List of practice Questions

One side of an equilateral triangle is equal to 1. Quantity A: The area of the triangle. Quantity B: 12.

What is the length of the diagonal of a cube that has a surface area of \(726 \, \text{in}^2\)?

A right circular cylinder of volume \(200\pi\) has a height of 8. Quantity A: 10. Quantity B: The circumference of the base.

If a sphere has a volume of \(268.08 \, \text{in}^3\), what is the approximate radius of the sphere?

If \(w = 18\), then which of the following is equal to \(w^2\)?

It takes no more than 40 minutes to run a race, but at least 30 minutes. What equation will model this in \(m\) minutes?

What is the equation of a line passing through the two points \((41,11)\) and \((4,-9)\)?

Quantity A: Double the measure of a single interior angle of an equilateral triangle.
Quantity B: The measure of a single interior angle of a (regular) hexagon.
Which statement is true?

A rectangle has a length that is twice its height. If the perimeter of that rectangle is \(20\text{ in}\), what is its area?

A triangle has two sides with length \(a\) and one side length \(b\). The length of side \(b = 14\) yard. If the length of \(a = 2\) times the length of side \(b\), what is the perimeter of the triangle?

Quantity A: The slope of a line parallel to \(4y + 18x = 13\).
Quantity B: The slope of a line perpendicular to \(6y - 16x = 15\).
Which of the following is true?

The general solution of the differential equation \[ (9x - 3y + 5) dy = (3x - y + 1) dx. \]

Last year the average (arithmetic mean) salary of the 10 employees of Company X was \$42,800. What is the average salary of the same 10 employees this year?
(1) For 8 of the 10 employees, this year's salary is 15 percent greater than last year's salary.
(2) For 2 of the 10 employees, this year's salary is the same as last year's salary.

If m and n are positive integers, is \((\sqrt{m})^n\) an integer?
(1) \((\sqrt{m})\) is an integer.
(2) \((\sqrt{n})\) is an integer.

In City X last April, was the average (arithmetic mean) daily high temperature greater than the median daily high temperature?
(1) In City X last April, the sum of the 30 daily high temperatures was 2,160°.
(2) In City X last April, 60 percent of the daily high temperatures were less than the average daily high temperature.

If \( \frac{x+y}{z}>0 \), is \(x<0\)?
(1) \(x<y\)
(2) \(z<0\)

If \$5,000 invested for one year at p percent simple annual interest yields \$500, what amount must be invested at k percent simple annual interest for one year to yield the same number of dollars?
(1) k = 0.8p
(2) k = 8

In the xy-plane, if line k has negative slope and passes through the point (-5,r), is the x-intercept of line k positive?
(1) The slope of line k is -5.
(2) r > 0

Is \(x>y\)?
(1) \(x = y + 2\)
(2) \( \frac{x}{2} = y - 1 \)

What is the value of \(w + q\)?
(1) \(3w = 3 - 3q\)
(2) \(5w + 5q = 5\)

Is \( \frac{5^{x+2}}{25}<1 \)?
(1) \( 5^x<1 \)
(2) \( x<0 \)

Is the standard deviation of the set of measurements \(x_1, x_2, x_3, ..., x_{20}\) less than 3?
(1) The variance for the set of measurements is 4.
(2) For each measurement, the difference between the mean and that measurement is 2.

If the units digit of integer n is greater than 2, what is the units digit of n?
(1) The units digit of n is the same as the units digit of n².
(2) The units digit of n is the same as the units digit of n³.

Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?