A circular well is constructed within a circular garden. The circumference of the well's opening is $\frac{1}{5}$ that of the garden. What is the area of the well's opening?

1. The area of the garden is $25\pi$ square meters.
2. The edging around the garden is $10\pi$ meters long.

The ages of all children in Group A are the same, and the ages of all children in Group B are the same. Is the age of a child in Group A less than the age of a child in Group B?

1. The sum of the ages of 3 children in Group A and 2 children in Group B is less than the sum of ages of 2 children in Group A and 4 children in Group B.
2. The sum of the ages of 4 children in Group A and 3 children in Group B is less than the sum of ages of 3 children in Group A and 4 children in Group B.

A bag holds 12 balls, each of which is colored white, black, gray, or green. If a person is to select a ball randomly from the bag, is the probability less than $\frac{1}{2}$ that the ball selected will be either white or green?

1. The probability that the person will select a gray ball is $\frac{1}{3}$.
2. The probability that the person will select a green ball is $\frac{1}{6}$.

If and are prime numbers, what is the value of ?

(1) is also a prime number

(2) and are both less than 5

If , , and are positive integers, is ?

(1)

(2)

If is a positive integer, is divisible by 10?

(1) is a multiple of 5

(2) is a multiple of 2

Rectangle has a diagonal of 10 feet, and rectangle has a diagonal of 20 feet. What is the ratio of the area of to the area of ?

(1) The ratio of length to width for each rectangle is the same.

(2) The width of rectangle is 100% longer than the width of rectangle .

Find the digit in the unit’s place for  .

Comprised mainly of rice, vegetables, and lentils, South Indians have a diet that derives most of its fiber from vegetarian sources and almost none from animal foods.

A factory has n workers. The factory gave a p% raise to all its workers, who were previously paid an average of $x per month. Which of the following represents the dollar value of the factory`s total monthly payroll expense for its workers?

Before Budapest was Budapest, it was Aquincum, a Celtic settlement that would go on to become the Roman capital of Lower Pannonia.

Commonly called spiral galaxies, disk galaxies are formed in the universe from earlier, less flat, galaxies accumulate the mass of smaller nearby galaxies and rotate faster, thus flattening.

According to one source, 11 percent of the population in France earns less annual income than the poverty line, while in Germany it is just 8 percent.

According to a recent study, people may feel as refreshed upon waking from sleep of poor quality, as long as they believe they have slept well, as from sleep of good quality.

As contrasted with other large mammals, which tend to seek shade during the day and remain inactive, the kit fox burrows to escape the desert heat.

Like the improvements to irrigation and crop rotation, chemical fertilization was developed long ago but has benefited from substantial advances in the last century.

The top five rubber-producing countries are fairly geographically concentrated and center around Malaysia, which can produce up to 1 million metric tons of rubber annually and is famous for the forests of Borneo.

Investigations along the Solo river in Indonesia have led some archeologists to debunk the idea of an era in which Homo erectus had still survived in then Homo sapiens' inhabited areas.

Skeptics view the increase in minimum wage not as a measure that will promote the economic well-being of lower-income citizens, as it is intended to be, rather as a step that will increase unemployment and have the opposite of its intended effect.

Investment by a scientist in an established theory, especially because it has helped to attribute unobservable causes to phenomena, makes it likely to overlook gaps in the observable data or justify them too readily.