The sum and product of three distinct positive integers are 15 and 45, respectively. What is the smallest integer?

The sum of thirteen consecutive integers is zero. What is the smallest integer?

X and Y are inversely proportional with each other. Given that X = 15,000 when Y = 162,500. Find X when Y = 328,400.

What is the value of $x - y$ from the following linear equations?
 

$$3x + 2y = 2$$

$$6x - 5y = -32$$

Solve for $x^2$ if $48^{1/x} = 4 \times 3^{1/x}.

Given the following equations:
 

$$ab = 1/8 \qquad ac = 3 \qquad bc = 6$$
 

Find the value of b.

What is the coefficient of the term involving $x^{-3}$ in the expansion of $\left( 2x + \dfrac{2}{x} \right)^5$?

The polynomial $x^3 + 4x^2 - 3x + 8$ is divided by $x - 5$. What is the remainder?

If a car can travel x km in y hours, how many hours can it travel a distance of z km?

If 8 men can cut 22 trees in a day, how many trees can 20 men cut in a day?

Albert can do a work in 1 hour, Bryan can do it in 2 hours, and Carl can do it in 4 hours. Working together from start, how long can they do the work?

Mario’s hat is four more than Alex’s hat and one-half that of Gabriel’s hat. If the total number of hats is 24, how many hats does Alex have?

The shipment of items is divided into two portions. If the difference between the portions is one-third of their average, what is the ratio of the larger portion to the smaller portion?

A group of musicians is composed of three drummers, four pianists, and seven guitarists. How many ways can a trio are formed with 1 pianist, 1 drummer, and 1 guitarist?

If $\left| 3t - 5 \right| \gt 4$, which of the following is correct?

How many ways can 6 persons be seated at a round table if one seat is reserved for a specific person?

If $xyz = 8$ and $x^2z = 18$, what is the value of $y/x$?

Find the non-zero solution to the equation $3x^4 - 27x^3 = 0$.

A line is divided into 12 equal parts. If the measure of each part is a prime integer, what is the possible length of the line?

Solve for D in the given partial fraction:

$$ \dfrac{4x^2 + 7x + 8}{x(x + 2)^3} = \dfrac{A}{x} + \dfrac{B}{x + 2} + \dfrac{C}{(x + 2)^2} + \dfrac{D}{(x + 2)^3} $$

Two cars A and B are traveling at the speed of 30 kph and 40 kph respectively on two different roads making an angle of 30° with each other. Car A is located 200 m from the intersection of the roads at the instant car B is 400 m from the intersection. After a lapse of 5 minutes, how far is car A from car B in meters.

A and B start at the same time from two places 154 km apart and travel toward each other. A travels 10 kph and B 8 kph. If B stopped 1 hour on the way, in how many hours will they meet?

The numbers 28, x + 2, 112, ... form a geometric progression. What is the 10^th term?

A jogger starts a course at a steady rate of 8 kph. Five minutes later, a second jogger took the same course at 10 kph. How long will it take for the second jogger to catch the first?

What is the middle term in the expansion of $(x^2 + 3x)^8$?

Find k so that the expression kx^2 - 3kx + 9 is a perfect square.

Determine the value of a if (x + 2) is a factor of (x³ - ax² + 7x + 10).

Express the following statement mathematically: 5 less than four times a certain number is 12.

The distance between the centers of the three circles which are mutually tangent to each other externally are 10, 12, and 14 units. The area of the smallest circle is:

In a class experiment, a student needs 5 liters of 6% solution. He found a 4% and a 10% solution in the laboratory. How many liters of each solution should he mix in order to obtain 5 liters of 6% solution?

How many 3-digit numbers greater than 300 can be made out from digits 0, 1, 2, 3, 4, 5, and 6 if repetition of digit is not allowed?

None is defective.

Two are defective.

Three or more are defective.

The constant of proportionality.

The volume at 420°K

The temperature when the volume is 2.625 liters.

Find the rate of pipe A in liters per minute.

Find the rate of pipe C in liters per minute

Find the capacity of the tank in liters.