One-fourth of a number is two-thirds of 15. What is the number?

Find the LCD of 3/10, 8/15, and 11/20.

In 4 years, Carlo will be twice as old as he was 4 years ago. How old is Carlo now?

Yesterday, it rained 2/3 cm in the morning and 5/12 cm in the afternoon. How much did it rain altogether?

The number 0.15 is equivalent to a fraction with denominator 40. What is the numerator of this fraction?

What is the sum of thirty percent of 18 and one-half of 13?

The perimeter of a square is 24 cm. If its sides are increased by 50%, what is the area of the new square?

One hundred and eight jars can be packed into six identical boxes. Using the same packaging requirement, how many boxes are needed to pack 144 jars?

Nicole can type a symbol (including space) on her cellphone at an average time of 0.4 second. How long will she finish typing the phrase MATH CHALLENGE 2018?

Compute the value of the expression $$(\frac{2}{5}-\frac{3}{10})\div(\frac{1}{2}+\frac{4}{5})$$ .

The sum of two numbers is 35 and their difference is 9. What is the bigger number?

A tank is two-thirds full of water. Twenty liters were taken from it, and the tank was then three-sevenths full. How much water should be poured into it to make it half full?

On a long street, Paula walked for 45 minutes at 3 km/h. Then she ran for half an hour, and she found out that she is now 6 km from the starting point. How fast did she run?

Bert can finish mowing the grass of a football field in 4 hours, while Randy can finish it in 7 hours. What part of the field is not yet mowed after they worked together for 2.5 hours?

The hottest temperature recorded in Philippine history was 107.96 °F in Tuguegarao City on May 11, 1969. What is this temperature in degrees Celsius?

During the start of school last year, there were 18 girls and 24 boys in Mrs. Garcia’s class. In the middle of the year, six pupils transferred to another school, and the ratio of girls to boys became 4:5. How many boys transferred to another school?

What is the difference between the sum of all even counting numbers less than 201 and the sum of all odd counting numbers less than 201?

A number is decreased by 30%, and the resulting number is then increased by 12.6. If the final number is 21 less than the original number, what is the original number?

Today is March 25. Nico will celebrate his birthday 100 days from now. When is Nico’s birthday?

A businessman buys sacks of rice at ₱1600 per sack, and sells them 120% up the price. How much is he selling each sack of rice?

When 2/3 is added to a number, the result is 1 1/6. What is the number?

The sum of the first twenty counting numbers is 210. Find the sum of the next twenty counting numbers.

The length of a rectangle is twice its width. If its perimeter is 24 cm, what is its area?

The least 3-digit number that is a multiple of 40 is 120 and the largest is 960. How many 3-digit multiples of 40 are there?

A man jogs from his house to his friend’s house at 4 km/h and back at 6 km/h. The entire journey takes 45 minutes. Find the distance between the man’s house and his friend’s.

The sum of four consecutive odd numbers is 96. What is the largest number?

Ken started playing basketball at 10:33 AM, and stopped at 2:29 PM. How many minutes was he playing?

On a map, 3 cm represents 25 km. How far apart are two cities if they are 6.6 cm apart on the map?

When the fraction 3/43 is expressed as a decimal, what is the first nonzero digit after the decimal point?

The fastest land animal is the cheetah. It can reach a speed of 120.7 km/h. What is this speed in meters per minute? Round your answer to a whole number.

A company finds 15 defective items in a box of 800 items. At this ratio, how many defective items can be expected in a box of 2560 items?

If the sum of two numbers is 24 and their difference is 96, what is their product?

A boy is 22 years younger than his father. In 2 years time, the sum of their ages will be 54. Find the present ages of the father and the son.

Diana is solving a math problem. By mistake, she multiplied by 12 then divided by 8 instead of multiplying by 8 and then dividing by 12. If she got 2 as an answer, what should have been the correct answer?

A standard traffic light turns green then yellow then red, then green, yellow, red, and so on. What is the 2018th light?

If the length of each side of a cube is increased by $$x\%$$ , the volume is increased by $$174.4\%$$ . What is $$x$$ ?

A farmer has chickens and goats. Altogether, the animals have 60 heads and 156 legs. How many of each animal does he have?

What fraction of all the 3-digit numbers are not divisible by 9?

A 180-page book has the same number of photos on each page. If the number of photos were reduced by 3 on each page, the number of pages would need to be increased by 30. How many photos are there all in all?

If 73 is one more than twice a number, what is 50% of the number?

Given that $$\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}=\frac{29}{20}$$ , what is $$\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\frac{5}{6}$$ ?

Two tanks contain an equal amount of water. When a pipe is attached between them, 4000 liters of water flows from one tank into the other, making the other tank contain six times more water than the first tank. How many liters of water did each tank contain originally?

Find the whole numbers M, N, P, and Q for which $$M+N=15$$ , $$M\times N=36$$ , $$P\times Q=84$$ , and $$Q=M+18$$ .

Find the value of $$\left(-\frac{1}{32}\right)^{-\frac{4}{5}}$$ .

Factor completely: $$4x^3 + 9x^2 - 4x - 9$$ .

The legs of a right triangle have lengths $$\sqrt{5}$$ cm and $$\sqrt{7}$$ cm. How long (in cm) is the median to the hypotenuse?

Find the sum of the numerator and the denominator when the repeating decimal 0.212121… is written as a fraction in lowest terms.

Let A and B be two distinct points on a circle. If the measure of major arc AB is 40° more than the measure of minor arc AB, find the measure of major arc AB.

Set A has 4 elements and is a subset of B which has 2022 elements. How many sets S are possible if A is a subset of S and S is a subset of B?

Find the measure in degrees of the smaller angle formed by the hands of a clock at 9:20.

Find the 4th term of an arithmetic sequence whose first three terms are x + 3, 2018, and x + 13.

An ant on the plane is traveling from (0, 0) to (5, 3). In each move it can go 1 unit up or 1 unit to the right. How many distinct paths of 8 moves can the ant take?

The sum of two numbers is 1 and their product is 2. Find the sum of their cubes.

The 3rd, 6th, and 10th terms of an arithmetic sequence form a geometric sequence. Find the common ratio.

Find the number of positive integers less than 500000 that contain the block 678, with the three digits appearing consecutively and in this order.

Solve for x in the equation $$x^2 + \frac{4}{x^2} = 9 + \frac{4}{9}$$ . Select all values of x that satisfy the equation.

Find the cosine of the smallest acute angle of the triangle whose side lengths are 4, 5, and 6.

How many ordered quadruples (a, b, c, d) of nonnegative integers satisfy a + b + c + d = 10?

Find the sum of two positive integers if their quotient, sum, and product are in the ratio 1 : 6 : 16.

A polynomial has remainder 20 when divided by x − 18, and remainder 18 when divided by x − 20. Find the remainder when it is divided by (x − 18)(x − 20).

Triangle ABC has sides AB = 6, BC = 9, and AC = 9. Point P is on side BC such that AP = 6. Find the ratio BP to CP.

Let S_m denote the sum of the first m terms of an arithmetic series. If $$\dfrac{S_{2n}}{S_n} = 3$$ for some integer n, find $$\dfrac{S_{5n}}{S_{3n}}$$ .

A sequence $$a_1, a_2, a_3, \ldots$$ satisfies that $$a_{n+1}$$ is the average of the first n terms for $$n \ge 2$$ . If $$a_1 = 1$$ and $$a_{2018} = 2018$$ , find $$a_2$$ .

Find the reciprocal of the sum of the reciprocals of x − y and x + y. Write your answer as a single expression.

A circle and a square have equal areas. The circle has circumference $$2\pi$$ . What is the length of the side of the square?

How many 5-letter strings can be made from the word MANGO if each string must start with a vowel?

A circle is divided by 3 points into 3 non-overlapping arcs whose measures are in the ratio $$5 : 5 : 2$$ . Find the smallest angle of the triangle formed by the 3 points.

Two fair dice are rolled. What is the probability that the product of the resulting numbers is an odd prime?

What is the area of the circle that passes through the points $$(0,0)$$ , $$(5,0)$$ , and $$(0,\sqrt{11})$$ ?

Solve for x in the equation $$x^3 + 3x^2 + 3x = 100$$ .

A point is chosen on a number line so that the sum of its distances from the points 1, 2, 3, 4, 5, and 6 is as small as possible. What is the value of this sum?

Find the sum of the infinite geometric series with first term 1 if the 3rd term is 27 times the 6th term.

Solve for x in the equation $$\sqrt{x - 6} + \sqrt{x + 6} = 6$$ .

Find the coordinates of the vertex of $$y = (x - 3)^2 + (x - 2)^2 + (x + 2)^2 + (x + 3)^2$$ .

A geometric sequence has first term 64 while the 7th and 11th terms are in the ratio $$2 : 3$$ . Find the 17th term.

Find the remainder when $$5x^4 + 3x^3 - 9x^2 + 32x - 4$$ is divided by $$x + 3$$ .

An equilateral triangle and a regular hexagon have the same perimeters. What is the ratio of the area of the triangle to the area of the hexagon?

Let q and r be the quotient and remainder, respectively, when a positive integer n is divided by 1000. For how many positive integers n having at most 5 digits is $$q + r$$ divisible by 111?

Inside square ABCD, a point is chosen so that it is equidistant from 3 points: the vertices A and B, and the midpoint of side CD. If this common distance is 5 cm, how long (in cm) is a side of the square?

In rectangle ABCD, with $$AB = 3$$ and $$AD = 8$$ , points P and Q are chosen on AB and AD, respectively, such that $$AP = AQ$$ . Find the largest possible area of quadrilateral CPQD.

A number is picked from the list of 5-digit positive integers whose digits have a sum of 43. Find the probability that this number has an even digit.

Evaluate the expression 1/(x^2 − xy − xz − yz) + 1/(z^2 − zx − zy + xy) when $$x = 1.8$$ , $$y = 1.7$$ , and $$z = 2.2$$ .

In a right triangle, the medians drawn from the vertices of the acute angles have lengths 9 and 13. Find the length of the hypotenuse.

In an arithmetic sequence $$a_1, a_2, a_3, \ldots$$ , suppose $$a_5 + a_9 + a_{13} = 5$$ and $$a_5 + a_6 + a_7 + a_8 + a_9 + a_{10} = 9$$ . Find the index $$m$$ such that $$a_m = 11$$ .