At a supermarket, Max buys a pair of shoes worth $45 , a $66 jacket, and a $175 DVD player. The cashier scans the shoes, the DVD player, and then the jacket, but Max insists that he would save money if the cashier scanned the more expensive items first. The cashier reluctantly does so, thus first scanning the DVD player, then the jacket, and finally the shoes. How many dollars does Max save by having the cashier follow his way?

(a)  

Compute 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99.

(a)  

Johnny is collecting pennies. He begins the month of February with 34 pennies in his collection. He collects 13 pennies in the first week of February, 9 in the second week, 6 in the third week, and 7 in the fourth week. How many pennies does Johnny have at the end of February?

(a)  

Evaluate: 290 + 9 + 2 + 492 + 5 + 393 + 3 + 0 + 1 + 5.

(a)  

What is 1 + (2 + (3 + (4 + (5 + 6) + 7) + 8) + 9) + 10?

(a)  

Erwin is selling vegetables with his dad at the farmer's market. Erwin's dad asks him to figure out how much money they should have in the cash register. Erwin thinks, "We started with $73 in change, and then we sold $14 worth of corn, $28 worth of tomatoes, $6 worth of peas, $12 worth of turnip greens, and $7 worth of carrots." How many dollars should they have in the cash register?

(a)  

Farmer Bob's dairy farm is ready for milking day. His 199 cows line up in the barn and he begins milking them. The first cow gives 4 pints of milk. The next cow gives 5 pints of milk. The next gives 6 pints, and so on, increasing by 1 pint each cow. How many pints of milk does the last cow give?

(a)  

What is the value of the sum 5 + 10 + 15 + . . . + 95 + 100?

(a)  

What is the sum of the first sixty-one positive integers?

(a)  

What is the sum of the first sixty-one non negative integers?

(a)  

What is the sum of the first forty positive even integers greater than 11?

(a)  

Enter the number of the following expressions that are equal to (5+61)+11+19.

(a) (61+5)+19+11

(b) 5+(61+11)+19

(c) 11+5+61+19

(d) 5+16+(11+91)

(e) (61+5+11+19)

(f) 11+(5+61+19)

(a)  

A math club is having a bake sale as a fundraiser to raise money for an upcoming trip. They sell 54 cookies at three for $1, and 20 cupcakes at $2 each, and 35 brownies at $1 each. If it cost the math club $15 to bake these items, what was their profit?

(a)  

Compute $$1\cdot100\cdot2\cdot50\cdot4\cdot25\cdot5\cdot20$$ .

(a)  

Over the summer, Stephanie read two books that were each exactly 223 pages long, and two books that were each 277 pages long. How many total pages did she read?

(a)  

The number 222,222 is equal to the product 37,037 ⠂6. What is the product of 37,037 and 27?

(a)  

Compute $$10+110\cdot0\cdot101+111$$ .

(a)  

Maria has $$\$15$$ in her bank account. To encourage Maria to save her money, her father promises to triple the amount in her bank account. Unknowingly, Maria's mother also promises to double the amount Maria has in her bank account. Finally, Maria's uncle says he will quadruple the amount Maria has. Maria first asks her father to triple her bank account balance, and she deposits the money, tripling the value of her bank account. Maria then asks her mother to double her current balance. She deposits this money, and finally asks her uncle to quadruple what she has. After she deposits her uncle's money, how many dollars does Maria have in her bank account?

(a)  

Steven owns a very orderly apple tree. The tree has 12 main branches, and each main branch has exactly 3 smaller branches. Each smaller branch has 3 apples, and there are 5 leaves surrounding each apple. How many leaves are on this apple tree?

(a)  

if $$n=8\times\left(\left(6\times3\right)\times125\right)$$ , find n!

(a)  

If a number ends in zeros, those zeros are called terminal zeros. For example, 40,000 has four terminal zeros, but 104,000 has just three terminal zeros. How many terminal zeros does the product of the number below have?

1 • 2 • 3 • 4 • … • 24 • 25

(a)  

Compute $$82\cdot15+5\cdot82\cdot10+7\cdot5\cdot82$$ .

(a)  

Find $$5\times174\times25\times2\times2\times2$$ .

(a)  

Cantaloupes, watermelons, and honeydews are all types of melon. Carrie has 11 cantaloupes. Karen has 2 times as many cantaloupes as Carrie has. Sam has 3 times as many watermelons as Karen has cantaloupes. Finally, Bobby has 5 times as many honeydews as Sam has watermelons. How many melons does the group have in total?

(a)  

Compute 4(2999) + 3(2999) + 2(2999) + 2998!

(a)  

Compute $$12\cdot45+12\cdot32+231\cdot12$$ !

(a)  

What is 9342 + (-438)719 + (-9340) + (-438)(-719)?

(a)  

What is the sum of all of the negative integers that are greater than $$-5$$ ?

(a)  

If I negate a certain number, $$n$$ , 905 times, I get -65.

If I negate $$n$$ 908 times, what number would I get?

Recall that negating a number $$x$$ means replacing it with $$-x$$ .

(a)  

James has a magic hat full of slips of paper with numbers on them. He gives the hat to his friend Anna who pulls 4 numbers out of the hat: 3, -4, -2, and 0.

James then pulls 3 numbers out of the hat: 2, 4, and 1. What is the sum of all of the numbers that James and Anna pulled out of the magic hat?

(a)  

I start by multiplying -4 by 3. I then multiply the answer by 2.

Then, I take the negation of the result. What number do I get at the end?

(a)  

Let $$a=-1$$ , let $$b=3$$ , and let $$c=-5$$ .

Calculate $$b\left(abc+5ab\right)+b\left(c+a\right)$$ !

(a)  

What is the value of $$210\cdot5+105\cdot\left(-9\right)$$ ?

(a)  

Find $$-6\left(-5-7-8\right)\left(-5\right)$$ .

(a)  

The city of Alexandria had a high temperature of $$18\degree$$ and a low temperature of $$-5\degree$$ on the same day. By how many degrees did the high temperature exceed the low temperature?

(a)  

Compute $$\left(1901+1902+\cdot\cdot\cdot+1993\right)-\left(101+102+\cdot\cdot\cdot+193\right)$$ !

(a)  

Find the value of $$100-98+96-94+92-90+\cdot\cdot\cdot+8-6+4-2$$

(a)  

Let a, b, and c be numbers.

Simplify the expression $$\left(a-\left(b-c\right)\right)-\left(\left(a-b\right)-c\right)$$ .

(a)  

Consider the following list of expressions:

(a) 100 + 100

(b) 100 - 100

(c) 100 + (-100)

(d) 100 - (-100)

(e) -100 + 100

(f) -100 + (-100)

(g) -100 - 100

(h) -100 - (-100)

How many of the expressions above are equal to 0?

(a)  

Maria's family must drive 136 miles to reach the beach. 15 miles after beginning, they stop for gas. 23 miles after the gas station, they stop for lunch. Then, they backtrack 2 miles to buy swimsuits. How many more miles must they drive to reach the beach?

(a)  

What is $$1-\left(2-\left(3-\left(4-\left(5-\left(6-\left(7-\left(8-\left(9-10\right)\right)\right)\right)\right)\right)\right)\right)$$ ?

(a)  

On a cold winter day in Utqiaġvik, Alaska, the thermometer showed $$-55\degree F$$ . However, because of a light wind, it actually felt $$17\degree F$$ colder than was shown on the thermometer. What temperature, in degrees Fahrenheit, did it feel like?

(a)  

Find 777 • 44 - 777 • 77 + 33 • 777.

(a)  

Compute 99 • 33 + 99  • 22 - 66 • 99 + 990

(a)  

Alice found a magic penny machine. The machine subtracts 5 pennies, then doubles all of the pennies left, then subtracts 30 pennies*, and then adds 26 pennies. Alice puts in 15 pennies. How many pennies will she get out of the machine?

*Note: Sometimes, this results in negative pennies, but that's OK because this is all magic.

(a)  

Multiply the negation of a positive number by the reciprocal of that same positive number. What is the product?

(a)  

Compute $$\left(2\cdot3\cdot4\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\right)$$ .

(a)  

Let $$a=\frac{1}{5}$$ , let $$b=\frac{1}{3}$$ , let $$c=3$$ , and let $$d=-\frac{1}{4}$$ .

Calculate $$\frac{1}{a\cdot\frac{1}{c}}+\frac{1}{b\cdot d}$$ .

(a)  

What is the reciprocal of $$\frac{1}{4}$$ minus the reciprocal of $$\frac{1}{13}$$ minus the reciprocal of $$-\frac{1}{23}$$ ?

(a)  

What number is 10 more than the quotient when 78 is divided by $$\frac{1}{2}$$ ?

(a)  

Compute $$\frac{124+104+84+64+44+24}{62+52+42+32+22+12}$$

(a)  

Sean adds up all the even integers from 2 to 500, inclusive. Julie adds up all the integers from 1 to 250, inclusive. What is Sean’s sum divided by Julie’s sum?

(a)  

Mary bought 5 pizzas for her math class and her friends. There are 13 students in Mary's math class, not including Mary. Mary also has 10 friends that are not in her math class. There are 10 slices in each pizza. If Mary wants to give an equal amount of pizza to each student in her math class, the teacher, each of her friends, and herself, how many slices should she give to each person?

(a)  

Carl has some paint, and he needs to paint his house. Each room requires 4 gallons of paint for the first coat, and then 2 gallons for the second coat. If he has 14 gallons of paint in his garage, 7 in the backyard, and he just bought 9 more, how many rooms can he paint?

(a)  

Find $$94\div57+33\div33+20\div57$$ .

(a)  

Compute $$11,999,999,982\div6$$ .

(a)  

There are 27 students in Mr. Anderson's math class, 18 students in Mr. LeBaron's math class, 15 students in Mr. Spry's math class, and 24 students in Mrs. Swanson's math class. All of these students are being split into groups for a field trip to the math museum. If there are 6 chaperones for the field trip and each chaperone can take one group of students, how many students will be in each group?

(a)  

Teddy has 18 strawberries, Bobby has 6 bananas, and Johnny has 12 peaches. If they want to divide up the fruit between the three of them evenly, how many pieces of fruit will each one receive?

(a)  

How many perfect squares are between 1000 and 2000?

(a)  

The sum $$1^2+2^2+3^2+...+25^2$$ is equal to $$5525$$ .

Evaluate $$2^2+4^2+6^2+...+50^2$$ .

(a)  

Let $$M=4a^2-2b^2+a$$ . Let $$j$$ be the value of $$M$$ when $$a=5$$ and $$b=3$$ , and let $$k$$ be the value of $$M$$ when $$a=-1$$ and $$b=4$$ . Calculate $$j+2k$$ .

(a)  

Find the value of n if

$$n=\left(4^2-2^2\right)+\left(6^2-4^2\right)+\left(8^2-6^2\right)-\left(2^2+4^2\right)+\left(4^2+6^2\right)-\left(6^2+8^2\right)$$ .

(a)  

The Indian mathematician Srinivasa Ramanujan (1887—1920) knew that there are four different positive integers A, B, C, and D such that $$A^3+B^3=1729$$ and $$C^3+D^3=1729$$ . What is the sum $$A+B+C+D$$ ?

(a)  

The squares of two consecutive positive integers differ by 67.

What is the greater of the two integers?

Hint: How do you get from one perfect square to the next quickly?

(a)  

The squares of two consecutive positive integers differ by 67.

What is the smaller of the two integers?

Hint: How do you get from one perfect square to the next quickly?

(a)  

Calculate $$\frac{(75+25)^2-75^2-25^2}{75\cdot25}$$ !

(a)  

What is the value of −𝑥² (𝑡 −𝑥)² if 𝑥 = −4 and 𝑡 = 3?

(a)  

For how many integers n is $$n^3$$ between $$-50$$ and $$50$$ ?

(a)  

Express $$5^{17}+5^{17}+5^{17}+5^{17}+5^{17}$$ as a power of 5.

note: Type only the power

(a)  

Express $$5^{55}+5^{55}+5^{55}+5^{55}+5^{55}$$ as a power of 5.

note: Type only the power

(a)  

Determine the number of digits in the value of $$2^{16}\cdot5^{13}$$ .

(a)  

Express the following number as a power of 2.

$$2^{10}\cdot4^{20}\cdot80^{30}$$

(Note: Type only the power)

(a)  

Find $$\left(2^{20}+2^{20}+2^{20}+2^{21}\right)\div2^{17}$$ .

(a)  

A village was founded four hundred years ago by a group of 20 people. In this village, the population triples every one hundred years. What is the population of the village today?

(a)  

For what value of $$x$$ is $$125\cdot5=5^x+5^x+5^x+5^x+5^x$$

(a)  

Let $$P=(2-3-4+7)^{2347}$$ and $$Q=(-2+3+4-7)^{2347}$$ .

What is the value of $$(2+3+4+7)^{P+Q}$$ ?

(a)  

Consecutive powers of 3 are added to form this sequence: $$3^0$$ , $$3^0+3^1$$ , $$3^0+3^1+3^2$$ , and so on. What is the value of the fourth term of this sequence?

(a)  

Express $$2^{12}$$ as a power of $$\frac{1}{8}$$ .

Hint: Can you write $$2^{12}$$ as a power of 8?

(type only the power)

(a)  

Find the integer k such that $$3^3+3^3+3^3=243\cdot3^k$$ .

(a)  

Evaluate the following expression.

$$\left(\frac{1}{4}\right)^3\cdot8^{-2}$$

(a)  

What number between 100 and 200 is both a perfect square and a multiple of 7?

(a)  

What is the greatest three-digit number that is a multiple of 13?

(a)  

What is the sum of all positive integers less than 100 that are multiples of 13?

(a)  

A bookstore has a sale on days of the month that are multiples of 5 (such as June 5, June 10...). A shoe store has a sale every 6 days. The shoe store has a sale on July 3. How many times in July do the two stores have sales on the same date?

(a)  

A school is arranging chairs in rows for an assembly. 12 chairs make a complete row, and right now there are 180 chairs total. The school wants to have as few empty seats as possible, but all rows of chairs must be complete. If 150 students will attend the assembly, how many chairs should be removed?

(a)  

A is the units digit in the four-digit number 463A. If 463A is divisible by 3 and by 4, then what are all the possible values of A?

(a)  

How many numbers from 1 through 400 have a 2 in the units place (ones place) and are divisible by 4?

(a)  

Find the remainder when $$8\cdot10^{80}+1^{80}$$ is divided by 9.

(a)  

A lucky integer is a positive integer which is divisible by the sum of its digits. What is the least positive multiple of 9 that is not a lucky integer?

(a)  

Alice chose five positive integers and found that their product was even. What is the maximum number of odd integers she could have chosen?

(a)  

Find all pairs of primes whose sum is 61.

(a)  

Find every number between 70 and 80 that is not prime and is not a multiple of 2, 3, or 5.

(a)  

Find the smallest composite number that has no prime factors less than 10.

(a)  

Each week, between 30 and students show up for an archery class run by Betty and Wilma. Usually the students break up into groups of equal size for target practice. However, this week, Betty noticed that she could not break the students up into multiple groups of equal size. Wilma noticed that if she and Betty both joined the students in practicing, they still could not break the archers up into groups of equal size. How many students showed up to the archery class this week?

(a)  

Jon teaches a fourth grade class at an elementary school where class sizes are always at least 20 students and at most 28. One day Jon decides that he wants to arrange the students in their desks in a rectangular grid with no gaps. Unfortunately for Jon he discovers that doing so could only result in one straight line of desks. How many students does Jon have in his class?

(a)  

Find the prime factorization of 252!

(note: use ' $$\times$$ ' to state the multiplication. e.g:

$$48=2^4\times3$$

What positive integer squared equals $$96\cdot486$$ ?

(a)  

If x, y, and z are positive integers and $$2^x\cdot\ 3^y\cdot\ 5^z=54000$$ , what is the value of x+y+z?

(a)  

In the prime factorization of $$24!$$ , what is the exponent of 3?

(Reminder: The number $$n!$$ is the product of the integers from 1 to n. For example, $$5!=5\cdot4\cdot3\cdot2\cdot1=120$$ .)

(a)  

Compute the $$\operatorname{lcm}[96,144]$$ !

(a)  

The number 16128 is a multiple of 6, 7, and 8. What is the smallest multiple of 6, 7, and 8 that is greater than 16128?

(a)  

What is the smallest positive integer greater than 1 that leaves a remainder of 1 when divided by each of 6, 7, and 8?

(a)  

A light flashes every 1 minute 15 seconds. Another flashes every 1 minute 40 seconds. Suppose they flash together at a certain time. What is the shortest amount of time (in minutes) that will elapse before both lights will again flash together?

(a)  

One computer in a lab is programmed to back up data at the turn of the minute every five minutes. Another computer is programmed to back up data at the turn of the minute every two minutes. Find the number of times in twenty-four hours that the two computers back up data at the same time.

(Assume that the computers do not back up at the start of the 24-hour period.)

(a)  

For how many integers n is $$28\div n$$ an integer?

(a)  

The product of two positive integers is 2005. If neither integer is 1, what is the sum of the two integers?

(a)  

The number 6545 can be written as a product of a pair of positive two-digit integers. What are these two integers?

(note: separate the answer using '&' and 'without space'. e.g 1&2)

(a)  

A teacher has a class with 32 students in it. If she wants to split the students into equal groups of at most 10 students each, what is the least number of groups that she needs?

(a)  

Compute $$\gcd\left(2^3\cdot\ 5^3\cdot\ 11^2,\ 3^2\cdot\ 5^2\cdot\ 11^1\right)$$

(a)  

Every bag of candy in the Grab-bag Candy store has the same number of candies. Tony and Kaya each grab some bags of candies. Tony gets a total of 70 candies and Kaya gets a total of 42 candies. What is the smallest possible number of bags Tony could have grabbed?

(a)  

Find the digit A such that 59,7A6 is a multiple of 36.

(a)  

For any positive integer n, the value of $$n!$$ is the product of the first n positive integers.

For example, $$4!=4\cdot3\cdot2\cdot1=24$$ . What is the greatest common divisor of $$5!$$ and $$7!$$ ?

(a)  

The least common multiple of two integers is 240, and the greatest common divisor is 24. Given that one of the integers is 48, what is the other integer?

(a)