (b) $$9377\times1525$$ Options: (A) Both Odd (B) Both Even (C) Odd, Even (D) Even, Odd Please choose an option from A-E to answer.	(D) Even, Odd
[]	1	When $$106$$ is divided by $$3$$, the remainder is． Options: (A) $$0$$ (B) $$1$$ (C) $$2$$ (D) $$3$$ Please choose an option from A-E to answer.	(B) $$1$$
[]	1	Find the value for lcm $$\left[ 4,6,8\right]$$. Options: (A) $$8$$ (B) $$12$$ (C) $$24$$ (D) $$48$$ Please choose an option from A-E to answer.	(C) $$24$$
[ "其它" ]	1	John, Mike, Emily and Nick want to buy some apples from Walmart where the apples are sold in pack of six. How many packs should they buy to get the same amount of apples for each one of them? Options: (A) $$3$$ (B) $$5$$ (C) $$6$$ (D) $$7$$ Please choose an option from A-E to answer.	(C) $$6$$
[]	1	$$1$$ thousand $$+9$$ hundreds $$+ 8$$ tens $$+ 18$$ ones $$=$$． Options: (A) $$1918$$ (B) $$1988$$ (C) $$1998$$ (D) $$19818$$ Please choose an option from A-E to answer.	(C) $$1998$$
[]	1	The product of all $$4$$ sides of a square is $$1296$$. The sum of all $$4$$ sides of the square is． Options: (A) $$24$$ (B) $$36$$ (C) $$48$$ (D) $$72$$ Please choose an option from A-E to answer.	(A) $$24$$
[ "其它" ]	1	Change a digit of the number $45879$ to make the new five-digit number be divisible by $125$. What is the new five-digit number? Options: (A) $$45870$$ (B) $$45875$$ (C) $$45579$$ (D) $45875$ and $45870$ Please choose an option from A-E to answer.	(B) $$45875$$
[ "其它" ]	1	In this fictional "Old Island", all the numbers contain only odd digits. The order of the counting numbers is as follows: 1, 3, 5, 7, $\cdots $ , 19, 31, 33, $\cdots $ What is the 31st counting number in the island? Options: (A) $$101$$ (B) $$111$$ (C) $$99$$ (D) $$113$$ (E) None of the above. Please choose an option from A-E to answer.	(B) $$111$$
[ "其它" ]	1	How many prime numbers are there between $120$ and $140$? Options: (A) $$4$$ (B) $$5$$ (C) $$6$$ (D) $$7$$ Please choose an option from A-E to answer.	(A) $$4$$
[]	1	Which of the following is not a prime number? Options: (A) $$41$$ (B) $$51$$ (C) $$61$$ (D) $$71$$ Please choose an option from A-E to answer.	(B) $$51$$
[]	1	Mike has $$17$$ apples and $$19$$ pears. He puts every $5$ fruits in each box. At least how many more fruits does he need to get $8$ boxes of fruits? (Adapted from 2001 Math Kangaroo Problem, Level 3-4, Question \#7) Options: (A) $$1$$ (B) $$2$$ (C) $$3$$ (D) $$4$$ (E) $$5$$ Please choose an option from A-E to answer.	(D) $$4$$
[]	1	A square has an area of $144\text{cm}^{2}$, what is the length of each side of the square? Options: (A) $10\text{cm}$ (B) $11\text{cm}$ (C) $12\text{cm}$ (D) $13\text{cm}$ Please choose an option from A-E to answer.	(C) $12\text{cm}$
[ "其它" ]	1	Vicky bought $26$ apples to divide to her $5$ cousins. If Vicky wants to give them all of the apples and also wants to make every cousin gets the same amount, at least how many more apples should Vicky buy? Options: (A) $$0$$ (B) $$1$$ (C) $$3$$ (D) $$5$$ (E) $$4$$ Please choose an option from A-E to answer.	(E) $$4$$
[]	1	If $$1\times2\times3\times4\times5\times6\times7\times8\times$$$$9\times10\times11\times12\times13\times$$$$14\times15 = 1307 674 368000$$, how many times does the digit "$$0$$" appear in the product $$10\times20\times30\times40\times50\times60\times$$$$70\times80\times90\times100\times110\times120\times130\times140\times150$$? Options: (A) $$15$$ (B) $$18$$ (C) $$19$$ (D) $$20$$ Please choose an option from A-E to answer.	(C) $$19$$
[]	1	If a natural number can be written as the sum of both two and three consecutive natural numbers, then we can call it a Think Number. What is the largest Think Number no larger than $5789$? Options: (A) $$5786$$ (B) $$5787$$ (C) $$5788$$ (D) $$5789$$ (E) $$5784$$ Please choose an option from A-E to answer.	(B) $$5787$$
[]	1	The sum of three $2-$digit consecutive numbers is the maximum 2-digit number. What is their product? Options: (A) $$99$$ (B) $$25900$$ (C) $$35904$$ (D) $$34589$$ (E) $$39804$$ Please choose an option from A-E to answer.	(C) $$35904$$
[]	1	A student thinks of a natural number. She divides the number by $$9$$ and the remainder is $$7$$. What is the remainder when double that number is divided by $$9$$? Options: (A) $$1$$ (B) $$2$$ (C) $$5$$ (D) $$6$$ Please choose an option from A-E to answer.	(C) $$5$$
[ "其它" ]	1	Timothy writes down the number 24. He reverses the digits to make the number 42. He then works out that 42 is 18 more than his starting number, 24. Nicole writes down a whole number between 10 and 99. She also reverses the digits of her number. She finds that this makes a number that is 72 more than her starting number. What was the last digit of Nicole's starting number? Options: (A) $$2$$ (B) $$3$$ (C) $$5$$ (D) $$7$$ (E) $$9$$ Please choose an option from A-E to answer.	(E) $$9$$
[]	1	How many whole numbers greater than $$0$$ whose square is equal to its square root? Options: (A) $$0$$ (B) $$1$$ (C) $$2$$ (D) $$4$$ Please choose an option from A-E to answer.	(B) $$1$$
[ "其它" ]	1	How many numbers of the following are divisible by $3$? $$\textasciitilde$$ $314\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} 528\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash~ ~ ~899\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash~ ~ ~1024\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash~ ~ ~1356\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash~ ~ ~3336$ $\textasciitilde$ $\textasciitilde$ Options: (A) $$3$$ (B) $$4$$ (C) $$5$$ (D) $$6$$ Please choose an option from A-E to answer.	(A) $$3$$
[]	1	Of the following, which has the largest odd factor? Options: (A) $$30$$ (B) $$32$$ (C) $$36$$ (D) $$40$$ Please choose an option from A-E to answer.	(A) $$30$$
[]	1	Is it possible to find two numbers such that if you add up the sum and the difference of these two numbers, you get $$999$$? If yes, please write it out. If not, please give your reason. Options: (A) Possible (B) Not possible Please choose an option from A-E to answer.	(B) Not possible
[]	1	Which of the following integers is not a multiple of $$45$$? Options: (A) $$765$$ (B) $$675$$ (C) $$585$$ (D) $$495$$ (E) $$305$$ Please choose an option from A-E to answer.	(E) $$305$$
[]	1	A whole number is a perfect square if it can be expressed as the product of two equal whole numbers. What is the sum of the first $10$ perfect squares? Options: (A) $$384$$ (B) $$385$$ (C) $$386$$ (D) $$387$$ Please choose an option from A-E to answer.	(B) $$385$$
[]	1	How many zeros does the number $$12^{2}\times15^{3}$$ end with? Options: (A) $$6$$ (B) $$12$$ (C) $$5$$ (D) $$3$$ (E) $$1$$ Please choose an option from A-E to answer.	(D) $$3$$
[]	1	Arthur writes down three two-digit integers. One is square, one is prime and one is triangular. She uses the digits $$1$$, $$2$$, $$3$$, $$4$$, $$5$$ and $$6$$ exactly once each. Which largest prime does he write? ． Options: (A) $$13 $$ (B) $$23 $$ (C) $$31 $$ (D) $$41 $$ (E) $$43$$ Please choose an option from A-E to answer.	(D) $$41 $$
[ "其它" ]	1	How many three-digit positive integers have an odd number of even digits? Options: (A) $$150$$ (B) $$250$$ (C) $$350$$ (D) $$450$$ (E) $$550$$ Please choose an option from A-E to answer.	(D) $$450$$
[]	1	How many different primes are in the prime factorization of $$2016$$? Options: (A) $$3$$ (B) $$4$$ (C) $$7$$ (D) $$8$$ Please choose an option from A-E to answer.	(A) $$3$$
[]	1	A whole number is a perfect square if it can be expressed as the product of two equal whole numbers. For example, $$9$$ is a perfect square since $$9= 3\times 3$$. How many perfect squares are greater than $$0$$ and less than $$1000$$? Options: (A) $$30$$ (B) $$31$$ (C) $$32$$ (D) $$33$$ Please choose an option from A-E to answer.	(B) $$31$$
[ "其它" ]	1	There are three whole numbers $A$, $B$ and $C$. $A\times B=45$, $B\times C=50$. $A+B+C=$~\uline{~~~~~~~~~~}~. Options: (A) $$20$$ (B) $$23$$ (C) $$24$$ (D) $$29$$ Please choose an option from A-E to answer.	(C) $$24$$
[]	1	Eddie has some baseball cards from the $$1920$$s. If he divides the number of cards he has by $$4$$, then he will have $$3$$ remaining cards; if he divides the number of cards he has by $$5$$, he will have $$4$$ remaining cards; if he divides the number of cards he has by $$7$$, he will have $$6$$ remaining cards. How many cards does Eddie have at least? Options: (A) $$139$$ (B) $$140$$ (C) $$141$$ (D) $$142$$ Please choose an option from A-E to answer.	(A) $$139$$
[]	1	The product of three $2-$digit consecutive even numbers is $$\overline{\textbackslash\#\textbackslash\#\textbackslash\#2}$$. What is their sum? Options: (A) $$42$$ (B) $$64$$ (C) $$50$$ (D) $$48$$ (E) $$52$$ Please choose an option from A-E to answer.	(D) $$48$$
[]	1	The square root of $$16$$ is ． Options: (A) $$2$$ (B) $$4$$ (C) $$16$$ (D) $$64$$ Please choose an option from A-E to answer.	(B) $$4$$
[]	1	Find the smallest prime number that is greater than $$90$$. Options: (A) $$91$$ (B) $$96$$ (C) $$97$$ (D) $$99$$ Please choose an option from A-E to answer.	(C) $$97$$
[ "其它" ]	0	Find the smallest whole number between $$14$$ and $$40$$ that is divisible by $$3$$ and by $$4$$. Options: (A) $$12$$ (B) $$16$$ (C) $$18$$ (D) $$24$$ (E) $$36$$ Please choose an option from A-E to answer.	(D) $$24$$
[]	1	The sum of the prime factors of $$231$$ is． Options: (A) $$21$$ (B) $$22$$ (C) $$152$$ (D) $$383$$ Please choose an option from A-E to answer.	(A) $$21$$
[]	1	I add up all even numbers between $$1$$ and $$101$$. Then from my total I subtract all odd numbers between $$0$$ and $$100$$. What is the result? Options: (A) $$0$$ (B) $$50$$ (C) $$100$$ (D) $$255$$ (E) $$2525$$ Please choose an option from A-E to answer.	(B) $$50$$
[]	1	The product of two whole numbers is $$42$$. Their sum \emph{cannot} be． Options: (A) $$43$$ (B) $$33$$ (C) $$23$$ (D) $$13$$ Please choose an option from A-E to answer.	(B) $$33$$
[]	1	The sum of two prime numbers is $$99$$. What is the difference between the two prime numbers? Options: (A) $$89$$ (B) $$92$$ (C) $$95$$ (D) $$97$$ Please choose an option from A-E to answer.	(C) $$95$$
[]	1	Andy writes down the largest two-digit prime such that each of its digits is prime. Baker writes down the smallest three-digit prime such that each of its digits is prime. Carl adds Andy\textquotesingle s number and Baker\textquotesingle s number. What answer does Carl obtain? ． Options: (A) $$174 $$ (B) $$185 $$ (C) $$198 $$ (D) $$209 $$ (E) $$296$$ Please choose an option from A-E to answer.	(E) $$296$$
[]	1	A multi-digit number$$\underbrace{20092009\cdot \cdot \cdot 2009}\_{n 2009s}736$$, can be divisible by ~$$11$$ . The smallest value of $$n$$ is． Options: (A) $$2$$ (B) $$3$$ (C) $$4$$ (D) $$5$$ Please choose an option from A-E to answer.	(B) $$3$$
[]	1	There are some flowers along the corridor arranged in the following order: $5$ purple, $3$ red, $2$ yellow, $2$ pink, $3$ red, $2$ yellow, $2$ pink $\cdots$ If there are $100$ flowers altogether, how many red flowers are there altogether? Options: (A) $$13$$ (B) $$16$$ (C) $$39$$ (D) $$42$$ Please choose an option from A-E to answer.	(D) $$42$$
[]	1	In the $${{9}^{\text{th}}}$$ Century BC, an Indian mathematician named Al Khwarizmi wrote a book about math calculations. Since his calculations were always written on a clay tablet, he was afraid the calculation process might be lost. So, he created a system to determine whether his calculations were correct. Example: $$1234+18983+18922=39039$$, $$1234$$ divided by $$9$$ yields a remainder of $$1$$, $$18983$$ divided by $$9$$ yields a remainder of $$2$$, $$18922$$ divided by $$9$$ yields a remainder of $$4$$, When the remainders are added up and divided by $$9$$, the remainder is $$7$$. Dividing the number on the right-hand side of the equals sign by $$9$$ yields a remainder of $$6$$. Therefore, $$7$$ does not equal $$6$$, making the above equation incorrect. Use the method above to determine whether the following equations are correct or not:． ①$$2638457+3521983+6745785=12907225$$, ②$$7832145-2167953=5664192$$. Options: (A) √√ (B) √$$\times $$ (C) $$\times $$√ (D) $$\times $$$$\times $$ Please choose an option from A-E to answer.	(C) $$\times $$√
[]	1	If a four-digit number $$5A2A$$ can be divisible by both $$4 $$ and $$5$$, the digit that $$A$$ represents is~\uline{~~~~~~~~~~}~. Options: (A) $$0$$ (B) $$1$$ (C) $$2$$ (D) $$5$$ (E) $$8$$ Please choose an option from A-E to answer.	(A) $$0$$
[]	1	If my school has four times as many girls as boys, then the number of girls minus the number of boys \emph{could} be． Options: (A) $$2013$$ (B) $$2011$$ (C) $$2009$$ (D) $$2008$$ Please choose an option from A-E to answer.	(A) $$2013$$
[ "其它" ]	0	The values of length and width of a rectangle are both prime numbers. If the area of that rectangle is $10$, what is its perimeter? Options: (A) $$5$$ (B) $$7$$ (C) $$10$$ (D) $$14$$ Please choose an option from A-E to answer.	(D) $$14$$
[]	1	Which of the following is divisible by all of the integers from $$1$$ to $$10$$ inclusive? Options: (A) $$23\times34$$ (B) $$34\times45$$ (C) $$45\times56$$ (D) $$56\times67$$ Please choose an option from A-E to answer.	(C) $$45\times56$$
[]	1	John's age is a multiple of $$7$$ this year. His age next year will be a multiple of $$6$$. What is John's age this year? Options: (A) $$14$$ (B) $$28$$ (C) $$35$$ (D) $$42$$ Please choose an option from A-E to answer.	(C) $$35$$
[]	1	What is the least possible remainder when an even number is divided by $$7$$? Options: (A) $$0$$ (B) $$1$$ (C) $$5$$ (D) $$6$$ Please choose an option from A-E to answer.	(A) $$0$$
[ "其它" ]	0	Which of the following is a multiple of $8$? Options: (A) $$18$$ (B) $$24$$ (C) $$28$$ (D) $$30$$ Please choose an option from A-E to answer.	(B) $$24$$
[ "其它" ]	1	There are three whole number $A$, $B$, $C$. $A\times B=35$, $B\times C=84$. $A+B+C=$~\uline{~~~~~~~~~~}~. Options: (A) $$20$$ (B) $$23$$ (C) $$24$$ (D) $$29$$ Please choose an option from A-E to answer.	(C) $$24$$
[]	1	If a whole number is divisible by $$111$$, then it must be divisible by ． Options: (A) $$5$$ (B) $$7$$ (C) $$11$$ (D) $$37$$ Please choose an option from A-E to answer.	(D) $$37$$
[ "其它" ]	0	Which of the following is an odd number？ Options: (A) $$490$$ (B) $$558$$ (C) $$36$$ (D) $$627$$ (E) $$452$$ Please choose an option from A-E to answer.	(D) $$627$$
[]	1	Find the biggest prime number that is smaller than $$50$$. Options: (A) $$43$$ (B) $$45$$ (C) $$47$$ (D) $$49$$ Please choose an option from A-E to answer.	(C) $$47$$
[]	1	Divide an odd number by $$4$$. The remainder is always． Options: (A) odd (B) even (C) $$1$$ (D) prime Please choose an option from A-E to answer.	(A) odd
[]	1	$$\left(\sqrt{64}+\sqrt{64}\right)^{2}=$$． Options: (A) $$16$$ (B) $$64$$ (C) $$128$$ (D) $$256$$ Please choose an option from A-E to answer.	(D) $$256$$
[]	0	The product of two whole numbers is $$5$$. What is the sum of these two numbers? Options: (A) $$10$$ (B) $$6$$ (C) $$5$$ (D) $$4$$ (E) None of the above Please choose an option from A-E to answer.	(B) $$6$$
[]	1	The thousands digit of the sum of 5+55+555+5555+55555 is ． Options: (A) $$1$$ (B) $$2$$ (C) $$3$$ (D) $$4$$ Please choose an option from A-E to answer.	(A) $$1$$
[]	1	The sum of an odd number and an even number is always． Options: (A) an odd number (B) an even number (C) a prime number (D) a multiple of $3$ Please choose an option from A-E to answer.	(A) an odd number
[ "其它" ]	1	Which of the following is correct? $72=2^{x}\times3^{y}$ $539=z^{2}\times11$ Options: (A) $x\textgreater y\textgreater z$ (B) $y\textgreater z\textgreater x$ (C) $x\textgreater y=z$ (D) $z\textgreater y\textgreater x$ (E) $z\textgreater x\textgreater y$ Please choose an option from A-E to answer.	(E) $z\textgreater x\textgreater y$
[]	1	If a natural number can be written as the sum of both two and three consecutive natural numbers, then we can call it a Think Number. What is the largest Think Number no larger than $2022$? Options: (A) $$2007$$ (B) $$2009$$ (C) $$2012$$ (D) $$2015$$ (E) $$2019$$ Please choose an option from A-E to answer.	(E) $$2019$$
[]	1	($$1999$$ Math League, Grade $$5$$, Question \#$$16$$) The average of two odd numbers is always ． Options: (A) odd$$ $$ (B) even$$ $$ (C) prime$$ $$ (D) whole$$ $$ Please choose an option from A-E to answer.	(D) whole$$ $$
[]	1	What is the missing number in the box?~\uline{~~~~~~~~~~}~ $$\square \div7=83 \rm R 4$$ Options: (A) $$332$$ (B) $$339$$ (C) $$581$$ (D) $$585$$ Please choose an option from A-E to answer.	(D) $$585$$
[]	1	If the last $$2$$ digits of an integer are $$84$$, the integer must be divisible by． Options: (A) $$4$$ (B) $$8$$ (C) $$9$$ (D) $$16$$ Please choose an option from A-E to answer.	(A) $$4$$
[]	1	Which of the following numbers are prime numbers? $$\textasciitilde$$ $103$~ ~ ~ ~ ~ ~ ~ ~ ~$115$~ ~ ~ ~ ~ ~ ~ ~ ~$127$~ ~ ~ ~ ~ ~ ~ ~ ~$139$ $$\textasciitilde$$ Options: (A) Only $103$ (B) $103$ and $$127$$ (C) $103$ and $139$ (D) $103$, $127$, and $139$ Please choose an option from A-E to answer.	(D) $103$, $127$, and $139$
[]	1	Which of the following is a prime number? Options: (A) $$39$$ (B) $$50$$ (C) $$79$$ (D) $$87$$ Please choose an option from A-E to answer.	(C) $$79$$
[]	1	It is known that the positive whole number $$n$$ is divisible by $$21$$ and by $$9$$. Which of the answers below can be the number of divisors of the number $$n$$? ($$2002$$ Math kangaroo Problems, Level $$7-8$$, Question \#$$21$$) Options: (A) $$3$$ (B) $$4$$ (C) $$5$$ (D) $$6$$ (E) $$7$$ Please choose an option from A-E to answer.	(D) $$6$$
[]	1	A prime number is a number greater than $$1$$ whose only whole number factors are itself and $$1$$. What is the smallest prime number greater than $$50$$? Options: (A) $$51$$ (B) $$52$$ (C) $$53$$ (D) $$59$$ Please choose an option from A-E to answer.	(C) $$53$$
[]	1	Find the greatest prime number that is smaller than $$50$$. Options: (A) $$43$$ (B) $$45$$ (C) $$47$$ (D) $$49$$ Please choose an option from A-E to answer.	(C) $$47$$
[]	1	Which of the following is the correct expression of quinary (base $5$ numeral system)? Options: (A) $\left (8231\right )\_5$ (B) $\left (2001\right )\_5$ (C) $\left (4341\right )\_7$ (D) $\left (2345\right )\_5$ Please choose an option from A-E to answer.	(B) $\left (2001\right )\_5$
[]	1	How many zeros does the number $$14^{3}\times15^{4}$$ end with? Options: (A) $$6$$ (B) $$12$$ (C) $$5$$ (D) $$3$$ (E) $$1$$ Please choose an option from A-E to answer.	(D) $$3$$
[ "其它" ]	1	How many prime numbers are there between $90$ and $110$? $$\textasciitilde$$ $$\textasciitilde$$ Options: (A) $3$ (B) $$4$$ (C) $$5$$ (D) $$6$$ Please choose an option from A-E to answer.	(C) $$5$$
[]	1	How many positive factors of $$36$$ are also multiples of $$4$$ ? Options: (A) $$2$$ (B) $$3$$ (C) $$4$$ (D) $$5$$ (E) $$6$$ Please choose an option from A-E to answer.	(B) $$3$$
[]	1	The product of two different primes hasdivisors. Options: (A) $$3$$ (B) $$4$$ (C) $$5$$ (D) $$6$$ Please choose an option from A-E to answer.	(B) $$4$$
[]	1	$$N$$ is a two$$-$$digit number. When $$N$$ is divided by $$9$$, the remainder is $$1$$. When $$N$$ is divided by $$10$$, the remainder is $$3$$. What is the remainder when $$N$$ is divided by $$11$$? ． Options: (A) $$0$$ (B) $$2$$ (C) $$4$$ (D) $$5$$ (E) $$7$$ Please choose an option from A-E to answer.	(E) $$7$$
[]	1	What are the last $2$ digits on the right in the expansion of the expression $2^{2018201}- 8$? Options: (A) $$12$$ (B) $$22$$ (C) $$44$$ (D) $$88$$ (E) None of the above Please choose an option from A-E to answer.	(C) $$44$$
[]	1	A student thinks of a natural number. She divides the number by $$9$$ and the remainder is $$7$$. What is the remainder when double 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) $$5$$
[]	1	How many factors of $$36$$ are also multiples of $$4$$ ? Options: (A) $$2$$ (B) $$3$$ (C) $$4$$ (D) $$5$$ (E) $$6$$ Please choose an option from A-E to answer.	(B) $$3$$
[]	1	♥ $$\times$$ ☺ $$=$$ ♦ ☺ is an even number. which of the following gives an odd answer? Options: (A) ♦ $$-\textasciitilde3$$ (B) ☺ $$+$$ ♦ (C) ☺ $$\times$$ ☺ (D) ♦ $$\times$$~♦ Please choose an option from A-E to answer.	(A) ♦ $$-\textasciitilde3$$
[ "其它" ]	1	What is the remainder when we divide $19^{2021}$ by $4$? Options: (A) $$0$$ (B) $$1$$ (C) $$2$$ (D) $$3$$ Please choose an option from A-E to answer.	(D) $$3$$
[]	1	Two whole numbers differ by $$1$$. If one number has $$3$$ digits and the other has $$4$$ digits, what is their sum? Options: (A) $$1001$$ (B) $$1100$$ (C) $$1999$$ (D) $$2001$$ Please choose an option from A-E to answer.	(C) $$1999$$
[]	1	What is the last digit of the smallest positive integer whose digits add to $$2022$$? ． Options: (A) $$5 $$ (B) $$6 $$ (C) $$ 7 $$ (D) $$8 $$ (E) $$9$$ Please choose an option from A-E to answer.	(E) $$9$$
[]	1	The greatest odd factor of $$30$$ is ． Options: (A) $$5$$ (B) $$6$$ (C) $$15$$ (D) $$21$$ Please choose an option from A-E to answer.	(C) $$15$$
[ "其它" ]	1	The greatest prime number that is a divisor of 16,384 is 2 because $16,384=2^{14}$. What is the sum of the digits of the greatest prime number that is a divisor of 16,383 ? Options: (A) $$3$$ (B) $$7$$ (C) $$10$$ (D) $$16$$ (E) $$22$$ Please choose an option from A-E to answer.	(C) $$10$$

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1

If a four-digit number $$5A2A$$ can be divisible by $20$, the digit that $$A$$ represents is . Options: (A) $$0$$ (B) $$1$$ (C) $$2$$ (D) $$5$$ (E) $$8$$ Please choose an option from A-E to answer.

(A) $$0$$

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1

If $$1994$$ is added to any odd number, the sum will always be． Options: (A) odd (B) even (C) $$1995$$ (D) $$0$$ Please choose an option from A-E to answer.

(A) odd

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1

How many whole numbers are greater than $$9$$ and less than $$60$$? Options: (A) $$49$$ (B) $$50$$ (C) $$51$$ (D) $$59$$ Please choose an option from A-E to answer.

(B) $$50$$

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1

If $$a$$, $$b$$ are prime numbers, and $$3a+7b=41$$, then $$a+b=$$． Options: (A) $$6$$ (B) $$7$$ (C) $$8$$ (D) $$9$$ Please choose an option from A-E to answer.

(B) $$7$$

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1

Cindy prepares burgers with two slices of beef each. A box of beef has $20$ slices. How many burgers can she prepare with all the three and a half box of beef? (Adapted from 2013 Math Kangaroo Problem, Level 3-4, Question \#7) Options: (A) $$10$$ (B) $$35$$ (C) $$45$$ (D) $$25$$ (E) $$30$$ Please choose an option from A-E to answer.

(B) $$35$$

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1

Today is $$1^{st}$$ January $$2023$$, which is a Sunday. Teacher Angel has $$5$$ candies in her bag. Every time she completed her Tuesday and Thursday class, she will award herself with $$2$$ candies. On which date would she have $$15$$ candies in her bag? Options: (A) $$15^{th}$$ January $$2023$$ (B) $$16^{th}$$ January $$2023$$ (C) $$17^{th}$$ January $$2023$$ (D) $$18^{th}$$ January $$2023$$ (E) $$19^{th}$$ January $$2023$$ Please choose an option from A-E to answer.

(C) $$17^{th}$$ January $$2023$$

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1

$$N$$ is a two$$-$$digit number. When $$N$$ is divided by $$5$$, the remainder is $$1$$. When $$N$$ is divided by $$11$$, the remainder is $$1$$. The smallest possible value of $N$ is~\uline{~~~~~~~~~~}~.(Adapted from $$2016$$ AMC $$8$$ Problem, Question \#$$5$$) Options: (A) $$51$$ (B) $$54$$ (C) $$56$$ (D) $$61$$ (E) $$67$$ Please choose an option from A-E to answer.

(C) $$56$$

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1

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: (A) $$15$$ (B) $$16$$ (C) $$17$$ (D) $$18$$ (E) $$20$$ Please choose an option from A-E to answer.

(D) $$18$$

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1

Summer has some nuts and wants to divide them equally to $5$ kids. Everyone can get $7$ nuts at most. How many nuts does Summer have at most? Options: (A) $$34$$ (B) $$35$$ (C) $$30$$ (D) $$39$$ (E) $$40$$ Please choose an option from A-E to answer.

(D) $$39$$

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1

The ones digit of $$9\times 8\times 7\times 6\times 5\times 4\times 3\times 3\times 4\times 5\times 6\times 7\times 8\times 9$$ is． Options: (A) $$0$$ (B) $$4$$ (C) $$6$$ (D) $$9$$ Please choose an option from A-E to answer.

(A) $$0$$

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1

How many 0s are there at the end of the product $$2\times3\times5\times7\times8\times12\times25$$. ． Options: (A) $$0$$ (B) $$1$$ (C) $$2$$ (D) $$3$$ Please choose an option from A-E to answer.

(D) $$3$$

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1

What is the sum of the ten-thousands\textquotesingle{} digit and the millions\textquotesingle{} digit of $$1234567890$$? Options: (A) $$7$$ (B) $$9$$ (C) $$10$$ (D) $$11$$ Please choose an option from A-E to answer.

(C) $$10$$

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1

Which of the following numbers is the odd one out? Options: (A) $$1138$$ (B) $$1226$$ (C) $$1324$$ (D) $$1416$$ (E) $$1854$$ Please choose an option from A-E to answer.

(E) $$1854$$

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1

The greatest odd factor of the product $$1\times 2\times 3\times 4\times 5\times 6$$ is． Options: (A) $$5$$ (B) $$15$$ (C) $$45$$ (D) $$75$$ Please choose an option from A-E to answer.

(C) $$45$$

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1

The product of any two multiples of $$3$$ must be a multiple of． Options: (A) $$6$$ (B) $$9$$ (C) $$12$$ (D) $$15$$ Please choose an option from A-E to answer.

(B) $$9$$

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1

There are three whole numbers $A$, $B$ and $C$. $A\times B=35$, $B\times C=84$. $A+B+C=$~\uline{~~~~~~~~~~}~. Options: (A) $$20$$ (B) $$23$$ (C) $$24$$ (D) $$29$$ Please choose an option from A-E to answer.

(C) $$24$$

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1

Determine whether the following calculations give odd or even numbers. (a) $$14327+21462-3583$$ (b) $$9377\times1525$$ Options: (A) Both Odd (B) Both Even (C) Odd, Even (D) Even, Odd Please choose an option from A-E to answer.

(D) Even, Odd

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1

When $$106$$ is divided by $$3$$, the remainder is． Options: (A) $$0$$ (B) $$1$$ (C) $$2$$ (D) $$3$$ Please choose an option from A-E to answer.

(B) $$1$$

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1

Find the value for lcm $$\left[ 4,6,8\right]$$. Options: (A) $$8$$ (B) $$12$$ (C) $$24$$ (D) $$48$$ Please choose an option from A-E to answer.

(C) $$24$$

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1

John, Mike, Emily and Nick want to buy some apples from Walmart where the apples are sold in pack of six. How many packs should they buy to get the same amount of apples for each one of them? Options: (A) $$3$$ (B) $$5$$ (C) $$6$$ (D) $$7$$ Please choose an option from A-E to answer.

(C) $$6$$

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1

$$1$$ thousand $$+9$$ hundreds $$+ 8$$ tens $$+ 18$$ ones $$=$$． Options: (A) $$1918$$ (B) $$1988$$ (C) $$1998$$ (D) $$19818$$ Please choose an option from A-E to answer.

(C) $$1998$$

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1

The product of all $$4$$ sides of a square is $$1296$$. The sum of all $$4$$ sides of the square is． Options: (A) $$24$$ (B) $$36$$ (C) $$48$$ (D) $$72$$ Please choose an option from A-E to answer.

(A) $$24$$

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1

Change a digit of the number $45879$ to make the new five-digit number be divisible by $125$. What is the new five-digit number? Options: (A) $$45870$$ (B) $$45875$$ (C) $$45579$$ (D) $45875$ and $45870$ Please choose an option from A-E to answer.

(B) $$45875$$

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1

In this fictional "Old Island", all the numbers contain only odd digits. The order of the counting numbers is as follows: 1, 3, 5, 7, $\cdots $ , 19, 31, 33, $\cdots $ What is the 31st counting number in the island? Options: (A) $$101$$ (B) $$111$$ (C) $$99$$ (D) $$113$$ (E) None of the above. Please choose an option from A-E to answer.

(B) $$111$$

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1

How many prime numbers are there between $120$ and $140$? Options: (A) $$4$$ (B) $$5$$ (C) $$6$$ (D) $$7$$ Please choose an option from A-E to answer.

(A) $$4$$

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1

Which of the following is not a prime number? Options: (A) $$41$$ (B) $$51$$ (C) $$61$$ (D) $$71$$ Please choose an option from A-E to answer.

(B) $$51$$

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1

Mike has $$17$$ apples and $$19$$ pears. He puts every $5$ fruits in each box. At least how many more fruits does he need to get $8$ boxes of fruits? (Adapted from 2001 Math Kangaroo Problem, Level 3-4, Question \#7) Options: (A) $$1$$ (B) $$2$$ (C) $$3$$ (D) $$4$$ (E) $$5$$ Please choose an option from A-E to answer.

(D) $$4$$

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1

A square has an area of $144\text{cm}^{2}$, what is the length of each side of the square? Options: (A) $10\text{cm}$ (B) $11\text{cm}$ (C) $12\text{cm}$ (D) $13\text{cm}$ Please choose an option from A-E to answer.

(C) $12\text{cm}$

[ "其它" ]

1

Vicky bought $26$ apples to divide to her $5$ cousins. If Vicky wants to give them all of the apples and also wants to make every cousin gets the same amount, at least how many more apples should Vicky buy? Options: (A) $$0$$ (B) $$1$$ (C) $$3$$ (D) $$5$$ (E) $$4$$ Please choose an option from A-E to answer.

(E) $$4$$

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1

If $$1\times2\times3\times4\times5\times6\times7\times8\times$$$$9\times10\times11\times12\times13\times$$$$14\times15 = 1307 674 368000$$, how many times does the digit "$$0$$" appear in the product $$10\times20\times30\times40\times50\times60\times$$$$70\times80\times90\times100\times110\times120\times130\times140\times150$$? Options: (A) $$15$$ (B) $$18$$ (C) $$19$$ (D) $$20$$ Please choose an option from A-E to answer.

(C) $$19$$

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1

If a natural number can be written as the sum of both two and three consecutive natural numbers, then we can call it a Think Number. What is the largest Think Number no larger than $5789$? Options: (A) $$5786$$ (B) $$5787$$ (C) $$5788$$ (D) $$5789$$ (E) $$5784$$ Please choose an option from A-E to answer.

(B) $$5787$$

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1

The sum of three $2-$digit consecutive numbers is the maximum 2-digit number. What is their product? Options: (A) $$99$$ (B) $$25900$$ (C) $$35904$$ (D) $$34589$$ (E) $$39804$$ Please choose an option from A-E to answer.

(C) $$35904$$

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1

A student thinks of a natural number. She divides the number by $$9$$ and the remainder is $$7$$. What is the remainder when double that number is divided by $$9$$? Options: (A) $$1$$ (B) $$2$$ (C) $$5$$ (D) $$6$$ Please choose an option from A-E to answer.

(C) $$5$$

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1

Timothy writes down the number 24. He reverses the digits to make the number 42. He then works out that 42 is 18 more than his starting number, 24. Nicole writes down a whole number between 10 and 99. She also reverses the digits of her number. She finds that this makes a number that is 72 more than her starting number. What was the last digit of Nicole's starting number? Options: (A) $$2$$ (B) $$3$$ (C) $$5$$ (D) $$7$$ (E) $$9$$ Please choose an option from A-E to answer.

(E) $$9$$

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1

How many whole numbers greater than $$0$$ whose square is equal to its square root? Options: (A) $$0$$ (B) $$1$$ (C) $$2$$ (D) $$4$$ Please choose an option from A-E to answer.

(B) $$1$$

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1

How many numbers of the following are divisible by $3$? $$\textasciitilde$$ $314\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} 528\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash~ ~ ~899\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash~ ~ ~1024\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash~ ~ ~1356\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash~ ~ ~3336$ $\textasciitilde$ $\textasciitilde$ Options: (A) $$3$$ (B) $$4$$ (C) $$5$$ (D) $$6$$ Please choose an option from A-E to answer.

(A) $$3$$

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1

Of the following, which has the largest odd factor? Options: (A) $$30$$ (B) $$32$$ (C) $$36$$ (D) $$40$$ Please choose an option from A-E to answer.

(A) $$30$$

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1

Is it possible to find two numbers such that if you add up the sum and the difference of these two numbers, you get $$999$$? If yes, please write it out. If not, please give your reason. Options: (A) Possible (B) Not possible Please choose an option from A-E to answer.

(B) Not possible

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1

Which of the following integers is not a multiple of $$45$$? Options: (A) $$765$$ (B) $$675$$ (C) $$585$$ (D) $$495$$ (E) $$305$$ Please choose an option from A-E to answer.

(E) $$305$$

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1

A whole number is a perfect square if it can be expressed as the product of two equal whole numbers. What is the sum of the first $10$ perfect squares? Options: (A) $$384$$ (B) $$385$$ (C) $$386$$ (D) $$387$$ Please choose an option from A-E to answer.

(B) $$385$$

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1

How many zeros does the number $$12^{2}\times15^{3}$$ end with? Options: (A) $$6$$ (B) $$12$$ (C) $$5$$ (D) $$3$$ (E) $$1$$ Please choose an option from A-E to answer.

(D) $$3$$

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1

Arthur writes down three two-digit integers. One is square, one is prime and one is triangular. She uses the digits $$1$$, $$2$$, $$3$$, $$4$$, $$5$$ and $$6$$ exactly once each. Which largest prime does he write? ． Options: (A) $$13 $$ (B) $$23 $$ (C) $$31 $$ (D) $$41 $$ (E) $$43$$ Please choose an option from A-E to answer.

(D) $$41 $$

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1

How many three-digit positive integers have an odd number of even digits? Options: (A) $$150$$ (B) $$250$$ (C) $$350$$ (D) $$450$$ (E) $$550$$ Please choose an option from A-E to answer.

(D) $$450$$

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1

How many different primes are in the prime factorization of $$2016$$? Options: (A) $$3$$ (B) $$4$$ (C) $$7$$ (D) $$8$$ Please choose an option from A-E to answer.

(A) $$3$$

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1

A whole number is a perfect square if it can be expressed as the product of two equal whole numbers. For example, $$9$$ is a perfect square since $$9= 3\times 3$$. How many perfect squares are greater than $$0$$ and less than $$1000$$? Options: (A) $$30$$ (B) $$31$$ (C) $$32$$ (D) $$33$$ Please choose an option from A-E to answer.

(B) $$31$$

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1

There are three whole numbers $A$, $B$ and $C$. $A\times B=45$, $B\times C=50$. $A+B+C=$~\uline{~~~~~~~~~~}~. Options: (A) $$20$$ (B) $$23$$ (C) $$24$$ (D) $$29$$ Please choose an option from A-E to answer.

(C) $$24$$

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1

Eddie has some baseball cards from the $$1920$$s. If he divides the number of cards he has by $$4$$, then he will have $$3$$ remaining cards; if he divides the number of cards he has by $$5$$, he will have $$4$$ remaining cards; if he divides the number of cards he has by $$7$$, he will have $$6$$ remaining cards. How many cards does Eddie have at least? Options: (A) $$139$$ (B) $$140$$ (C) $$141$$ (D) $$142$$ Please choose an option from A-E to answer.

(A) $$139$$

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1

The product of three $2-$digit consecutive even numbers is $$\overline{\textbackslash\#\textbackslash\#\textbackslash\#2}$$. What is their sum? Options: (A) $$42$$ (B) $$64$$ (C) $$50$$ (D) $$48$$ (E) $$52$$ Please choose an option from A-E to answer.

(D) $$48$$

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1

The square root of $$16$$ is ． Options: (A) $$2$$ (B) $$4$$ (C) $$16$$ (D) $$64$$ Please choose an option from A-E to answer.

(B) $$4$$

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1

Find the smallest prime number that is greater than $$90$$. Options: (A) $$91$$ (B) $$96$$ (C) $$97$$ (D) $$99$$ Please choose an option from A-E to answer.

(C) $$97$$

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0

Find the smallest whole number between $$14$$ and $$40$$ that is divisible by $$3$$ and by $$4$$. Options: (A) $$12$$ (B) $$16$$ (C) $$18$$ (D) $$24$$ (E) $$36$$ Please choose an option from A-E to answer.

(D) $$24$$

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1

The sum of the prime factors of $$231$$ is． Options: (A) $$21$$ (B) $$22$$ (C) $$152$$ (D) $$383$$ Please choose an option from A-E to answer.

(A) $$21$$

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1

I add up all even numbers between $$1$$ and $$101$$. Then from my total I subtract all odd numbers between $$0$$ and $$100$$. What is the result? Options: (A) $$0$$ (B) $$50$$ (C) $$100$$ (D) $$255$$ (E) $$2525$$ Please choose an option from A-E to answer.

(B) $$50$$

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1

The product of two whole numbers is $$42$$. Their sum \emph{cannot} be． Options: (A) $$43$$ (B) $$33$$ (C) $$23$$ (D) $$13$$ Please choose an option from A-E to answer.

(B) $$33$$

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1

The sum of two prime numbers is $$99$$. What is the difference between the two prime numbers? Options: (A) $$89$$ (B) $$92$$ (C) $$95$$ (D) $$97$$ Please choose an option from A-E to answer.

(C) $$95$$

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1

Andy writes down the largest two-digit prime such that each of its digits is prime. Baker writes down the smallest three-digit prime such that each of its digits is prime. Carl adds Andy\textquotesingle s number and Baker\textquotesingle s number. What answer does Carl obtain? ． Options: (A) $$174 $$ (B) $$185 $$ (C) $$198 $$ (D) $$209 $$ (E) $$296$$ Please choose an option from A-E to answer.

(E) $$296$$

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1

A multi-digit number$$\underbrace{20092009\cdot \cdot \cdot 2009}\_{n 2009s}736$$, can be divisible by ~$$11$$ . The smallest value of $$n$$ is． Options: (A) $$2$$ (B) $$3$$ (C) $$4$$ (D) $$5$$ Please choose an option from A-E to answer.

(B) $$3$$

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1

There are some flowers along the corridor arranged in the following order: $5$ purple, $3$ red, $2$ yellow, $2$ pink, $3$ red, $2$ yellow, $2$ pink $\cdots$ If there are $100$ flowers altogether, how many red flowers are there altogether? Options: (A) $$13$$ (B) $$16$$ (C) $$39$$ (D) $$42$$ Please choose an option from A-E to answer.

(D) $$42$$

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1

In the $${{9}^{\text{th}}}$$ Century BC, an Indian mathematician named Al Khwarizmi wrote a book about math calculations. Since his calculations were always written on a clay tablet, he was afraid the calculation process might be lost. So, he created a system to determine whether his calculations were correct. Example: $$1234+18983+18922=39039$$, $$1234$$ divided by $$9$$ yields a remainder of $$1$$, $$18983$$ divided by $$9$$ yields a remainder of $$2$$, $$18922$$ divided by $$9$$ yields a remainder of $$4$$, When the remainders are added up and divided by $$9$$, the remainder is $$7$$. Dividing the number on the right-hand side of the equals sign by $$9$$ yields a remainder of $$6$$. Therefore, $$7$$ does not equal $$6$$, making the above equation incorrect. Use the method above to determine whether the following equations are correct or not:． ①$$2638457+3521983+6745785=12907225$$, ②$$7832145-2167953=5664192$$. Options: (A) √√ (B) √$$\times $$ (C) $$\times $$√ (D) $$\times $$$$\times $$ Please choose an option from A-E to answer.

(C) $$\times $$√

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1

If a four-digit number $$5A2A$$ can be divisible by both $$4 $$ and $$5$$, the digit that $$A$$ represents is~\uline{~~~~~~~~~~}~. Options: (A) $$0$$ (B) $$1$$ (C) $$2$$ (D) $$5$$ (E) $$8$$ Please choose an option from A-E to answer.

(A) $$0$$

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1

If my school has four times as many girls as boys, then the number of girls minus the number of boys \emph{could} be． Options: (A) $$2013$$ (B) $$2011$$ (C) $$2009$$ (D) $$2008$$ Please choose an option from A-E to answer.

(A) $$2013$$

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0

The values of length and width of a rectangle are both prime numbers. If the area of that rectangle is $10$, what is its perimeter? Options: (A) $$5$$ (B) $$7$$ (C) $$10$$ (D) $$14$$ Please choose an option from A-E to answer.

(D) $$14$$

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1

Which of the following is divisible by all of the integers from $$1$$ to $$10$$ inclusive? Options: (A) $$23\times34$$ (B) $$34\times45$$ (C) $$45\times56$$ (D) $$56\times67$$ Please choose an option from A-E to answer.

(C) $$45\times56$$

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1

John's age is a multiple of $$7$$ this year. His age next year will be a multiple of $$6$$. What is John's age this year? Options: (A) $$14$$ (B) $$28$$ (C) $$35$$ (D) $$42$$ Please choose an option from A-E to answer.

(C) $$35$$

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1

What is the least possible remainder when an even number is divided by $$7$$? Options: (A) $$0$$ (B) $$1$$ (C) $$5$$ (D) $$6$$ Please choose an option from A-E to answer.

(A) $$0$$

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0

Which of the following is a multiple of $8$? Options: (A) $$18$$ (B) $$24$$ (C) $$28$$ (D) $$30$$ Please choose an option from A-E to answer.

(B) $$24$$

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1

There are three whole number $A$, $B$, $C$. $A\times B=35$, $B\times C=84$. $A+B+C=$~\uline{~~~~~~~~~~}~. Options: (A) $$20$$ (B) $$23$$ (C) $$24$$ (D) $$29$$ Please choose an option from A-E to answer.

(C) $$24$$

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If a whole number is divisible by $$111$$, then it must be divisible by ． Options: (A) $$5$$ (B) $$7$$ (C) $$11$$ (D) $$37$$ Please choose an option from A-E to answer.

(D) $$37$$

[ "其它" ]

0

Which of the following is an odd number？ Options: (A) $$490$$ (B) $$558$$ (C) $$36$$ (D) $$627$$ (E) $$452$$ Please choose an option from A-E to answer.

(D) $$627$$

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1

Find the biggest prime number that is smaller than $$50$$. Options: (A) $$43$$ (B) $$45$$ (C) $$47$$ (D) $$49$$ Please choose an option from A-E to answer.

(C) $$47$$

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1

Divide an odd number by $$4$$. The remainder is always． Options: (A) odd (B) even (C) $$1$$ (D) prime Please choose an option from A-E to answer.

(A) odd

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1

$$\left(\sqrt{64}+\sqrt{64}\right)^{2}=$$． Options: (A) $$16$$ (B) $$64$$ (C) $$128$$ (D) $$256$$ Please choose an option from A-E to answer.

(D) $$256$$

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The product of two whole numbers is $$5$$. What is the sum of these two numbers? Options: (A) $$10$$ (B) $$6$$ (C) $$5$$ (D) $$4$$ (E) None of the above Please choose an option from A-E to answer.

(B) $$6$$

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1

The thousands digit of the sum of 5+55+555+5555+55555 is ． Options: (A) $$1$$ (B) $$2$$ (C) $$3$$ (D) $$4$$ Please choose an option from A-E to answer.

(A) $$1$$

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The sum of an odd number and an even number is always． Options: (A) an odd number (B) an even number (C) a prime number (D) a multiple of $3$ Please choose an option from A-E to answer.

(A) an odd number

[ "其它" ]

1

Which of the following is correct? $72=2^{x}\times3^{y}$ $539=z^{2}\times11$ Options: (A) $x\textgreater y\textgreater z$ (B) $y\textgreater z\textgreater x$ (C) $x\textgreater y=z$ (D) $z\textgreater y\textgreater x$ (E) $z\textgreater x\textgreater y$ Please choose an option from A-E to answer.

(E) $z\textgreater x\textgreater y$

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1

If a natural number can be written as the sum of both two and three consecutive natural numbers, then we can call it a Think Number. What is the largest Think Number no larger than $2022$? Options: (A) $$2007$$ (B) $$2009$$ (C) $$2012$$ (D) $$2015$$ (E) $$2019$$ Please choose an option from A-E to answer.

(E) $$2019$$

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($$1999$$ Math League, Grade $$5$$, Question \#$$16$$) The average of two odd numbers is always ． Options: (A) odd$$ $$ (B) even$$ $$ (C) prime$$ $$ (D) whole$$ $$ Please choose an option from A-E to answer.

(D) whole$$ $$

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What is the missing number in the box?~\uline{~~~~~~~~~~}~ $$\square \div7=83 \rm R 4$$ Options: (A) $$332$$ (B) $$339$$ (C) $$581$$ (D) $$585$$ Please choose an option from A-E to answer.

(D) $$585$$

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1

If the last $$2$$ digits of an integer are $$84$$, the integer must be divisible by． Options: (A) $$4$$ (B) $$8$$ (C) $$9$$ (D) $$16$$ Please choose an option from A-E to answer.

(A) $$4$$

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1

Which of the following numbers are prime numbers? $$\textasciitilde$$ $103$~ ~ ~ ~ ~ ~ ~ ~ ~$115$~ ~ ~ ~ ~ ~ ~ ~ ~$127$~ ~ ~ ~ ~ ~ ~ ~ ~$139$ $$\textasciitilde$$ Options: (A) Only $103$ (B) $103$ and $$127$$ (C) $103$ and $139$ (D) $103$, $127$, and $139$ Please choose an option from A-E to answer.

(D) $103$, $127$, and $139$

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1

Which of the following is a prime number? Options: (A) $$39$$ (B) $$50$$ (C) $$79$$ (D) $$87$$ Please choose an option from A-E to answer.

(C) $$79$$

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1

It is known that the positive whole number $$n$$ is divisible by $$21$$ and by $$9$$. Which of the answers below can be the number of divisors of the number $$n$$? ($$2002$$ Math kangaroo Problems, Level $$7-8$$, Question \#$$21$$) Options: (A) $$3$$ (B) $$4$$ (C) $$5$$ (D) $$6$$ (E) $$7$$ Please choose an option from A-E to answer.

(D) $$6$$

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1

A prime number is a number greater than $$1$$ whose only whole number factors are itself and $$1$$. What is the smallest prime number greater than $$50$$? Options: (A) $$51$$ (B) $$52$$ (C) $$53$$ (D) $$59$$ Please choose an option from A-E to answer.

(C) $$53$$

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1

Find the greatest prime number that is smaller than $$50$$. Options: (A) $$43$$ (B) $$45$$ (C) $$47$$ (D) $$49$$ Please choose an option from A-E to answer.

(C) $$47$$

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1

Which of the following is the correct expression of quinary (base $5$ numeral system)? Options: (A) $\left (8231\right )\_5$ (B) $\left (2001\right )\_5$ (C) $\left (4341\right )\_7$ (D) $\left (2345\right )\_5$ Please choose an option from A-E to answer.

(B) $\left (2001\right )\_5$

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How many zeros does the number $$14^{3}\times15^{4}$$ end with? Options: (A) $$6$$ (B) $$12$$ (C) $$5$$ (D) $$3$$ (E) $$1$$ Please choose an option from A-E to answer.

(D) $$3$$

[ "其它" ]

1

How many prime numbers are there between $90$ and $110$? $$\textasciitilde$$ $$\textasciitilde$$ Options: (A) $3$ (B) $$4$$ (C) $$5$$ (D) $$6$$ Please choose an option from A-E to answer.

(C) $$5$$

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1

How many positive factors of $$36$$ are also multiples of $$4$$ ? Options: (A) $$2$$ (B) $$3$$ (C) $$4$$ (D) $$5$$ (E) $$6$$ Please choose an option from A-E to answer.

(B) $$3$$

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1

The product of two different primes hasdivisors. Options: (A) $$3$$ (B) $$4$$ (C) $$5$$ (D) $$6$$ Please choose an option from A-E to answer.

(B) $$4$$

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1

$$N$$ is a two$$-$$digit number. When $$N$$ is divided by $$9$$, the remainder is $$1$$. When $$N$$ is divided by $$10$$, the remainder is $$3$$. What is the remainder when $$N$$ is divided by $$11$$? ． Options: (A) $$0$$ (B) $$2$$ (C) $$4$$ (D) $$5$$ (E) $$7$$ Please choose an option from A-E to answer.

(E) $$7$$

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What are the last $2$ digits on the right in the expansion of the expression $2^{2018201}- 8$? Options: (A) $$12$$ (B) $$22$$ (C) $$44$$ (D) $$88$$ (E) None of the above Please choose an option from A-E to answer.

(C) $$44$$

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A student thinks of a natural number. She divides the number by $$9$$ and the remainder is $$7$$. What is the remainder when double 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) $$5$$

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How many factors of $$36$$ are also multiples of $$4$$ ? Options: (A) $$2$$ (B) $$3$$ (C) $$4$$ (D) $$5$$ (E) $$6$$ Please choose an option from A-E to answer.

(B) $$3$$

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♥ $$\times$$ ☺ $$=$$ ♦ ☺ is an even number. which of the following gives an odd answer? Options: (A) ♦ $$-\textasciitilde3$$ (B) ☺ $$+$$ ♦ (C) ☺ $$\times$$ ☺ (D) ♦ $$\times$$~♦ Please choose an option from A-E to answer.

(A) ♦ $$-\textasciitilde3$$

[ "其它" ]

1

What is the remainder when we divide $19^{2021}$ by $4$? Options: (A) $$0$$ (B) $$1$$ (C) $$2$$ (D) $$3$$ Please choose an option from A-E to answer.

(D) $$3$$

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Two whole numbers differ by $$1$$. If one number has $$3$$ digits and the other has $$4$$ digits, what is their sum? Options: (A) $$1001$$ (B) $$1100$$ (C) $$1999$$ (D) $$2001$$ Please choose an option from A-E to answer.

(C) $$1999$$

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1

What is the last digit of the smallest positive integer whose digits add to $$2022$$? ． Options: (A) $$5 $$ (B) $$6 $$ (C) $$ 7 $$ (D) $$8 $$ (E) $$9$$ Please choose an option from A-E to answer.

(E) $$9$$

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The greatest odd factor of $$30$$ is ． Options: (A) $$5$$ (B) $$6$$ (C) $$15$$ (D) $$21$$ Please choose an option from A-E to answer.

(C) $$15$$

[ "其它" ]

1

The greatest prime number that is a divisor of 16,384 is 2 because $16,384=2^{14}$. What is the sum of the digits of the greatest prime number that is a divisor of 16,383 ? Options: (A) $$3$$ (B) $$7$$ (C) $$10$$ (D) $$16$$ (E) $$22$$ Please choose an option from A-E to answer.

(C) $$10$$