For two positive integers and , is divisible by ?

(1)

(2) and are both odd

A treasure hunt competition requires a team of 4 students. There are 6 students who are willing to participate: John, Edward, Milner, Luiz, Howard and Paul. However, Edward and Milner do not want to be on a team together, while Paul only wants to be on a team if Edward is also. How many different teams can be formed?

If function f(z) represents the sum of the distinct prime factors of z, then what is the value of f(f(250))?

If and are two consecutive even integers such that and , then which of the following describes the range of possible values for ?

If x = ${100}^{\frac{b}{a}}$, and a ≠ 0, is x an integer?

(1) $\frac{b^6}{a^6}$ is an integer

(2) a − 2b = 0

According to seasoned investors, the fluctuation in various global indices over the last five years indicate the possibility that there might be a correlation between a company's social media presence and its share price.

If and , is ?

(1)

(2)

What is the value of ?

(1)

(2)

Skilled builders and masons, grand living spaces and efficient bath complexes were built by the Harappans without aid of advanced tools or machinery.

In a period of time when athletes typically have stayed away from politics, Jesse Owens was among those public figures who petitioned the United States government to boycott the 1936 Berlin Olympics.

If efforts to decrease the cost of tuition for higher education are successful, much more students will enter college in the next decade than entered during the 1970s and 1980s, a period during which college enrollments reached an all-time high.

In a particular experiment on shopper behavior, two aisles in a retail store were painted differently. One aisle was painted with bright, cheerful colors whereas the other was painted in uniform black and gray. Over a three month period, it was noticed that sales from the aisle painted in bright and cheerful colors were nearly twice those from the aisle painted in black and gray. This study shows that the use of color has a significant impact on shoppers' purchasing behavior.

Which of the following, if true, would most strengthen the conclusion drawn in the experiment above?

If and are positive integers both greater than , is divisible by ?

(1) is a multiple of

(2)

What is the smallest integer for which is divisible by 1,000?

A common problem reported by violinists is unilateral hearing loss, a consequence of holding the violin too close to one ear for many years.

In the last 100 years, the amount of sulfates in the atmosphere decreased considerably over the past century, while the concentration of greenhouse gases is more than twice what it was.

There is a 25% chance that any given tourist will stop at the snack bar after arriving at a certain bus station. If four random tourists arrive at the station, what are the odds that exactly two of them will stop at the snack bar?

In the -plane, is point closer to than to ?

(1) lies on the line

(2) lies on the line

A laboratory has two cylindrical containers. The first has a height of 40cm and a base with a 10cm radius. The second has a height of 10 cm and a base with a radius of 40cm.  If the first container is filled to exactly half its height, then poured into the second container, then to what percent of capacity will the second container be filled?