Algebra

Geometry

Number Theory

Counting/Probability

Misc.

100

If A$B = (A+B)/(A-B), then what is 3$(1$4)?

2/7

100

Triangle ABC is an equilateral triangle with perimeter 12. What is it's area?

4*sqrt(3)

100

What is the prime factorization of 7!

(PS: n! is the product of all numbers from 1 to n. Eg: 3! = 3*2*1 and 5! = 5*4*3*2*1)

2^{4}*3^{2}*5*7

100

Mr. Donald is the unluckiest man in the world. In a game, he flips 5 fair coins, hoping to get all 5 of them tails. What's the probability instead, all 5 are heads?

1/32

100

The sum of two numbers is 20, and their difference is 26. What is their product?

-69

200

Rebecca and Jacob both have x dollars. After Rebecca stupidly gambles $1000 away, together, they have $1400. How much did Jacob have at first?

$1200

200

A square of area 16 is inscribed in a circle. What is the area of the circle.

(PS: Inscribing a square in a circle means that we fit the largest square possible inside a circle)

8π

200

How many factors does 2000 have

20

200

A long time ago in a galaxy far far away, there exists the planet of Lalaland. License plates for starships here must consist of 2 letters, followed by 3 numbers. How many license plates are possible?

676000

200

In Qwerty Uiop Middle school, there are 3 math classes offered: Addition, Subtraction and Multiplication (The school thinks Division is a waste of time). Out of all the students, 50 take no math classes, 30 take addition, 20 take subtraction, 10 take multiplication, 10 take both addition and subtraction, 5 take both addition and multiplication, and 5 take both subtraction and multiplication. 1 person takes all 3 courses, like a show off. How many students are there in the school?

91

300

At Central Park Zoo, there are only elephants and penguins. One day, Sarah, having nothing else to do in life, counts 40 heads and 112 legs at the zoo. How many penguins are there

24

300

Pythagoras the painter drops a 3*3*3 cube into a bucket of red paint. He then cuts the cube into 27 1*1*1 cubes. What is the sum of the number of cubes with no faces painted, and the number of cubes with 2 faces painted

13

300

What is the units digit of the number 15! + 7^{2021}

(PS: n! is the product of all numbers from 1 to n. Eg: 3! = 3*2*1 and 5! = 5*4*3*2*1)

7

300

Candyman Andyman has 10 candies in front of him, consisting of 3 Twix's, 2 skittles, 4 M&M's and 1 apple, for some reason. When he picks 3 "candies", what is the probability all of them are Twix's

1/120

300

4 friends have a chat. Assume that exactly 1 person is lying

A: Stupid B!, You are the Liar!!!

B: No A! YOU are the Liar!!!!

C: B is a liar, but I am not

D: Neither me nor C is the liar.

Who is the liar?

B

400

In a science lab, there exist 2 beakers of volume 1000 mL. One of them is filled with 300 mL of a 40% acid solution, and the second one is filled completely with 80% acid solution. How much solution must be transferred to the first beaker so the solution is 50% acid.

100 mL

400

A right circular cone rested on a table contains water. It is sliced in half vertically. What fraction of the water is in the upper half of the cone

1/8

400

2210 in base 3 is same as what base 11 number?

69

400

In the 2022 FIFA World Cup in Qatar, there will be 8 groups, each with 4 teams. For some reason, each team plays all teams in their group twice instead of once, before the top team from each group plays each of the other top teams once. How many games are played?

124

400

If 74A52B1 and 326AB4C are divisible by 3, C can be 3 possible values. What is their sum?

12

500

Yan is somewhere between his home and the stadium. To get to the stadium he can walk directly to the stadium, or else he can walk home and then ride his bicycle to the stadium. He rides 7 times as fast as he walks, and both choices require the same amount of time. What is the ratio of Yan's distance from his home to his distance from the stadium?

3:4

500

A farmer and a goat are having a conversation:

Farmer: OK now, Mr. Goat. I had enough of this behavior. Every time I leave you alone, you run away.

Goat: I only do this because SOMEONE doesn't give me enough grass to eat.

Farmer: WHAT!!!! YOU CAN TALK!

Goat: OF COURSE I CAN TALK, STUPID!!!!

Farmer: Ok, what about this. I will tie you up to the corner of a square barn of length 2 m, with a rope of length 4 m, and you can graze all you want in the area you can reach.

Goat: But how much area will I get for my grazing????

14π

500

How many whole numbers less than 1000 are neither multiples of 3 nor 5

532

500

3 red ducks, 2 blue ducks and 1 green duck stand in a line. In how many ways can you arrange them, such that the blue ducks are always next to each other. Assume the blue ducks are distinguishable, but the red ducks are not.

40

500

2 congruent circles with radius x, pass through the other's center. What is the area of the region common to both circles

x^{2}(2π/3 + sqrt(3)/2)

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